Posts Tagged scalar field

Recent Postings from scalar field

How chameleons core dwarfs with cusps

The presence of a scalar field that couples nonminimally and universally to matter can enhance gravitational forces on cosmological scales while restoring general relativity in the Solar neighborhood. In the intermediate regime, kinematically inferred masses experience an additional radial dependence with respect to the underlying distribution of matter, which is caused by the increment of gravitational forces with increasing distance from the Milky Way center. The same effect can influence the internal kinematics of subhalos and cause cuspy matter distributions to appear core-like. Specializing to the chameleon model as a worked example, we demonstrate this effect by tracing the scalar field from the outskirts of the Milky Way halo to its interior, simultaneously fitting observed velocity dispersions of chemo-dynamically discriminated red giant populations in the Fornax and Sculptor dwarf spheroidals. Whereas in standard gravity these observations suggest that the matter distribution of the dwarfs is cored, we find that in the presence of a chameleon field the assumption of a cuspy Navarro-Frenk-White profile becomes perfectly compatible with the data. Importantly, chameleon models also predict the existence of slopes between two stellar subcomponents that in Newtonian gravity would be interpreted as a depletion of matter in the dwarf center. Hence, an observation of such an apparently pathological scenario may serve as a smoking gun for the presence of a chameleon field or a similar modification of gravity, independent of baryonic feedback effects. In general, measuring the dynamic mass profiles of the Milky Way dwarfs provides stronger constraints than those inferred from the screening scale of the Solar System since these are located at greater distances from the halo center.

Galileons and strong gravity [Cross-Listing]

In the context of a cubic Galileon model in which the Vainshtein mechanism suppresses the scalar field interactions with matter, we study low-density stars with slow rotation and static relativistic stars. We develop an expansion scheme to find approximated solutions inside the Vainshtein radius, and show that deviations from General Relativity (GR), while considering rotation, are also suppressed by the Vainshtein mechanism. In a quadratic coupling model, in which the scalarisation effect can significantly enhance deviations from GR in normal scalar tensor gravity, the Galileon term successfully suppress the large deviations away from GR. Moreover, using a realistic equation of state, we construct solutions for a relativistic star, and show that deviations from GR are more suppressed for higher density objects. However, we found that the scalar field solution ceases to exist above a critical density, which roughly corresponds to the maximum mass of a neutron star. This indicates that, for a compact object described by a polytropic equation of state, the configuration that would collapse into a black hole cannot support a non-trivial scalar field.

Galileons and strong gravity

In the context of a cubic Galileon model in which the Vainshtein mechanism suppresses the scalar field interactions with matter, we study low-density stars with slow rotation and static relativistic stars. We develop an expansion scheme to find approximated solutions inside the Vainshtein radius, and show that deviations from General Relativity (GR), while considering rotation, are also suppressed by the Vainshtein mechanism. In a quadratic coupling model, in which the scalarisation effect can significantly enhance deviations from GR in normal scalar tensor gravity, the Galileon term successfully suppress the large deviations away from GR. Moreover, using a realistic equation of state, we construct solutions for a relativistic star, and show that deviations from GR are more suppressed for higher density objects. However, we found that the scalar field solution ceases to exist above a critical density, which roughly corresponds to the maximum mass of a neutron star. This indicates that, for a compact object described by a polytropic equation of state, the configuration that would collapse into a black hole cannot support a non-trivial scalar field.

Raytracing simulations of coupled dark energy models

Dark matter and dark energy are usually assumed to be independent, coupling only gravitationally. An extension to this simple picture is to model dark energy as a scalar field which is directly coupled to the cold dark matter fluid. Such a non-trivial coupling in the dark sector leads to a fifth force and a time-dependent dark matter particle mass. In this work we examine the impact that dark energy-dark matter couplings have on weak lensing statistics by constructing realistic simulated weak-lensing maps using raytracing techniques through a suite of N-body cosmological simulations. We construct maps for an array of different lensing quantities, covering a range of scales from a few arcminutes to several degrees. The concordance $\Lambda$CDM model is compared to different coupled dark energy models, described either by an exponential scalar field potential (standard coupled dark energy scenario) or by a SUGRA potential (bouncing model). We analyse several statistical quantities, in particular the power spectrum, the probability distribution function and the moments of the effective convergence. Our weak lensing results, with sources at low redshifts ($z=1$ and $z=2$), are largely consistent with previous work on CMB lensing by Carbone et al. 2013. The most significant differences from the $\Lambda$CDM model are due to the enhanced growth of the perturbations and to the effective friction terms which arise in the non-linear dynamics. For the most extreme models, we see differences in the power spectra as large as 40\% compared to the $\Lambda$CDM model. The different time evolution of the matter overdensity can account for most of the differences, but when controlling for this using a $\Lambda$CDM model having the same normalization, the overall signal is smaller due to the friction terms appearing in the equation of motion for dark matter particles.

A Minimal Sub-Planckian Axion Inflation Model with Large Tensor-to-Scalar Ratio [Cross-Listing]

We present a miminal axion inflation model which can generate a large tensor-to-scalar ratio while remaining sub-Planckian. The modulus of a complex scalar field $\Phi$ with a $\lambda |\Phi|^4$ potential couples directly to the gauge field of a strongly-coupled sector via a term of the form $(|\Phi|/M_{Pl})^{m} F \tilde{F}$. This generates a minimum of the potential which is aperiodic in the phase. The resulting inflation model is equivalent to a $\phi^{4/(m+1)}$ chaotic inflation model. For the natural case of a leading-order portal-like interaction $\Phi^{\dagger}\Phi F \tilde{F}$, the model is equivalent to a $\phi^{4/3}$ chaotic inflation model and predicts a tensor-to-scalar ratio $r = 16/3N = 0.097$ and a scalar spectral index $n_{s} = 1-5/3N = 0.970$. The value of $|\Phi|$ remains sub-Planckian throughout the observable era of inflation, with $|\Phi| \lesssim 0.01 M_{Pl}$ for $N \lesssim 60$ when $\lambda \sim 1$.

A Minimal Sub-Planckian Axion Inflation Model with Large Tensor-to-Scalar Ratio

We present a miminal axion inflation model which can generate a large tensor-to-scalar ratio while remaining sub-Planckian. The modulus of a complex scalar field $\Phi$ with a $\lambda |\Phi|^4$ potential couples directly to the gauge field of a strongly-coupled sector via a term of the form $(|\Phi|/M_{Pl})^{m} F \tilde{F}$. This generates a minimum of the potential which is aperiodic in the phase. The resulting inflation model is equivalent to a $\phi^{4/(m+1)}$ chaotic inflation model. For the natural case of a leading-order portal-like interaction $\Phi^{\dagger}\Phi F \tilde{F}$, the model is equivalent to a $\phi^{4/3}$ chaotic inflation model and predicts a tensor-to-scalar ratio $r = 16/3N = 0.097$ and a scalar spectral index $n_{s} = 1-5/3N = 0.970$. The value of $|\Phi|$ remains sub-Planckian throughout the observable era of inflation, with $|\Phi| \lesssim 0.01 M_{Pl}$ for $N \lesssim 60$ when $\lambda \sim 1$.

A Minimal Sub-Planckian Axion Inflation Model with Large Tensor-to-Scalar Ratio [Cross-Listing]

We present a miminal axion inflation model which can generate a large tensor-to-scalar ratio while remaining sub-Planckian. The modulus of a complex scalar field $\Phi$ with a $\lambda |\Phi|^4$ potential couples directly to the gauge field of a strongly-coupled sector via a term of the form $(|\Phi|/M_{Pl})^{m} F \tilde{F}$. This generates a minimum of the potential which is aperiodic in the phase. The resulting inflation model is equivalent to a $\phi^{4/(m+1)}$ chaotic inflation model. For the natural case of a leading-order portal-like interaction $\Phi^{\dagger}\Phi F \tilde{F}$, the model is equivalent to a $\phi^{4/3}$ chaotic inflation model and predicts a tensor-to-scalar ratio $r = 16/3N = 0.097$ and a scalar spectral index $n_{s} = 1-5/3N = 0.970$. The value of $|\Phi|$ remains sub-Planckian throughout the observable era of inflation, with $|\Phi| \lesssim 0.01 M_{Pl}$ for $N \lesssim 60$ when $\lambda \sim 1$.

Baryon Asymmetries in the Natural Inflation Model

A variation of Affleck-Dine mechanism was proposed to generate the observed baryon asymmetry in [1], in which the inflaton was assumed to be a complex scalar field with a weakly broken $U(1)$ symmetry, and the baryon asymmetry generation was easily unified with the stage of inflation and reheating. We adapt this mechanism to natural inflation scenarios and compare the results with those in chaotic inflation models. We compute the net particle number obtained at the end of inflation and transform it into net baryon number after reheatings. We observed that in natural inflation models, the desired baryon-to-photon ratio can be achieved equally well as in chaotic models.

Stationary Black Holes with Time-Dependent Scalar Fields [Cross-Listing]

It has been well known since the 1970s that stationary black holes do not generically support scalar hair. Most of the no-hair theorems which support this depend crucially upon the assumption that the scalar field has no time dependence. Here we fill in this omission by ruling out the existence of stationary black hole solutions even when the scalar field may have time dependence. Our proof is fairly general, and in particular applies to non-canonical scalar fields and certain non-asymptotically flat spacetimes. It also does not rely upon the spacetime being a black hole.

Stationary Black Holes with Time-Dependent Scalar Fields [Cross-Listing]

It has been well known since the 1970s that stationary black holes do not generically support scalar hair. Most of the no-hair theorems which support this depend crucially upon the assumption that the scalar field has no time dependence. Here we fill in this omission by ruling out the existence of stationary black hole solutions even when the scalar field may have time dependence. Our proof is fairly general, and in particular applies to non-canonical scalar fields and certain non-asymptotically flat spacetimes. It also does not rely upon the spacetime being a black hole.

Creation of wormholes by quantum tunnelling in modified gravity theories

We study the process of quantum tunnelling in scalar-tensor theories in which the scalar field is non-minimally coupled to gravity. In these theories gravitational instantons can deviate substantially from sphericity and can in fact develop a neck – a feature prohibited in theories with minimal coupling. Such instantons with necks lead to the materialisation of bubble geometries containing a wormhole region. We clarify the relationship of neck geometries to violations of the null energy condition, and also derive a bound on the size of the neck relative to that of the instanton.

Creation of wormholes by quantum tunnelling in modified gravity theories

We study the process of quantum tunnelling in scalar-tensor theories in which the scalar field is non-minimally coupled to gravity. In these theories gravitational instantons can deviate substantially from sphericity and can in fact develop a neck – a feature prohibited in theories with minimal coupling. Such instantons with necks lead to the materialisation of bubble geometries containing a wormhole region. We clarify the relationship of neck geometries to violations of the null energy condition, and also derive a bound on the size of the neck relative to that of the instanton.

Geometric creation of quantized vorticity by frame dragging [Cross-Listing]

We consider a complex scalar field in background metrics that exhibit frame-dragging, in particular the BTZ metric in 2+1 dimensional spacetime, and the Kerr metric in 3+1 dimensional spacetime. In the equation of motion for the scalar field, which is a nonlinear Klein-Gordon equation, we identify and isolate the terms arising from frame-dragging that correspond to the Coriolis force and the centrifugal force, which produce local rotation in the field. The field physically describes a superfluid, which can rotate only through the creation of quantized vortices. We demonstrate such vortex creation through numerical simulation of a simplified metric that exhibits frame-dragging.

Geometric creation of quantized vorticity by frame dragging [Cross-Listing]

We consider a complex scalar field in background metrics that exhibit frame-dragging, in particular the BTZ metric in 2+1 dimensional spacetime, and the Kerr metric in 3+1 dimensional spacetime. In the equation of motion for the scalar field, which is a nonlinear Klein-Gordon equation, we identify and isolate the terms arising from frame-dragging that correspond to the Coriolis force and the centrifugal force, which produce local rotation in the field. The field physically describes a superfluid, which can rotate only through the creation of quantized vortices. We demonstrate such vortex creation through numerical simulation of a simplified metric that exhibits frame-dragging.

Geometric creation of quantized vorticity by frame dragging [Cross-Listing]

We consider a complex scalar field in background metrics that exhibit frame-dragging, in particular the BTZ metric in 2+1 dimensional spacetime, and the Kerr metric in 3+1 dimensional spacetime. In the equation of motion for the scalar field, which is a nonlinear Klein-Gordon equation, we identify and isolate the terms arising from frame-dragging that correspond to the Coriolis force and the centrifugal force, which produce local rotation in the field. The field physically describes a superfluid, which can rotate only through the creation of quantized vortices. We demonstrate such vortex creation through numerical simulation of a simplified metric that exhibits frame-dragging.

Implications of the primordial anisotropy for a scalar field with non-minimal kinetic coupling

We consider a scalar field with a kinetic term non-minimally coupled to gravity in an anisotropic background. Various potentials for the scalar field are considered. By explicit examples, we show that how the anisotropy can change the dynamics of the scalar field compared with the isotropic background.

Partial Differential Equations with Random Noise in Inflationary Cosmology [Cross-Listing]

Random noise arises in many physical problems in which the observer is not tracking the full system. A case in point is inflationary cosmology, the current paradigm for describing the very early universe, where one is often interested only in the time-dependence of a subsystem. In inflationary cosmology it is assumed that a slowly rolling scalar field leads to an exponential increase in the size of space. At the end of this phase, the scalar field begins to oscillate and transfers its energy to regular matter. This transfer typically involves a parametric resonance instability. This article reviews work which the author has done in collaboration with Walter Craig studying the role which random noise can play in the parametric resonance instability of matter fields in the presence of the oscillatory inflaton field. We find that the particular idealized form of the noise studied here renders the instability more effective. As a corollary, we obtain a new proof of Anderson localization.

Partial Differential Equations with Random Noise in Inflationary Cosmology [Cross-Listing]

Random noise arises in many physical problems in which the observer is not tracking the full system. A case in point is inflationary cosmology, the current paradigm for describing the very early universe, where one is often interested only in the time-dependence of a subsystem. In inflationary cosmology it is assumed that a slowly rolling scalar field leads to an exponential increase in the size of space. At the end of this phase, the scalar field begins to oscillate and transfers its energy to regular matter. This transfer typically involves a parametric resonance instability. This article reviews work which the author has done in collaboration with Walter Craig studying the role which random noise can play in the parametric resonance instability of matter fields in the presence of the oscillatory inflaton field. We find that the particular idealized form of the noise studied here renders the instability more effective. As a corollary, we obtain a new proof of Anderson localization.

Partial Differential Equations with Random Noise in Inflationary Cosmology [Cross-Listing]

Random noise arises in many physical problems in which the observer is not tracking the full system. A case in point is inflationary cosmology, the current paradigm for describing the very early universe, where one is often interested only in the time-dependence of a subsystem. In inflationary cosmology it is assumed that a slowly rolling scalar field leads to an exponential increase in the size of space. At the end of this phase, the scalar field begins to oscillate and transfers its energy to regular matter. This transfer typically involves a parametric resonance instability. This article reviews work which the author has done in collaboration with Walter Craig studying the role which random noise can play in the parametric resonance instability of matter fields in the presence of the oscillatory inflaton field. We find that the particular idealized form of the noise studied here renders the instability more effective. As a corollary, we obtain a new proof of Anderson localization.

Partial Differential Equations with Random Noise in Inflationary Cosmology [Cross-Listing]

Random noise arises in many physical problems in which the observer is not tracking the full system. A case in point is inflationary cosmology, the current paradigm for describing the very early universe, where one is often interested only in the time-dependence of a subsystem. In inflationary cosmology it is assumed that a slowly rolling scalar field leads to an exponential increase in the size of space. At the end of this phase, the scalar field begins to oscillate and transfers its energy to regular matter. This transfer typically involves a parametric resonance instability. This article reviews work which the author has done in collaboration with Walter Craig studying the role which random noise can play in the parametric resonance instability of matter fields in the presence of the oscillatory inflaton field. We find that the particular idealized form of the noise studied here renders the instability more effective. As a corollary, we obtain a new proof of Anderson localization.

The double attractor behavior of induced inflation

We describe an induced inflation, which refers to a class of inflationary models with a generalized non-minimal coupling $\xi g(\phi) R$ and a specific scalar potential. The defining property of these models is that the scalar field takes a vev in the vacuum and thus induces an effective Planck mass. We study this model as a function of the coupling parameter $\xi$. At large $\xi$, the predictions of the theory are known to have an attractor behavior, converging to a universal result independent on the choice of the function $g(\phi)$. We find that at small $\xi$, the theory approaches a second attractor. The inflationary predictions of this class of theories continuously interpolate between those of the Starobinsky model and the predictions of the simplest chaotic inflation with a quadratic potential.

The double attractor behavior of induced inflation

We describe an induced inflation, which refers to a class of inflationary models with a generalized non-minimal coupling $\xi g(\phi) R$ and a specific scalar potential. The defining property of these models is that the scalar field takes a vev in the vacuum and thus induces an effective Planck mass. We study this model as a function of the coupling parameter $\xi$. At large $\xi$, the predictions of the theory are known to have an attractor behavior, converging to a universal result independent on the choice of the function $g(\phi)$. We find that at small $\xi$, the theory approaches a second attractor. The inflationary predictions of this class of theories continuously interpolate between those of the Starobinsky model and the predictions of the simplest chaotic inflation with a quadratic potential.

The double attractor behavior of induced inflation [Cross-Listing]

We describe an induced inflation, which refers to a class of inflationary models with a generalized non-minimal coupling $\xi g(\phi) R$ and a specific scalar potential. The defining property of these models is that the scalar field takes a vev in the vacuum and thus induces an effective Planck mass. We study this model as a function of the coupling parameter $\xi$. At large $\xi$, the predictions of the theory are known to have an attractor behavior, converging to a universal result independent on the choice of the function $g(\phi)$. We find that at small $\xi$, the theory approaches a second attractor. The inflationary predictions of this class of theories continuously interpolate between those of the Starobinsky model and the predictions of the simplest chaotic inflation with a quadratic potential.

The double attractor behavior of induced inflation [Cross-Listing]

We describe an induced inflation, which refers to a class of inflationary models with a generalized non-minimal coupling $\xi g(\phi) R$ and a specific scalar potential. The defining property of these models is that the scalar field takes a vev in the vacuum and thus induces an effective Planck mass. We study this model as a function of the coupling parameter $\xi$. At large $\xi$, the predictions of the theory are known to have an attractor behavior, converging to a universal result independent on the choice of the function $g(\phi)$. We find that at small $\xi$, the theory approaches a second attractor. The inflationary predictions of this class of theories continuously interpolate between those of the Starobinsky model and the predictions of the simplest chaotic inflation with a quadratic potential.

An extension of cosmological dynamics with York time [Cross-Listing]

It has been suggested that the York parameter $T$ (effectively the scalar extrinsic curvature of a spatial hypersurface) may play the role of a fundamental time parameter. In a flat, forever expanding cosmology the York parameter remains always negative, taking values $T=-\infty$ at the big bang and approaching some finite non-positive value as $t\rightarrow\infty$, $t$ being the usual cosmological time coordinate. Based on previous results concerning a simple, spatially flat cosmological model with a scalar field, we provide a temporal extension of this model to include times’ $T>0$, an epoch not covered by the cosmological time coordinate $t$, and discuss the dynamics of this other side’ and its significance.

From Kinks to Compactons

This work deals with the presence of localized structures in relativistic systems described by a single real scalar field in two-dimensional spacetime. We concentrate on kinks and compactons in models with standard kinematics, and we develop a procedure that help us to smoothly go from kinks to compactons in the suggested scenario. We also show how the procedure works in the braneworld scenario, for flat brane in the five-dimensional spacetime with a single extra dimension of infinite extent. The brane unveils a hybrid profile when the kink becomes a compacton, behaving as a thick or thin brane, depending on the extra dimension being inside or outside a compact space.

From Kinks to Compactons [Cross-Listing]

This work deals with the presence of localized structures in relativistic systems described by a single real scalar field in two-dimensional spacetime. We concentrate on kinks and compactons in models with standard kinematics, and we develop a procedure that help us to smoothly go from kinks to compactons in the suggested scenario. We also show how the procedure works in the braneworld scenario, for flat brane in the five-dimensional spacetime with a single extra dimension of infinite extent. The brane unveils a hybrid profile when the kink becomes a compacton, behaving as a thick or thin brane, depending on the extra dimension being inside or outside a compact space.

Simulating the universe(s) II: phenomenology of cosmic bubble collisions in full General Relativity [Cross-Listing]

Observing the relics of collisions between bubble universes would provide direct evidence for the existence of an eternally inflating Multiverse; the non-observation of such events can also provide important constraints on inflationary physics. Realizing these prospects requires quantitative predictions for observables from the properties of the possible scalar field Lagrangians underlying eternal inflation. Building on previous work, we establish this connection in detail. We perform a fully relativistic numerical study of the phenomenology of bubble collisions in models with a single scalar field, computing the comoving curvature perturbation produced in a wide variety of models. We also construct a set of analytic predictions, allowing us to identify the phenomenologically relevant properties of the scalar field Lagrangian. The agreement between the analytic predictions and numerics in the relevant regions is excellent, and allows us to generalize our results beyond the models we adopt for the numerical studies. Specifically, the signature is completely determined by the spatial profile of the colliding bubble just before the collision, and the de Sitter invariant distance between the bubble centers. The analytic and numerical results support a power-law fit with an index $1< \kappa \lesssim 2$. For collisions between identical bubbles, we establish a lower-bound on the observed amplitude of collisions that is set by the present energy density in curvature.

Simulating the universe(s) II: phenomenology of cosmic bubble collisions in full General Relativity

Observing the relics of collisions between bubble universes would provide direct evidence for the existence of an eternally inflating Multiverse; the non-observation of such events can also provide important constraints on inflationary physics. Realizing these prospects requires quantitative predictions for observables from the properties of the possible scalar field Lagrangians underlying eternal inflation. Building on previous work, we establish this connection in detail. We perform a fully relativistic numerical study of the phenomenology of bubble collisions in models with a single scalar field, computing the comoving curvature perturbation produced in a wide variety of models. We also construct a set of analytic predictions, allowing us to identify the phenomenologically relevant properties of the scalar field Lagrangian. The agreement between the analytic predictions and numerics in the relevant regions is excellent, and allows us to generalize our results beyond the models we adopt for the numerical studies. Specifically, the signature is completely determined by the spatial profile of the colliding bubble just before the collision, and the de Sitter invariant distance between the bubble centers. The analytic and numerical results support a power-law fit with an index $1< \kappa \lesssim 2$. For collisions between identical bubbles, we establish a lower-bound on the observed amplitude of collisions that is set by the present energy density in curvature.

B-modes and the Nature of Inflation [Cross-Listing]

Observations of the cosmic microwave background do not yet determine whether inflation was driven by a slowly-rolling scalar field or involved another physical mechanism. In this paper we discuss the prospects of using the power spectra of scalar and tensor modes to probe the nature of inflation. We focus on the leading modification to the slow-roll dynamics, which entails a sound speed $c_s$ for the scalar fluctuations. We derive analytically a lower bound on $c_s$ in terms of a given tensor-to-scalar ratio $r$, taking into account the difference in the freeze-out times between the scalar and tensor modes. We find that any detection of primordial B-modes with $r > 0.01$ implies a lower bound on $c_s$ that is stronger than the bound derived from the absence of non-Gaussianity in the Planck data. Our analytic expectation is confirmed by a joint analysis of data from WMAP, Planck and BICEP2, which leads to $c_s > 0.25$ (95$\%$CL). This~bound is tantalizingly close to a critical value for the sound speed, $(c_s)_\star = 0.47$ (corresponding to $(f_{NL}^{equil})_\star = -0.93$), which we show serves as a threshold for non-trivial dynamics beyond slow-roll. We also discuss how an order-one level of equilateral non-Gaussianity is a natural observational target for other extensions of the canonical paradigm.

B-modes and the Nature of Inflation

Observations of the cosmic microwave background do not yet determine whether inflation was driven by a slowly-rolling scalar field or involved another physical mechanism. In this paper we discuss the prospects of using the power spectra of scalar and tensor modes to probe the nature of inflation. We focus on the leading modification to the slow-roll dynamics, which entails a sound speed $c_s$ for the scalar fluctuations. We derive analytically a lower bound on $c_s$ in terms of a given tensor-to-scalar ratio $r$, taking into account the difference in the freeze-out times between the scalar and tensor modes. We find that any detection of primordial B-modes with $r > 0.01$ implies a lower bound on $c_s$ that is stronger than the bound derived from the absence of non-Gaussianity in the Planck data. Our analytic expectation is confirmed by a joint analysis of data from WMAP, Planck and BICEP2, which leads to $c_s > 0.25$ (95$\%$CL). This~bound is tantalizingly close to a critical value for the sound speed, $(c_s)_\star = 0.47$ (corresponding to $(f_{NL}^{equil})_\star = -0.93$), which we show serves as a threshold for non-trivial dynamics beyond slow-roll. We also discuss how an order-one level of equilateral non-Gaussianity is a natural observational target for other extensions of the canonical paradigm.

B-modes and the Nature of Inflation [Cross-Listing]

Observations of the cosmic microwave background do not yet determine whether inflation was driven by a slowly-rolling scalar field or involved another physical mechanism. In this paper we discuss the prospects of using the power spectra of scalar and tensor modes to probe the nature of inflation. We focus on the leading modification to the slow-roll dynamics, which entails a sound speed $c_s$ for the scalar fluctuations. We derive analytically a lower bound on $c_s$ in terms of a given tensor-to-scalar ratio $r$, taking into account the difference in the freeze-out times between the scalar and tensor modes. We find that any detection of primordial B-modes with $r > 0.01$ implies a lower bound on $c_s$ that is stronger than the bound derived from the absence of non-Gaussianity in the Planck data. Our analytic expectation is confirmed by a joint analysis of data from WMAP, Planck and BICEP2, which leads to $c_s > 0.25$ (95$\%$CL). This~bound is tantalizingly close to a critical value for the sound speed, $(c_s)_\star = 0.47$ (corresponding to $(f_{NL}^{equil})_\star = -0.93$), which we show serves as a threshold for non-trivial dynamics beyond slow-roll. We also discuss how an order-one level of equilateral non-Gaussianity is a natural observational target for other extensions of the canonical paradigm.

Explaining the Proton Radius Puzzle with Disformal Scalars [Replacement]

We analyse the consequences of a disformal interaction between a massless scalar and matter particles in the context of atomic physics. We focus on the displacement of the atomic energy levels that it induces, and in particular the change in the Lamb shift between the 2s and 2p states. We find that the correction to the Lamb shift depends on the mass of the fermion orbiting around the nucleus, implying a larger effect for muonic atoms. Taking the cut-off scale describing the effective scalar field theory close to the QCD scale, we find that the disformal interaction can account for the observed difference in the proton radius of muonic versus electronic Hydrogen. Explaining the proton radius puzzle is only possible when the scalar field is embedded in non-linear theories which alleviate constraints from collider and stellar physics. Short distance properties of the Galileon where non-perturbative effects in vacuum are present ensure that unitarity is preserved in high energy particle collisions. In matter, the chameleon mechanism alleviates the constraints on disformal interactions coming from the burning rates for stellar objects. We show how to combine these two properties in a single model which renders the proposed explanation of the proton radius puzzle viable.

Explaining the Proton Radius Puzzle with Disformal Scalars [Replacement]

We analyse the consequences of a disformal interaction between a massless scalar and matter particles in the context of atomic physics. We focus on the displacement of the atomic energy levels that it induces, and in particular the change in the Lamb shift between the 2s and 2p states. We find that the correction to the Lamb shift depends on the mass of the fermion orbiting around the nucleus, implying a larger effect for muonic atoms. Taking the cut-off scale describing the effective scalar field theory close to the QCD scale, we find that the disformal interaction can account for the observed difference in the proton radius of muonic versus electronic Hydrogen. Explaining the proton radius puzzle is only possible when the scalar field is embedded in non-linear theories which alleviate constraints from collider and stellar physics. Short distance properties of the Galileon where non-perturbative effects in vacuum are present ensure that unitarity is preserved in high energy particle collisions. In matter, the chameleon mechanism alleviates the constraints on disformal interactions coming from the burning rates for stellar objects. We show how to combine these two properties in a single model which renders the proposed explanation of the proton radius puzzle viable.

Explaining the Proton Radius Puzzle with Disformal Scalars [Replacement]

We analyse the consequences of a disformal interaction between a massless scalar and matter particles in the context of atomic physics. We focus on the displacement of the atomic energy levels that it induces, and in particular the change in the Lamb shift between the 2s and 2p states. We find that the correction to the Lamb shift depends on the mass of the fermion orbiting around the nucleus, implying a larger effect for muonic atoms. Taking the cut-off scale describing the effective scalar field theory close to the QCD scale, we find that the disformal interaction can account for the observed difference in the proton radius of muonic versus electronic Hydrogen. Explaining the proton radius puzzle is only possible when the scalar field is embedded in non-linear theories which alleviate constraints from collider and stellar physics. Short distance properties of the Galileon where non-perturbative effects in vacuum are present ensure that unitarity is preserved in high energy particle collisions. In matter, the chameleon mechanism alleviates the constraints on disformal interactions coming from the burning rates for stellar objects. We show how to combine these two properties in a single model which renders the proposed explanation of the proton radius puzzle viable.

Explaining the Proton Radius Puzzle with Disformal Scalars [Cross-Listing]

We analyse the consequences of a disformal interaction between a massless scalar and matter particles in the context of atomic physics. We focus on the displacement of the atomic energy levels that it induces, and in particular the change in the Lamb shift between the 2s and 2p states. We find that the correction to the Lamb shift depends on the mass of the fermion orbiting around the nucleus, implying a larger effect for muonic atoms. Taking the cut-off scale describing the effective scalar field theory close to the QCD scale, we find that the disformal interaction can account for the observed difference in the proton radius of muonic versus electronic Hydrogen. Explaining the proton radius puzzle is only possible when the scalar field is embedded in non-linear theories which alleviate constraints from collider and stellar physics. Short distance properties of the Galileon where non-perturbative effects in vacuum are present ensure that unitarity is preserved in high energy particle collisions. In matter, the chameleon mechanism alleviates the constraints on disformal interactions coming from the burning rates for stellar objects. We show how to combine these two properties in a single model which renders the proposed explanation of the proton radius puzzle viable.

Explaining the Proton Radius Puzzle with Disformal Scalars

We analyse the consequences of a disformal interaction between a massless scalar and matter particles in the context of atomic physics. We focus on the displacement of the atomic energy levels that it induces, and in particular the change in the Lamb shift between the 2s and 2p states. We find that the correction to the Lamb shift depends on the mass of the fermion orbiting around the nucleus, implying a larger effect for muonic atoms. Taking the cut-off scale describing the effective scalar field theory close to the QCD scale, we find that the disformal interaction can account for the observed difference in the proton radius of muonic versus electronic Hydrogen. Explaining the proton radius puzzle is only possible when the scalar field is embedded in non-linear theories which alleviate constraints from collider and stellar physics. Short distance properties of the Galileon where non-perturbative effects in vacuum are present ensure that unitarity is preserved in high energy particle collisions. In matter, the chameleon mechanism alleviates the constraints on disformal interactions coming from the burning rates for stellar objects. We show how to combine these two properties in a single model which renders the proposed explanation of the proton radius puzzle viable.

Explaining the Proton Radius Puzzle with Disformal Scalars [Cross-Listing]

We analyse the consequences of a disformal interaction between a massless scalar and matter particles in the context of atomic physics. We focus on the displacement of the atomic energy levels that it induces, and in particular the change in the Lamb shift between the 2s and 2p states. We find that the correction to the Lamb shift depends on the mass of the fermion orbiting around the nucleus, implying a larger effect for muonic atoms. Taking the cut-off scale describing the effective scalar field theory close to the QCD scale, we find that the disformal interaction can account for the observed difference in the proton radius of muonic versus electronic Hydrogen. Explaining the proton radius puzzle is only possible when the scalar field is embedded in non-linear theories which alleviate constraints from collider and stellar physics. Short distance properties of the Galileon where non-perturbative effects in vacuum are present ensure that unitarity is preserved in high energy particle collisions. In matter, the chameleon mechanism alleviates the constraints on disformal interactions coming from the burning rates for stellar objects. We show how to combine these two properties in a single model which renders the proposed explanation of the proton radius puzzle viable.

Cosmic acceleration in non-canonical scalar field model - An interacting scenario [Replacement]

In this paper we have studied the dynamics of accelerating scenario within the framework of scalar field models possessing a non-canonical kinetic term. In this toy model, the scalar field is allowed to interact with the dark matter component through a source term. We have assumed a specific form for the coupling term and then have studied the dynamics of the scalar field having a constant equation of state parameter. We have also carried out the dynamical system study of such interacting non-canonical scalar field models for power law potentials.

Cosmic acceleration in non-canonical scalar field model - An interacting scenario [Cross-Listing]

In this paper we have studied the dynamics of accelerating scenario within the framework of scalar field models possessing a non-canonical kinetic term. In this toy model, the scalar field is allowed to interact with the dark matter component through a source term. We have assumed a specific form for the coupling term and then have studied the dynamics of the scalar field having a constant equation of state parameter. We have also carried out the dynamical system study of such interacting non-canonical scalar field models for power law potentials.

Arbitrary scalar-field and Tachyon cosmological models

Tachyon scalar field in FRW universe considered, then scalar field and some important cosmological parameters for two special cases of scalar potential discussed. First we assume the exponential potential scalar field and then consider hyperbolic cosine type scalar-field potentials. In both cases we obtain behavior of the Hubble, deceleration and EoS parameters.

Arbitrary scalar-field and Tachyon cosmological models

Tachyon scalar field in FRW universe considered, then scalar field and some important cosmological parameters for two special cases of scalar potential discussed. First we assume the exponential potential scalar field and then consider hyperbolic cosine type scalar-field potentials. In both cases we obtain behavior of the Hubble, deceleration and EoS parameters.

Wightman function and the Casimir effect for a Robin sphere in a constant curvature space

We evaluate the Wightman function, the mean field squared and the vacuum expectation value (VEV) of the energy-momentum tensor for a scalar field with Robin boundary condition on a spherical shell in the background of a constant negative curvature space. For the coefficient in the boundary condition there is a critical value above which the scalar vacuum becomes unstable. In both interior and exterior regions, the VEVs are decomposed into the boundary-free and sphere-induced contributions. For the latter, rapidly convergent integral representations are provided. In the region inside the sphere, the eigenvalues are expressed in terms of the zeros of the combination of the associated Legendre function and its derivative and the decomposition is achieved by making use of the Abel-Plana type summation formula for the series over these zeros. The sphere-induced contribution to the VEV of the field squared is negative for Dirichlet boundary condition and positive for Neumann one. At distances from the sphere larger than the curvature scale of the background space the suppression of the vacuum fluctuations in the gravitational field corresponding to the negative curvature space is stronger compared with the case of the Minkowskian bulk. In particular, the decay of the VEVs with the distance is exponential for both massive and massless fields. The corresponding results are generalized for spaces with spherical bubbles and for cosmological models with negative curvature spaces.

Universality classes for models of inflation

We show that the cosmological evolution of a scalar field in a potential can be obtained from a renormalisation group equation. The slow roll regime of inflation models is understood in this context as the slow evolution close to a fixed point, described by the methods of renormalisation group. This explains in part the universality observed in the predictions of a certain number of inflation models. We illustrate this behavior on a certain number of examples and discuss it in the context of the AdS/CFT correspondence.

Universality classes for models of inflation [Cross-Listing]

We show that the cosmological evolution of a scalar field in a potential can be obtained from a renormalisation group equation. The slow roll regime of inflation models is understood in this context as the slow evolution close to a fixed point, described by the methods of renormalisation group. This explains in part the universality observed in the predictions of a certain number of inflation models. We illustrate this behavior on a certain number of examples and discuss it in the context of the AdS/CFT correspondence.

Universality classes for models of inflation [Cross-Listing]

We show that the cosmological evolution of a scalar field in a potential can be obtained from a renormalisation group equation. The slow roll regime of inflation models is understood in this context as the slow evolution close to a fixed point, described by the methods of renormalisation group. This explains in part the universality observed in the predictions of a certain number of inflation models. We illustrate this behavior on a certain number of examples and discuss it in the context of the AdS/CFT correspondence.

Universality classes for models of inflation [Replacement]

We show that the cosmological evolution of a scalar field in a potential can be obtained from a renormalisation group equation. The slow roll regime of inflation models is understood in this context as the slow evolution close to a fixed point, described by the methods of renormalisation group. This explains in part the universality observed in the predictions of a certain number of inflation models. We illustrate this behavior on a certain number of examples and discuss it in the context of the AdS/CFT correspondence.

Universality classes for models of inflation [Replacement]

We show that the cosmological evolution of a scalar field in a potential can be obtained from a renormalisation group equation. The slow roll regime of inflation models is understood in this context as the slow evolution close to a fixed point, described by the methods of renormalisation group. This explains in part the universality observed in the predictions of a certain number of inflation models. We illustrate this behavior on a certain number of examples and discuss it in the context of the AdS/CFT correspondence.

Universality classes for models of inflation [Replacement]

We show that the cosmological evolution of a scalar field in a potential can be obtained from a renormalisation group equation. The slow roll regime of inflation models is understood in this context as the slow evolution close to a fixed point, described by the methods of renormalisation group. This explains in part the universality observed in the predictions of a certain number of inflation models. We illustrate this behavior on a certain number of examples and discuss it in the context of the AdS/CFT correspondence.

Universality classes for models of inflation [Replacement]

We show that the cosmological evolution of a scalar field in a potential can be obtained from a renormalisation group equation. The slow roll regime of inflation models is understood in this context as the slow evolution close to a fixed point, described by the methods of renormalisation group. This explains in part the universality observed in the predictions of a certain number of inflation models. We illustrate this behavior on a certain number of examples and discuss it in the context of the AdS/CFT correspondence.