Posts Tagged perturbation

Recent Postings from perturbation

Gravity Dual of Quantum Information Metric

We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.

Gravity Dual of Quantum Information Metric [Replacement]

We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.

Matter Mixing in Core-collapse Supernova Ejecta: Large Density Perturbations in the Progenitor Star?

Matter mixing is one important topic in the study of core-collapse supernova (CCSN) explosions. In this paper, we perform two-dimensional hydrodynamic simulations to reproduce the high velocity $^{56}$Ni clumps observed in SN 1987A. This is the first time that large density perturbation is proposed in the CCSN progenitor to generate Rayleigh-Taylor (RT) instability and make the effective matter mixing. In the case of a spherical explosion, RT instability is efficient at both C+O/He and He/H interfaces of the SN progenitor. Radial coherent structures shown in perturbation patterns are important for obtaining high velocity $^{56}$Ni clumps. We can also obtain matter mixing features and high velocity $^{56}$Ni clumps in some cases of aspherical explosion. We find that one of the most favorable models in our work has a combination of bipolar and equatorially asymmetric explosions in which at least 25\% of density perturbation is introduced at different composition interfaces of the CCSN progenitor. These simulation results are comparable to the observational findings of SN 1987A.

Path-integral Evidence

Here we present a Bayesian formalism for the goodness-of-fit that is the evidence for a fixed functional form over the evidence for all functions that are a general perturbation about this form. This is done under the assumption that the statistical properties of the data can be modelled by a multivariate Gaussian distribution. We use this to show how one can optimise an experiment to find evidence for a fixed function over perturbations about this function. We apply this formalism to an illustrative problem of measuring perturbations in the dark energy equation of state about a cosmological constant.

WIMP isocurvature perturbation and small scale structure

The adiabatic component of perturbations is damped during the kinetic decoupling due to the collision with relativistic component on sub-horizon scales. However the isocurvature part is free from the damping and could be large enough to make a substantial contribution to the formation of small scale structure. We explicitly study the weakly interacting massive particles as dark matter with an early matter dominated period before radiation domination and show that the isocurvature perturbation is generated during the phase transition and leaves imprint in the observable signatures for the small scale structure.

WIMP isocurvature perturbation and small scale structure [Cross-Listing]

The adiabatic component of perturbations is damped during the kinetic decoupling due to the collision with relativistic component on sub-horizon scales. However the isocurvature part is free from the damping and could be large enough to make a substantial contribution to the formation of small scale structure. We explicitly study the weakly interacting massive particles as dark matter with an early matter dominated period before radiation domination and show that the isocurvature perturbation is generated during the phase transition and leaves imprint in the observable signatures for the small scale structure.

Scale Invariant Resummed Perturbation at Finite Temperatures

We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories. The resulting convergence and scale dependence of optimized thermodynamical quantities, here illustrated up to two-loop order, are drastically improved as compared to standard perturbative expansions, as well as to other related methods such as the screened perturbation or (resummed) hard-thermal-loop perturbation, that miss RG invariance as we explain. Being very general and easy to implement, our method is a potential analytical alternative to deal with the phase transitions of field theories such as thermal QCD.

Baryo-Leptogenesis induced by modified gravities in the primordial Universe [Cross-Listing]

The long-standing problem of the asymmetry between matter and antimatter in the Universe is, in this paper, analysed in the context of the modified theories of gravity. In particular we study two models of $f(R)$ theories of gravitation that, with the opportune choice of the free parameters, introduce little perturbation to the scale factor of the Universe in the radiation dominated (RD) phase predicted by general relativity (GR), i.e., $a(t)\sim t^{1/2}$. This little perturbation generates a Ricci scalar different by zero, i.e., $R\neq 0$ that reproduces the correct magnitude for the asymmetry factor $\eta$ computed in the frame of the theories of the gravitational baryogenesis and gravitational leptogenesis. The opportune choice of the free parameters is discussed in order to obtain results coherent with experimental data. Furthermore, the form of the potential $V$, for the scalar-tensor theory conformally equivalent to the $f(R)$ theory which reproduces the right asymmetry factor, is here obtained.

Baryo-Leptogenesis induced by modified gravities in the primordial Universe

The long-standing problem of the asymmetry between matter and antimatter in the Universe is, in this paper, analysed in the context of the modified theories of gravity. In particular we study two models of $f(R)$ theories of gravitation that, with the opportune choice of the free parameters, introduce little perturbation to the scale factor of the Universe in the radiation dominated (RD) phase predicted by general relativity (GR), i.e., $a(t)\sim t^{1/2}$. This little perturbation generates a Ricci scalar different by zero, i.e., $R\neq 0$ that reproduces the correct magnitude for the asymmetry factor $\eta$ computed in the frame of the theories of the gravitational baryogenesis and gravitational leptogenesis. The opportune choice of the free parameters is discussed in order to obtain results coherent with experimental data. Furthermore, the form of the potential $V$, for the scalar-tensor theory conformally equivalent to the $f(R)$ theory which reproduces the right asymmetry factor, is here obtained.

Baryo-Leptogenesis induced by modified gravities in the primordial Universe [Cross-Listing]

The long-standing problem of the asymmetry between matter and antimatter in the Universe is, in this paper, analysed in the context of the modified theories of gravity. In particular we study two models of $f(R)$ theories of gravitation that, with the opportune choice of the free parameters, introduce little perturbation to the scale factor of the Universe in the radiation dominated (RD) phase predicted by general relativity (GR), i.e., $a(t)\sim t^{1/2}$. This little perturbation generates a Ricci scalar different by zero, i.e., $R\neq 0$ that reproduces the correct magnitude for the asymmetry factor $\eta$ computed in the frame of the theories of the gravitational baryogenesis and gravitational leptogenesis. The opportune choice of the free parameters is discussed in order to obtain results coherent with experimental data. Furthermore, the form of the potential $V$, for the scalar-tensor theory conformally equivalent to the $f(R)$ theory which reproduces the right asymmetry factor, is here obtained.

The chiral condensate from renormalization group optimized perturbation

Our recently developed variant of variationnally optimized perturbation (OPT), in particular consistently incorporating renormalization group properties (RGOPT), is adapted to the calculation of the QCD spectral density of the Dirac operator and the related chiral quark condensate $\langle \bar q q \rangle$ in the chiral limit, for $n_f=2$ and $n_f=3$ massless quarks. The results of successive sequences of approximations at two-, three-, and four-loop orders of this modified perturbation, exhibit a remarkable stability. We obtain $\langle \bar q q\rangle^{1/3}_{n_f=2}(2\, {\rm GeV}) = -(0.833-0.845) \bar\Lambda_2 $, and $ \langle\bar q q\rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) = -(0.814-0.838) \bar\Lambda_3 $ where the range spanned by the first and second numbers (respectively four- and three-loop order results) defines our theoretical error, and $\bar\Lambda_{n_f}$ is the basic QCD scale in the $\overline{MS}$-scheme. We obtain a moderate suppression of the chiral condensate when going from $n_f=2$ to $n_f=3$. We compare these results with some other recent determinations from other nonperturbative methods (mainly lattice and spectral sum rules).

The chiral condensate from renormalization group optimized perturbation [Cross-Listing]

Our recently developed variant of variationnally optimized perturbation (OPT), in particular consistently incorporating renormalization group properties (RGOPT), is adapted to the calculation of the QCD spectral density of the Dirac operator and the related chiral quark condensate $\langle \bar q q \rangle$ in the chiral limit, for $n_f=2$ and $n_f=3$ massless quarks. The results of successive sequences of approximations at two-, three-, and four-loop orders of this modified perturbation, exhibit a remarkable stability. We obtain $\langle \bar q q\rangle^{1/3}_{n_f=2}(2\, {\rm GeV}) = -(0.833-0.845) \bar\Lambda_2 $, and $ \langle\bar q q\rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) = -(0.814-0.838) \bar\Lambda_3 $ where the range spanned by the first and second numbers (respectively four- and three-loop order results) defines our theoretical error, and $\bar\Lambda_{n_f}$ is the basic QCD scale in the $\overline{MS}$-scheme. We obtain a moderate suppression of the chiral condensate when going from $n_f=2$ to $n_f=3$. We compare these results with some other recent determinations from other nonperturbative methods (mainly lattice and spectral sum rules).

Neutrino Mixing with Non-Zero $\theta_{13}$ and CP Violation in the 3-3-1 Model Based on $S_4$ Flavor Symmetry

The 3-3-1 model proposed in 2011 based on discrete symmetry $S_4$ responsible for the neutrino and quark masses is updated, in which the non-zero $\theta_{13}$ is focused. Neutrino masses and mixings are consistent with the most recent data on neutrino oscillations without perturbation. The new feature is adding a new $SU(3)_L$ anti-sextet lying in doublet under $S_4$ which can result the non-zero $\theta_{13}$ without perturbation, and consequently, the number of Higgs multiplets required is less than those of other models based on non-Abelian discrete symmetries and the 3-3-1 models. The exact tribimaximal form obtained with the breaking $S_4 \rightarrow Z_3$ in charged lepton sector and $S_4 \rightarrow \mathcal{K}$ in neutrino sector. If both breakings $S_4\rightarrow \mathcal{K}$ and $\mathcal{K} \rightarrow Z_2$ are taken place in neutrino sector, the realistic neutrino spectrum is obtained without perturbation. The upper bound on neutrino mass and the effective mass governing neutrinoless double beta decay at the tree level are presented. The model predicts the Dirac CP violation phase $\delta=292.45^\circ$ in the normal spectrum (with $\theta_{23}\neq \frac{\pi}{4}$) and $\delta=303.14^\circ$ in the inverted spectrum.

Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole [Replacement]

We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar $\psi_4$ using semi-analytical methods. The metric perturbation is then reconstructed from $\psi_4$ in an (outgoing) radiation gauge, adding the appropriate non-radiative contributions arising from the shifts in mass and angular momentum of the spacetime. As a demonstration we calculate the generalized redshift $U$ as a function of the orbital frequencies $\Omega_r$ and $\Omega_\phi$ to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of $U$. In Kerr, we provide completely novel values of $U$ for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper.

Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole

We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar $\psi_4$ using semi-analytical methods. The metric perturbation is then reconstructed from $\psi_4$ in an (outgoing) radiation gauge, adding the appropriate non-radiative contributions arising from the shifts in mass and angular momentum of the spacetime. As a demonstration we calculate the generalized redshift $U$ as a function of the orbital frequencies $\Omega_r$ and $\Omega_\phi$ to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of $U$. In Kerr, we provide completely novel values of $U$ for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper.

Fast spectral source integration in black hole perturbation calculations

This paper presents a new technique for achieving spectral accuracy and fast computational performance in a class of black hole perturbation and gravitational self-force calculations involving extreme mass ratios and generic orbits. Called \emph{spectral source integration} (SSI), this method should see widespread future use in problems that entail (i) point-particle description of the small compact object, (ii) frequency domain decomposition, and (iii) use of the background eccentric geodesic motion. Frequency domain approaches are widely used in both perturbation theory flux-balance calculations and in local gravitational self-force calculations. Recent self-force calculations in Lorenz gauge, using the frequency domain and method of extended homogeneous solutions, have been able to accurately reach eccentricities as high as $e \simeq 0.7$. We show here SSI successfully applied to Lorenz gauge. In a double precision Lorenz gauge code, SSI enhances the accuracy of results and makes a factor of three improvement in the overall speed. The primary initial application of SSI–for us its \emph{raison d’\^{e}tre}–is in an arbitrary precision \emph{Mathematica} code that computes perturbations of eccentric orbits in the Regge-Wheeler gauge to extraordinarily high accuracy (e.g., 200 decimal places). These high accuracy eccentric orbit calculations would not be possible without the exponential convergence of SSI. We believe the method will extend to work for inspirals on Kerr, and will be the subject of a later publication. SSI borrows concepts from discrete-time signal processing and is used to calculate the mode normalization coefficients in perturbation theory via sums over modest numbers of points around an orbit. A variant of the idea is used to obtain spectral accuracy in solution of the geodesic orbital motion.

Stability of the Early Universe in Bigravity Theory [Replacement]

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lema$\hat{\i}$tre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-$0$ mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the St\"uckelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

Stability of the Early Universe in Bigravity Theory [Replacement]

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lema$\hat{\i}$tre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-$0$ mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the St\"uckelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

Stability of the Early Universe in Bigravity Theory [Replacement]

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lema$\hat{\i}$tre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-$0$ mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the St\"uckelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

Stability of the Early Universe in Bigravity Theory [Cross-Listing]

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lema$\hat{\i}$tre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-$0$ mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the St\"uckelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

Stability of the Early Universe in Bigravity Theory [Cross-Listing]

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lema$\hat{\i}$tre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-$0$ mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the St\"uckelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

Stability of the Early Universe in Bigravity Theory

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lema$\hat{\i}$tre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-$0$ mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the St\"uckelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

Phenomenology of dark energy: general features of large-scale perturbations [Replacement]

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $\Lambda$CDM at intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $\Lambda$CDM. (3) The gravitational slip parameter $\eta$ – the ratio of the space part of the metric perturbation to the time part – is bounded from above. For Brans-Dicke-type theories $\eta$ is at most unity. For more general theories, $\eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.

Phenomenology of dark energy: general features of large-scale perturbations [Replacement]

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $\Lambda$CDM at intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $\Lambda$CDM. (3) The gravitational slip parameter $\eta$ – the ratio of the space part of the metric perturbation to the time part – is bounded from above. For Brans-Dicke-type theories $\eta$ is at most unity. For more general theories, $\eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.

Phenomenology of dark energy: general features of large-scale perturbations

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $\Lambda$CDM at intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $\Lambda$CDM. (3) The gravitational slip parameter $\eta$ – the ratio of the space part of the metric perturbation to the time part – is bounded from above. For Brans-Dicke-type theories $\eta$ is at most unity. For more general theories, $\eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.

Phenomenology of dark energy: general features of large-scale perturbations [Cross-Listing]

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $\Lambda$CDM at intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $\Lambda$CDM. (3) The gravitational slip parameter $\eta$ – the ratio of the space part of the metric perturbation to the time part – is bounded from above. For Brans-Dicke-type theories $\eta$ is at most unity. For more general theories, $\eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.

Phenomenology of dark energy: general features of large-scale perturbations [Replacement]

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $\Lambda$CDM at intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $\Lambda$CDM. (3) The gravitational slip parameter $\eta$ – the ratio of the space part of the metric perturbation to the time part – is bounded from above. For Brans-Dicke-type theories $\eta$ is at most unity. For more general theories, $\eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.

Phenomenology of dark energy: general features of large-scale perturbations [Cross-Listing]

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $\Lambda$CDM at intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $\Lambda$CDM. (3) The gravitational slip parameter $\eta$ – the ratio of the space part of the metric perturbation to the time part – is bounded from above. For Brans-Dicke-type theories $\eta$ is at most unity. For more general theories, $\eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.

Phenomenology of dark energy: general features of large-scale perturbations [Replacement]

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $\Lambda$CDM at intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $\Lambda$CDM. (3) The gravitational slip parameter $\eta$ – the ratio of the space part of the metric perturbation to the time part – is bounded from above. For Brans-Dicke-type theories $\eta$ is at most unity. For more general theories, $\eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.

Phenomenology of dark energy: general features of large-scale perturbations [Cross-Listing]

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $\Lambda$CDM at intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $\Lambda$CDM. (3) The gravitational slip parameter $\eta$ – the ratio of the space part of the metric perturbation to the time part – is bounded from above. For Brans-Dicke-type theories $\eta$ is at most unity. For more general theories, $\eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.

Primordial Power Spectra of EiBI Inflation in Strong Gravity Limit [Cross-Listing]

We investigate the scalar and the tensor perturbations of the $\varphi^2$ inflation model in the strong-gravity limit of Eddington-inspired Born-Infeld (EiBI) theory. In order to consider the strong EiBI-gravity effect, we take the value of $\kappa$ large, where $\kappa$ is the EiBI theory parameter. The energy density of the Universe at the early stage is very high, and the Universe is in a strong-gravity regime. Therefore, the perturbation feature is not altered from what was investigated earlier. At the attractor inflationary stage, however, the feature is changed in the strong EiBI-gravity limit. The correction to the scalar perturbation in this limit comes mainly via the background matter field, while that to the tensor perturbation comes directly from the gravity ($\kappa$) effect. The change in the value of the scalar spectrum is little compared with that in the weak EiBI-gravity limit, or in GR. The form of the tensor spectrum is the same with that in the weak limit, but the value of the spectrum can be suppressed down to zero in the strong limit. Therefore, the resulting tensor-to-scalar ratio can also be suppressed in the same way, which makes $\varphi^2$ model in EiBI theory viable.

Primordial Power Spectra of EiBI Inflation in Strong Gravity Limit

We investigate the scalar and the tensor perturbations of the $\varphi^2$ inflation model in the strong-gravity limit of Eddington-inspired Born-Infeld (EiBI) theory. In order to consider the strong EiBI-gravity effect, we take the value of $\kappa$ large, where $\kappa$ is the EiBI theory parameter. The energy density of the Universe at the early stage is very high, and the Universe is in a strong-gravity regime. Therefore, the perturbation feature is not altered from what was investigated earlier. At the attractor inflationary stage, however, the feature is changed in the strong EiBI-gravity limit. The correction to the scalar perturbation in this limit comes mainly via the background matter field, while that to the tensor perturbation comes directly from the gravity ($\kappa$) effect. The change in the value of the scalar spectrum is little compared with that in the weak EiBI-gravity limit, or in GR. The form of the tensor spectrum is the same with that in the weak limit, but the value of the spectrum can be suppressed down to zero in the strong limit. Therefore, the resulting tensor-to-scalar ratio can also be suppressed in the same way, which makes $\varphi^2$ model in EiBI theory viable.

Primordial Power Spectra of EiBI Inflation in Strong Gravity Limit [Cross-Listing]

We investigate the scalar and the tensor perturbations of the $\varphi^2$ inflation model in the strong-gravity limit of Eddington-inspired Born-Infeld (EiBI) theory. In order to consider the strong EiBI-gravity effect, we take the value of $\kappa$ large, where $\kappa$ is the EiBI theory parameter. The energy density of the Universe at the early stage is very high, and the Universe is in a strong-gravity regime. Therefore, the perturbation feature is not altered from what was investigated earlier. At the attractor inflationary stage, however, the feature is changed in the strong EiBI-gravity limit. The correction to the scalar perturbation in this limit comes mainly via the background matter field, while that to the tensor perturbation comes directly from the gravity ($\kappa$) effect. The change in the value of the scalar spectrum is little compared with that in the weak EiBI-gravity limit, or in GR. The form of the tensor spectrum is the same with that in the weak limit, but the value of the spectrum can be suppressed down to zero in the strong limit. Therefore, the resulting tensor-to-scalar ratio can also be suppressed in the same way, which makes $\varphi^2$ model in EiBI theory viable.

A relativistic signature in large-scale structure: Scale-dependent bias from single-field inflation

In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the density field on large scales — even if the primordial metric perturbation is Gaussian. This imprints a relativistic signature in large-scale structure which is potentially observable, for example via a scale-dependent galaxy bias. The effect has been derived and then confirmed by independent calculations, using second-order perturbation theory. Recently, the physical reality of this relativistic effect has been disputed. The counter-argument is based on the claim that a very long wavelength curvature perturbation can be removed by a coordinate transformation. We argue that while this is true locally, the large-scale curvature cannot be removed by local coordinate transformations. The transformation itself contains the long-wavelength modes and thus includes the correlation. We show how the separate universe approach can be used to understand this correlation, confirming the results of perturbation theory.

A relativistic signature in large-scale structure: Scale-dependent bias from single-field inflation [Cross-Listing]

In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the density field on large scales — even if the primordial metric perturbation is Gaussian. This imprints a relativistic signature in large-scale structure which is potentially observable, for example via a scale-dependent galaxy bias. The effect has been derived and then confirmed by independent calculations, using second-order perturbation theory. Recently, the physical reality of this relativistic effect has been disputed. The counter-argument is based on the claim that a very long wavelength curvature perturbation can be removed by a coordinate transformation. We argue that while this is true locally, the large-scale curvature cannot be removed by local coordinate transformations. The transformation itself contains the long-wavelength modes and thus includes the correlation. We show how the separate universe approach can be used to understand this correlation, confirming the results of perturbation theory.

Inclusion of isospin breaking effects in lattice simulations [Cross-Listing]

Isospin symmetry is explicitly broken in the Standard Model by the mass and electric charge of the up and down quarks. These effects represent a perturbation of hadronic amplitudes at the percent level. Although these contributions are small, they play a crucial role in hadronic and nuclear physics. Moreover, as lattice computations are becoming increasingly precise, it is becoming more and more important to include these effects in numerical simulations. We summarize here how to properly define QCD and QED on a finite and discrete space-time so that isospin corrections to hadronic observables can be computed ab-initio and we review the main results on the isospin corrections to the hadron spectrum. We mainly focus on the recent work going beyond the electro-quenched approximation.

Dark energy and non-linear power spectrum [Cross-Listing]

We investigate the effects of homogeneous general dark energy on the non-linear matter perturbation in fully general relativistic context. Taking into account the next-to-leading corrections, the total power spectrum with general dark energy deviates from the LambdaCDM spectrum, which is nearly identical to that in the Einstein-de Sitter universe, as large as a few percent at scales comparable to that for the baryon acoustic oscillations and increases on smaller scales. The contribution from the curvature perturbation, which is absent in the Newtonian theory, exhibits even more drastic difference larger than 100%, while the amplitude is heavily suppressed on all scales.

Dark energy and non-linear power spectrum [Cross-Listing]

We investigate the effects of homogeneous general dark energy on the non-linear matter perturbation in fully general relativistic context. Taking into account the next-to-leading corrections, the total power spectrum with general dark energy deviates from the LambdaCDM spectrum, which is nearly identical to that in the Einstein-de Sitter universe, as large as a few percent at scales comparable to that for the baryon acoustic oscillations and increases on smaller scales. The contribution from the curvature perturbation, which is absent in the Newtonian theory, exhibits even more drastic difference larger than 100%, while the amplitude is heavily suppressed on all scales.

Dark energy and non-linear power spectrum

We investigate the effects of homogeneous general dark energy on the non-linear matter perturbation in fully general relativistic context. Taking into account the next-to-leading corrections, the total power spectrum with general dark energy deviates from the LambdaCDM spectrum, which is nearly identical to that in the Einstein-de Sitter universe, as large as a few percent at scales comparable to that for the baryon acoustic oscillations and increases on smaller scales. The contribution from the curvature perturbation, which is absent in the Newtonian theory, exhibits even more drastic difference larger than 100%, while the amplitude is heavily suppressed on all scales.

Dark energy and non-linear power spectrum [Cross-Listing]

We investigate the effects of homogeneous general dark energy on the non-linear matter perturbation in fully general relativistic context. Taking into account the next-to-leading corrections, the total power spectrum with general dark energy deviates from the LambdaCDM spectrum, which is nearly identical to that in the Einstein-de Sitter universe, as large as a few percent at scales comparable to that for the baryon acoustic oscillations and increases on smaller scales. The contribution from the curvature perturbation, which is absent in the Newtonian theory, exhibits even more drastic difference larger than 100%, while the amplitude is heavily suppressed on all scales.

Spherical "Top-Hat" Collapse in a Modified Chaplygin Gas Dominated Universe

Considering perturbation growth in spherical Top-Hat model of structure formation in a generalized Chaplygin gas dominated universe, we want to study this scenario with modified Chaplygin gas model. Different parameters of this scenario for positive and negative values of A are computed. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts for different values of alpha are computed; the results are in relatively good agreement with current observational data.

Spherical "Top-Hat" Collapse in a Modified Chaplygin Gas Dominated Universe [Cross-Listing]

Considering perturbation growth in spherical Top-Hat model of structure formation in a generalized Chaplygin gas dominated universe, we want to study this scenario with modified Chaplygin gas model. Different parameters of this scenario for positive and negative values of A are computed. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts for different values of alpha are computed; the results are in relatively good agreement with current observational data.

Spherical "Top-Hat" Collapse in a Modified Chaplygin Gas Dominated Universe [Replacement]

Considering perturbation growth in spherical Top-Hat model of structure formation in a generalized Chaplygin gas dominated universe, we want to study this scenario with a modified Chaplygin gas model. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts are also computed; the results are in relatively good agreement with current observational data.

Spherical "Top-Hat" Collapse in a Modified Chaplygin Gas Dominated Universe [Replacement]

Considering perturbation growth in spherical Top-Hat model of structure formation in a generalized Chaplygin gas dominated universe, we want to study this scenario with a modified Chaplygin gas model. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts are also computed; the results are in relatively good agreement with current observational data.

Effects of large-scale non-axisymmetric perturbations in the mean-field solar dynamo [Replacement]

We explore a response of a non-linear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation which is anchored at r=0.9R has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric with respect to the equator perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric field depends on the turbulent magnetic Reynolds number R_m. In the range of R_m=10^{4-6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a non-linear alpha-effect and magnetic buoyancy. In the stationary state the large-scale magnetic field demonstrates a phenomenon of "active longitudes" with cyclic 180 degree "flip-flop" changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However this effect disappears in the model which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period, and carries important information about the dynamo process.

Effects of large-scale non-axisymmetric perturbations in the mean-field solar dynamo [Replacement]

We explore a response of a non-linear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation which is anchored at r=0.9R has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric with respect to the equator perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric field depends on the turbulent magnetic Reynolds number R_m. In the range of R_m=10^{4-6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a non-linear alpha-effect and magnetic buoyancy. In the stationary state the large-scale magnetic field demonstrates a phenomenon of "active longitudes" with cyclic 180 degree "flip-flop" changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However this effect disappears in the model which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period, and carries important information about the dynamo process.

Effects of large-scale non-axisymmetric perturbations in the mean-field solar dynamo

We explore a response of the non-linear non-axisymmetric mean-field solar dynamo model to the shallow non-axisymmetric perturbations with the strength of 1G. The amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, the depth of perturbation. It is found that perturbation which is anchored at the 0.9R have a profound effect and it produce the transient magnetic cycle of the axisymmetric magnetic field if it is initiated at the growing phase of the cycle. The non-symmetric about equator perturbation results the hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric field depends on how well the magnetic helicity is conserved. In the range of Rm=10^{4-6} the evolution returns to the normal course in the next cycle and the non-axisymmetric field is generated due to non-linear alpha-effect and the magnetic buoyancy. In the stationary state of evolution the large-scale magnetic field demonstrate, the phenomena of the "active longitude" and the cyclic 180 degree flip-flop of the orientation of the large-scale magnetic field. We do not use any assumptions about the non-axisymmetric distribution of the turbulent parameters. The flip-flop effect is demonstrated for the first time in the solar type dynamo model. This effect disappears in the model which includes meridional circulation. The rotation periods of the equatorial dipole evolves from the period of 25.2 days during the relaxation epoch to the period of 27 days at the stationary state of evolution.

On the coupling of vector fields to the Gauss-Bonnet invariant

Inflationary models including vector fields have attracted a great deal of attention over the past decade. Such an interest owes to the fact that they might contribute to, or even be fully responsible for, the curvature perturbation imprinted in the CMB. However, the necessary breaking of the vector field’s conformal invariance during inflation is not without problems. In recent years it has been realized that a number of instabilities endangering the consistency of the theory arise when the conformal invariance is broken by means of a non-minimal coupling to gravity. In this paper we consider a massive vector field non-minimally coupled to gravity through the Gauss-Bonnet invariant, and investigate whether the vector can obtain a nearly scale-invariant perturbation spectrum while evading the emergence of perturbative instabilities. We find that the strength of the coupling must be extremely small if the vector field is to have a chance to contribute to the total curvature perturbation.

On the coupling of vector fields to the Gauss-Bonnet invariant [Cross-Listing]

Inflationary models including vector fields have attracted a great deal of attention over the past decade. Such an interest owes to the fact that they might contribute to, or even be fully responsible for, the curvature perturbation imprinted in the CMB. However, the necessary breaking of the vector field’s conformal invariance during inflation is not without problems. In recent years it has been realized that a number of instabilities endangering the consistency of the theory arise when the conformal invariance is broken by means of a non-minimal coupling to gravity. In this paper we consider a massive vector field non-minimally coupled to gravity through the Gauss-Bonnet invariant, and investigate whether the vector can obtain a nearly scale-invariant perturbation spectrum while evading the emergence of perturbative instabilities. We find that the strength of the coupling must be extremely small if the vector field is to have a chance to contribute to the total curvature perturbation.

On the coupling of vector fields to the Gauss-Bonnet invariant [Cross-Listing]

Inflationary models including vector fields have attracted a great deal of attention over the past decade. Such an interest owes to the fact that they might contribute to, or even be fully responsible for, the curvature perturbation imprinted in the CMB. However, the necessary breaking of the vector field’s conformal invariance during inflation is not without problems. In recent years it has been realized that a number of instabilities endangering the consistency of the theory arise when the conformal invariance is broken by means of a non-minimal coupling to gravity. In this paper we consider a massive vector field non-minimally coupled to gravity through the Gauss-Bonnet invariant, and investigate whether the vector can obtain a nearly scale-invariant perturbation spectrum while evading the emergence of perturbative instabilities. We find that the strength of the coupling must be extremely small if the vector field is to have a chance to contribute to the total curvature perturbation.

 

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