# Posts Tagged scalar field

## Recent Postings from scalar field

### Dynamical Casimir effect in superconducting circuits: a numerical approach [Cross-Listing]

We present a numerical analysis of the particle creation for a quantum field in the presence of time dependent boundary conditions. Having in mind recent experiments involving superconducting circuits, we consider their description in terms of a scalar field in a one dimensional cavity satisfying generalized boundary conditions that involve a time-dependent linear combination of the field and its spatial and time derivatives. We evaluate numerically the Bogoliubov transformation between {\it in} and {\it out}-states and find that the rate of particle production strongly depends on whether the spectrum of the unperturbed cavity is equidistant or not, and also on the amplitude of the temporal oscillations of the boundary conditions. We provide analytic justifications for the different regimes found numerically.

### An effective field theory during inflation II: stochastic dynamics and power spectrum suppression

We obtain the non-equilibrium effective action of an inflaton like scalar field --the system-- by tracing over sub Hubble degrees of freedom of environmental'' light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflaton-like field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super Hubble fluctuations of the inflaton field, $\mathcal{P}(k;\eta) = \mathcal{P}_0(k)\,e^{-\gamma(k;\eta)}$ where $\mathcal{P}_0(k)$ is the nearly scale invariant power spectrum in absence of coupling. $\gamma(k;\eta)>0$ describes the suppression of the power spectrum, it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action for the case of a heavy scalar field of mass $M \gg H$, this case yields a local Fermi'' limit with a very weak self-interaction of the inflaton-like field and dissipative terms that are suppressed by powers of $H/M$. We conjecture on the possibility that the large scale anomalies in the CMB may originate in dissipative processes from inflaton coupling to sub-Hubble degrees of freedom.

### An effective field theory during inflation II: stochastic dynamics and power spectrum suppression [Cross-Listing]

We obtain the non-equilibrium effective action of an inflaton like scalar field --the system-- by tracing over sub Hubble degrees of freedom of environmental'' light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflaton-like field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super Hubble fluctuations of the inflaton field, $\mathcal{P}(k;\eta) = \mathcal{P}_0(k)\,e^{-\gamma(k;\eta)}$ where $\mathcal{P}_0(k)$ is the nearly scale invariant power spectrum in absence of coupling. $\gamma(k;\eta)>0$ describes the suppression of the power spectrum, it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action for the case of a heavy scalar field of mass $M \gg H$, this case yields a local Fermi'' limit with a very weak self-interaction of the inflaton-like field and dissipative terms that are suppressed by powers of $H/M$. We conjecture on the possibility that the large scale anomalies in the CMB may originate in dissipative processes from inflaton coupling to sub-Hubble degrees of freedom.

### An effective field theory during inflation II: stochastic dynamics and power spectrum suppression [Cross-Listing]

We obtain the non-equilibrium effective action of an inflaton like scalar field --the system-- by tracing over sub Hubble degrees of freedom of environmental'' light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflaton-like field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super Hubble fluctuations of the inflaton field, $\mathcal{P}(k;\eta) = \mathcal{P}_0(k)\,e^{-\gamma(k;\eta)}$ where $\mathcal{P}_0(k)$ is the nearly scale invariant power spectrum in absence of coupling. $\gamma(k;\eta)>0$ describes the suppression of the power spectrum, it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action for the case of a heavy scalar field of mass $M \gg H$, this case yields a local Fermi'' limit with a very weak self-interaction of the inflaton-like field and dissipative terms that are suppressed by powers of $H/M$. We conjecture on the possibility that the large scale anomalies in the CMB may originate in dissipative processes from inflaton coupling to sub-Hubble degrees of freedom.

### An effective field theory during inflation II: stochastic dynamics and power spectrum suppression [Cross-Listing]

We obtain the non-equilibrium effective action of an inflaton like scalar field --the system-- by tracing over sub Hubble degrees of freedom of environmental'' light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflaton-like field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super Hubble fluctuations of the inflaton field, $\mathcal{P}(k;\eta) = \mathcal{P}_0(k)\,e^{-\gamma(k;\eta)}$ where $\mathcal{P}_0(k)$ is the nearly scale invariant power spectrum in absence of coupling. $\gamma(k;\eta)>0$ describes the suppression of the power spectrum, it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action for the case of a heavy scalar field of mass $M \gg H$, this case yields a local Fermi'' limit with a very weak self-interaction of the inflaton-like field and dissipative terms that are suppressed by powers of $H/M$. We conjecture on the possibility that the large scale anomalies in the CMB may originate in dissipative processes from inflaton coupling to sub-Hubble degrees of freedom.

### Radiative corrections to the Higgs boson couplings in the model with an additional real singlet scalar field

We calculate renormalized Higgs boson couplings with gauge bosons and fermions at the one-loop level in the model with an additional isospin singlet real scalar field. These coupling constants can deviate from the predictions in the standard model due to tree-level mixing effects and one-loop contributions of the extra neutral scalar boson. We investigate how they can be significant under the theoretical constraints from perturbative unitarity and vacuum stability and also the condition of avoiding the wrong vacuum. Furthermore, comparing with the predictions in the Type I two Higgs doublet model, we numerically demonstrate how the singlet extension model can be distinguished and identified by using precision measurements of the Higgs boson couplings at future collider experiments.

### Trapping effects in inflation: blue spectrum at small scales

We consider the inflationary model in which the inflaton $\phi$ couples to another scalar field $\chi$ via the interaction $g^2(\phi-\phi_0)^2\chi^2$ with a small coupling constant $g$ ($g^2 \sim 10^{-7}$). We assume that there is a sequence of "trapping points" $\phi_{0i}$ along the inflationary trajectory where particles of $\chi$-field become massless and are rather effectively produced. We calculate the power spectrum of inflaton field fluctuations originated from a backreaction of $\chi$-particles produced, using the Schwinger's "in-in" formalism. We show that the primary curvature power spectrum produced by these backreaction effects is blue, which leads to a strong overproduction of primordial black holes (PBHs) in subsequent radiation era.

### Trapping effects in inflation: blue spectrum at small scales [Cross-Listing]

We consider the inflationary model in which the inflaton $\phi$ couples to another scalar field $\chi$ via the interaction $g^2(\phi-\phi_0)^2\chi^2$ with a small coupling constant $g$ ($g^2 \sim 10^{-7}$). We assume that there is a sequence of "trapping points" $\phi_{0i}$ along the inflationary trajectory where particles of $\chi$-field become massless and are rather effectively produced. We calculate the power spectrum of inflaton field fluctuations originated from a backreaction of $\chi$-particles produced, using the Schwinger's "in-in" formalism. We show that the primary curvature power spectrum produced by these backreaction effects is blue, which leads to a strong overproduction of primordial black holes (PBHs) in subsequent radiation era.

### Searching for scalar gravitational interactions in current and future cosmological data

Modified gravity theories often contain a scalar field of gravitational strength which interacts with matter. We examine constraints on the range and the coupling strength of a scalar gravitational degree of freedom using a subset of current data that can be safely analyzed within the linear perturbation theory. Using a model-independent implementation of scalar-tensor theories in MGCAMB in terms of two functions of the scale factor describing the mass and the coupling of the scalar degree of freedom, we derive constraints on the $f(R)$, generalized chameleon, Symmetron and Dilaton models. Since most of the large scale structure data available today is from relatively low redshifts, only a limited range of observed scales is in the linear regime, leading to relatively weak constraints. We then perform a forecast for a future large scale structure survey, such as Large Synoptic Survey Telescope (LSST), which will map a significant volume at higher redshifts, and show that it will produce much stronger constraints on scalar interactions in specific models. We also perform a principal component analysis and find that future surveys should be able to provide tight constraints on several eigenmodes of the scalar mass evolution.

### Dynamical fine-tuning of initial conditions for small field inflations [Cross-Listing]

Small-field inflation (SFI) is widely considered to be unnatural because an extreme fine-tuning of the initial condition is necessary for sufficiently large e-folding. In this paper, we show that the unnaturally-looking initial condition can be dynamically realised without any fine-tuning if the SFI occurs after rapid oscillations of the inflaton field and particle creations by preheating. In fact, if the inflaton field $\phi$ is coupled to another scalar field $\chi$ through the interaction $g^2 \chi^2 \phi^2$ and the vacuum energy during the small field inflation is given by $\lambda M^4$, the initial value can be dynamically set at $(\sqrt{\lambda}/g) M^2/M_{\rm pl}$, which is much smaller than the typical scale of the potential $M.$ This solves the initial condition problem in the new inflation model or some classes of the hilltop inflation models.

### Dynamical fine-tuning of initial conditions for small field inflations

Small-field inflation (SFI) is widely considered to be unnatural because an extreme fine-tuning of the initial condition is necessary for sufficiently large e-folding. In this paper, we show that the unnaturally-looking initial condition can be dynamically realised without any fine-tuning if the SFI occurs after rapid oscillations of the inflaton field and particle creations by preheating. In fact, if the inflaton field $\phi$ is coupled to another scalar field $\chi$ through the interaction $g^2 \chi^2 \phi^2$ and the vacuum energy during the small field inflation is given by $\lambda M^4$, the initial value can be dynamically set at $(\sqrt{\lambda}/g) M^2/M_{\rm pl}$, which is much smaller than the typical scale of the potential $M.$ This solves the initial condition problem in the new inflation model or some classes of the hilltop inflation models.

### Dynamical fine-tuning of initial conditions for small field inflations [Cross-Listing]

Small-field inflation (SFI) is widely considered to be unnatural because an extreme fine-tuning of the initial condition is necessary for sufficiently large e-folding. In this paper, we show that the unnaturally-looking initial condition can be dynamically realised without any fine-tuning if the SFI occurs after rapid oscillations of the inflaton field and particle creations by preheating. In fact, if the inflaton field $\phi$ is coupled to another scalar field $\chi$ through the interaction $g^2 \chi^2 \phi^2$ and the vacuum energy during the small field inflation is given by $\lambda M^4$, the initial value can be dynamically set at $(\sqrt{\lambda}/g) M^2/M_{\rm pl}$, which is much smaller than the typical scale of the potential $M.$ This solves the initial condition problem in the new inflation model or some classes of the hilltop inflation models.

### Beginning inflation in an inhomogeneous universe [Cross-Listing]

Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the inhomogeneities is comparable to the initial Hubble length, and overdense regions collapse and form black holes, because underdense regions continue expanding, allowing inflation to eventually begin. This establishes that inflation can arise from a general class of highly inhomogeneous initial conditions and solve the horizon and flatness problems, at least as long as the variations in the scalar field do not include values that exceed the inflationary plateau.

### Beginning inflation in an inhomogeneous universe [Cross-Listing]

Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the inhomogeneities is comparable to the initial Hubble length, and overdense regions collapse and form black holes, because underdense regions continue expanding, allowing inflation to eventually begin. This establishes that inflation can arise from a general class of highly inhomogeneous initial conditions and solve the horizon and flatness problems, at least as long as the variations in the scalar field do not include values that exceed the inflationary plateau.

### Beginning inflation in an inhomogeneous universe

Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the inhomogeneities is comparable to the initial Hubble length, and overdense regions collapse and form black holes, because underdense regions continue expanding, allowing inflation to eventually begin. This establishes that inflation can arise from a general class of highly inhomogeneous initial conditions and solve the horizon and flatness problems, at least as long as the variations in the scalar field do not include values that exceed the inflationary plateau.

### Dark Energy Parametrization motivated by Scalar Field Dynamics [Cross-Listing]

We propose a new Dark Energy parametrization based on the dynamics of a scalar field. We use an equation of state w=(x-1)/(x+1), with x=E_k/V, the ratio of kinetic energy E_k=\dotphi^2/2 and potential V. The equation of motion gives x=(L/6)(V/3H^2) and has a solution x=([(1+y)^2+2 L/3]^{1/2}-(1+y))/2 where y\equiv \rmm/V and L= (V'/V)^2 (1+q)^2, q=\ddotphi/V'. The resulting EoS is w=[6+ L- 6 \sqrt((1+y)^2+2L/3)]/(L+6y). Since the universe is accelerating at present time we use the slow roll approximation in which case we have |q|<< 1 and L\simeq (V'/V)^2. However, the derivation of w is exact and has no approximation. By choosing an appropriate ansatz for L we obtain a wide class of behavior for the evolution of Dark Energy without the need to specify the potential V. The EoS w can either grow and later decrease, or other way around, as a function of redshift and it is constraint between -1\leq w\leq 1 as for any canonical scalar field with only gravitational interaction. To determine the dynamics of Dark Energy we calculate the background evolution and its perturbations, since they are important to discriminate between different DE models. Our parametrization follows closely the dynamics of a scalar field scalar fields and the function L allow us to connect it with the potential V(phi) of the scalar field phi.

### Quantum supersymmetric FRW cosmology with a scalar field [Cross-Listing]

We analyze the quantum supersymmetryc cosmological FRW model with a scalar field, with a conditional probability density with the scalar field identified as time. The Hilbert space has a spinorial structure and has only one consistent solution, with a conserved probability density. The dynamics of the scale factor is obtained from its mean value. The uncertainty relations are fulfilled and the corresponding fluctuations are consistent with a semiclassical Universe.

### General relativity as an attractor for scalar-torsion cosmology [Cross-Listing]

We study flat Friedmann-Lemaitre-Robertson-Walker cosmological models for a scalar field coupled nonminimally to teleparallel gravity with generic coupling and potential functions. The goal in this paper is to determine the conditions under which the cosmological evolution tends to the limit where the variation of the gravitational "constant" ceases and the system evolves close to general relativity. These conditions can be read off from the approximate analytical solutions describing the process in matter and potential domination eras. Only those models where the GR limit exists and is an attractor can be considered viable. We expect the results to hold in the original "pure tetrad" formulation as well as in the recently suggested covariant formulation of the teleparallel theory. In the former case the GR attractor simultaneously provides a mechanism how cosmological evolution suppresses the problematic degrees of freedom stemming from the lack of local Lorentz invariance.

### From topological to non-topological solitons: kinks, domain walls and Q-balls in a scalar field model with non-trivial vacuum manifold [Cross-Listing]

We consider a scalar field model with a self-interaction potential that possesses a discrete vacuum manifold. We point out that this model allows for both topological as well as non-topological solitons. In (1+1) dimensions both type of solutions have finite energy, while in (3+1) dimensions, the topological solitons have finite energy per unit area only and correspond to domain walls. Non-topological solitons with finite energy do exist in (3+1) dimensions due to a non-trivial phase of the scalar field and an associated U(1) symmetry of the model, though. We construct these so-called Q-ball solutions numerically, point out the differences to previous studies with different scalar field potentials and also discuss the influence of a minimal coupling to both gravity as well as a U(1) gauge field. In this latter case, the conserved Noether charge Q can be interpreted as the electric charge of the solution.

### From topological to non-topological solitons: kinks, domain walls and Q-balls in a scalar field model with non-trivial vacuum manifold

We consider a scalar field model with a self-interaction potential that possesses a discrete vacuum manifold. We point out that this model allows for both topological as well as non-topological solitons. In (1+1) dimensions both type of solutions have finite energy, while in (3+1) dimensions, the topological solitons have finite energy per unit area only and correspond to domain walls. Non-topological solitons with finite energy do exist in (3+1) dimensions due to a non-trivial phase of the scalar field and an associated U(1) symmetry of the model, though. We construct these so-called Q-ball solutions numerically, point out the differences to previous studies with different scalar field potentials and also discuss the influence of a minimal coupling to both gravity as well as a U(1) gauge field. In this latter case, the conserved Noether charge Q can be interpreted as the electric charge of the solution.

### Impact of other scalar fields on oscillons after hilltop inflation

Oscillons are spatially localized and relatively stable field fluctuations which can form after inflation under suitable conditions. In order to reheat the universe, the fields which dominate the energy density after inflation have to couple to other degrees of freedom and finally produce the matter particles present in the universe today. In this study, we use lattice simulations to investigate how such couplings can affect the formation and stability of oscillons. We focus on models of hilltop inflation, where we have recently shown that hill crossing oscillons generically form, and consider the coupling to an additional scalar field which, depending on the value of the coupling parameter, can get resonantly enhanced from the inhomogeneous inflaton field. We find that three cases are realized: without a parametric resonance, the additional scalar field has no effects on the oscillons. For a fast and strong parametric resonance of the other scalar field, oscillons are strongly suppressed. For a delayed parametric resonance, on the other hand, the oscillons get imprinted on the other scalar field and their stability is even enhanced compared to the single-field oscillons.

### Impact of other scalar fields on oscillons after hilltop inflation [Cross-Listing]

Oscillons are spatially localized and relatively stable field fluctuations which can form after inflation under suitable conditions. In order to reheat the universe, the fields which dominate the energy density after inflation have to couple to other degrees of freedom and finally produce the matter particles present in the universe today. In this study, we use lattice simulations to investigate how such couplings can affect the formation and stability of oscillons. We focus on models of hilltop inflation, where we have recently shown that hill crossing oscillons generically form, and consider the coupling to an additional scalar field which, depending on the value of the coupling parameter, can get resonantly enhanced from the inhomogeneous inflaton field. We find that three cases are realized: without a parametric resonance, the additional scalar field has no effects on the oscillons. For a fast and strong parametric resonance of the other scalar field, oscillons are strongly suppressed. For a delayed parametric resonance, on the other hand, the oscillons get imprinted on the other scalar field and their stability is even enhanced compared to the single-field oscillons.

### Impact of other scalar fields on oscillons after hilltop inflation [Cross-Listing]

Oscillons are spatially localized and relatively stable field fluctuations which can form after inflation under suitable conditions. In order to reheat the universe, the fields which dominate the energy density after inflation have to couple to other degrees of freedom and finally produce the matter particles present in the universe today. In this study, we use lattice simulations to investigate how such couplings can affect the formation and stability of oscillons. We focus on models of hilltop inflation, where we have recently shown that hill crossing oscillons generically form, and consider the coupling to an additional scalar field which, depending on the value of the coupling parameter, can get resonantly enhanced from the inhomogeneous inflaton field. We find that three cases are realized: without a parametric resonance, the additional scalar field has no effects on the oscillons. For a fast and strong parametric resonance of the other scalar field, oscillons are strongly suppressed. For a delayed parametric resonance, on the other hand, the oscillons get imprinted on the other scalar field and their stability is even enhanced compared to the single-field oscillons.

### Static black holes with axial symmetry in asymptotically AdS$_4$ spacetime [Replacement]

The known static electro-vacuum black holes in a globally AdS$_4$ background have an event horizon which is geometrically a round sphere. In this work we argue that the situation is different in models with matter fields possessing an explicit dependence on the azimuthal angle $\varphi$, which, however, does not manifest at the level of the energy-momentum tensor. As a result, the full solutions are axially symmetric only, possessing a single (timelike) Killing vector field. Explicit examples of such static black holes are constructed in Einstein--(complex) scalar field and Einstein--Yang-Mills theories. The basic properties of these solutions are discussed, looking for generic features. For example, we notice that the horizon has an oblate spheroidal shape for solutions with a scalar field and a prolate one for black holes with Yang-Mills fields. The deviation from sphericity of the horizon geometry manifests itself in the holographic stress-tensor. Finally, based on the results obtained in the probe limit, we conjecture the existence in the Einstein-Maxwell theory of static black holes with axial symmetry only.

### The complete Brans-Dicke theory [Replacement]

The most general completion of Brans-Dicke gravity is found when energy is exchanged in a uniquely defined way between the scalar field and ordinary matter. The theory contains a new parameter (integration constant from the integration procedure) and when this is switched off, Brans-Dicke theory emerges. As usually, the vacuum theory can be defined from the complete Brans-Dicke theory when the matter energy-momentum tensor vanishes. However, additionally, the complete family of vacuum theories is found, consistent with the free wave equation for the scalar field. The subclass of this family with identically covariantly conserved energy-momentum tensor is identified and, thus, can be supplemented by any equation of motion for the scalar field.

### The complete Brans-Dicke theory [Replacement]

The most general completion of Brans-Dicke gravity is found when energy is exchanged in a uniquely defined way between the scalar field and ordinary matter. The theory contains a new parameter (integration constant from the integration procedure) and when this is switched off, Brans-Dicke theory emerges. As usually, the vacuum theory can be defined from the complete Brans-Dicke theory when the matter energy-momentum tensor vanishes. However, additionally, the complete family of vacuum theories is found, consistent with the free wave equation for the scalar field. The subclass of this family with identically covariantly conserved energy-momentum tensor is identified and, thus, can be supplemented by any equation of motion for the scalar field.

### Cosmology with nonminimal kinetic coupling and a Higgs-like potential [Replacement]

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as $\kappa G^{\mu\nu}\phi_{,\mu}\phi_{,\nu}$, and the Higgs-like potential $V(\phi)=\frac{\lambda}{4}(\phi^2-\phi_0^2)^2$. Using the dynamical system method, we analyze stationary points, their stability, and all possible asymptotical regimes of the model under consideration. We show that the Higgs field with the kinetic coupling provides an existence of accelerated regimes of the Universe evolution. There are three possible cosmological scenarios with acceleration: (i) {\em The late-time inflation} when the Hubble parameter tends to the constant value, $H(t)\to H_\infty=(\frac23 \pi G\lambda\phi_0^4)^{1/2}$ as $t\to\infty$, while the scalar field tends to zero, $\phi(t)\to 0$, so that the Higgs potential reaches its local maximum $V(0)=\frac14 \lambda\phi_0^4$. (ii) {\em The Big Rip} when $H(t)\sim(t_*-t)^{-1}\to\infty$ and $\phi(t)\sim(t_*-t)^{-2}\to\infty$ as $t\to t_*$. (iii) {\em The Little Rip} when $H(t)\sim t^{1/2}\to\infty$ and $\phi(t)\sim t^{1/4}\to\infty$ as $t\to\infty$. Also, we derive modified slow-roll conditions for the Higgs field and demonstrate that they lead to the Little Rip scenario.

### Cosmology with nonminimal kinetic coupling and a Higgs-like potential [Replacement]

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as $\kappa G^{\mu\nu}\phi_{,\mu}\phi_{,\nu}$, and the Higgs-like potential $V(\phi)=\frac{\lambda}{4}(\phi^2-\phi_0^2)^2$. Using the dynamical system method, we analyze stationary points, their stability, and all possible asymptotical regimes of the model under consideration. We show that the Higgs field with the kinetic coupling provides an existence of accelerated regimes of the Universe evolution. There are three possible cosmological scenarios with acceleration: (i) {\em The late-time inflation} when the Hubble parameter tends to the constant value, $H(t)\to H_\infty=(\frac23 \pi G\lambda\phi_0^4)^{1/2}$ as $t\to\infty$, while the scalar field tends to zero, $\phi(t)\to 0$, so that the Higgs potential reaches its local maximum $V(0)=\frac14 \lambda\phi_0^4$. (ii) {\em The Big Rip} when $H(t)\sim(t_*-t)^{-1}\to\infty$ and $\phi(t)\sim(t_*-t)^{-2}\to\infty$ as $t\to t_*$. (iii) {\em The Little Rip} when $H(t)\sim t^{1/2}\to\infty$ and $\phi(t)\sim t^{1/4}\to\infty$ as $t\to\infty$. Also, we derive modified slow-roll conditions for the Higgs field and demonstrate that they lead to the Little Rip scenario.

### Scalar field critical collapse in 2+1 dimensions [Cross-Listing]

We carry out numerical experiments in the critical collapse of a spherically symmetric massless scalar field in 2+1 spacetime dimensions in the presence of a negative cosmological constant and compare them against a new theoretical model. We approximate the true critical solution as the $n=4$ Garfinkle solution, matched at the lightcone to a Vaidya-like solution, and corrected to leading order for the effect of $\Lambda<0$. This approximation is only $C^3$ at the lightcone and has three growing modes. We {\em conjecture} that pointwise it is a good approximation to a yet unknown true critical solution that is analytic with only one growing mode (itself approximated by the top mode of our amended Garfinkle solution). With this conjecture, we predict a Ricci-scaling exponent of $\gamma=8/7$ and a mass-scaling exponent of $\delta=16/23$, compatible with our numerical experiments.

### Kerr black holes with self-interacting scalar hair: hairier but not heavier [Cross-Listing]

The maximal ADM mass for (mini-)boson stars (BSs) -- gravitating solitons of Einstein's gravity minimally coupled to a free, complex, mass $\mu$, Klein-Gordon field -- is $M_{\rm ADM}^{\rm max}\sim M_{Pl}^2/\mu$. Adding quartic self-interactions to the scalar field theory, described by the Lagrangian $\mathcal{L}_I=\lambda |\Psi|^4$, the maximal ADM mass becomes $M_{\rm ADM}^{\rm max}\sim \sqrt{\lambda}M_{Pl}^3/\mu^2$. Thus, for mini-BSs, astrophysically interesting masses require ultra-light scalar fields, whereas self-interacting BSs can reach such values for bosonic particles with Standard Model range masses. We investigate how these same self-interactions affect Kerr black holes with scalar hair (KBHsSH) [1], which can be regarded as (spinning) BSs in stationary equilibrium with a central horizon. Remarkably, whereas the ADM mass scales in the same way as for BSs, the \textit{horizon mass} $M_H$ does not increases with the coupling $\lambda$, and, for fixed $\mu$, it is maximized at the "Hod point", corresponding to the extremal Kerr black hole obtained in the vanishing hair limit. This mass is always $M_{\rm H}^{\rm max }\sim M_{\rm Pl}^2/\mu$. Thus, introducing these self-interactions, the black hole spacetimes may become considerably "hairier" but the trapped regions cannot become "heavier". We present evidence this observation also holds in a model with $\mathcal{L}_I= \beta|\Psi|^6-\lambda|\Psi|^4$; if it extends to \textit{general} scalar field models, KBHsSH with astrophysically interesting horizon masses \textit{require} ultra-light scalar fields. Their existence, therefore, would be a smoking gun for such (beyond the Standard Model) particles.

### Relativistic Mean-Field Models with Scaled Hadron Masses and Couplings: Hyperons and Maximum Neutron Star Mass

An equation of state of cold nuclear matter with an arbitrary isotopic composition is studied within a relativistic mean-field approach with hadron masses and coupling constants depending self-consistently on the scalar mean-field. All hadron masses decrease universally with the scalar field growth, whereas meson-nucleon coupling constants can vary differently. More specifically we focus on two modifications of the KVOR model studied previously. One extension of the model (KVORcut) demonstrates that the equation of state stiffens if the increase of the scalar-field magnitude with the density is bounded from above at some value for baryon densities above the saturation nuclear density. This can be realized if the nucleon vector-meson coupling constant changes rapidly as a function of the scalar field slightly above the desired value. The other version of the model (MKVOR) utilizes a smaller value of the nucleon effective mass at the nuclear saturation density and a saturation of the scalar field in the isospin asymmetric matter induced by a strong variation of the nucleon isovector-meson coupling constant as function of the scalar field. A possibility of hyperonization of the matter in neutron star interiors is incorporated. Our equations of state fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, direct Urca constraint, gravitational-baryon mass constraint and the constraint on the maximum mass of the neutron stars.

### Relativistic Mean-Field Models with Scaled Hadron Masses and Couplings: Hyperons and Maximum Neutron Star Mass [Cross-Listing]

An equation of state of cold nuclear matter with an arbitrary isotopic composition is studied within a relativistic mean-field approach with hadron masses and coupling constants depending self-consistently on the scalar mean-field. All hadron masses decrease universally with the scalar field growth, whereas meson-nucleon coupling constants can vary differently. More specifically we focus on two modifications of the KVOR model studied previously. One extension of the model (KVORcut) demonstrates that the equation of state stiffens if the increase of the scalar-field magnitude with the density is bounded from above at some value for baryon densities above the saturation nuclear density. This can be realized if the nucleon vector-meson coupling constant changes rapidly as a function of the scalar field slightly above the desired value. The other version of the model (MKVOR) utilizes a smaller value of the nucleon effective mass at the nuclear saturation density and a saturation of the scalar field in the isospin asymmetric matter induced by a strong variation of the nucleon isovector-meson coupling constant as function of the scalar field. A possibility of hyperonization of the matter in neutron star interiors is incorporated. Our equations of state fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, direct Urca constraint, gravitational-baryon mass constraint and the constraint on the maximum mass of the neutron stars.

### Late time solution for interacting scalar in accelerating spaces [Cross-Listing]

We consider stochastic inflation in an interacting scalar field in spatially homogeneous accelerating space-times with a constant principal slow roll parameter $\epsilon$. We show that, if the scalar potential is scale invariant (which is the case when scalar contains quartic self-interaction and couples non-minimally to gravity), the late-time solution on accelerating FLRW spaces can be described by a probability distribution function (PDF) $\rho$ which is a function of $\varphi/H$ only, where $\varphi=\varphi(\vec x)$ is the scalar field and $H=H(t)$ denotes the Hubble parameter. We give explicit late-time solutions for $\rho\rightarrow \rho_\infty(\varphi/H)$, and thereby find the order $\epsilon$ corrections to the Starobinsky-Yokoyama result. This PDF can then be used to calculate e.g. various $n-$point functions of the (self-interacting) scalar field, which are valid at late times in arbitrary accelerating space-times with $\epsilon=$ constant.

### Late time solution for interacting scalar in accelerating spaces [Cross-Listing]

We consider stochastic inflation in an interacting scalar field in spatially homogeneous accelerating space-times with a constant principal slow roll parameter $\epsilon$. We show that, if the scalar potential is scale invariant (which is the case when scalar contains quartic self-interaction and couples non-minimally to gravity), the late-time solution on accelerating FLRW spaces can be described by a probability distribution function (PDF) $\rho$ which is a function of $\varphi/H$ only, where $\varphi=\varphi(\vec x)$ is the scalar field and $H=H(t)$ denotes the Hubble parameter. We give explicit late-time solutions for $\rho\rightarrow \rho_\infty(\varphi/H)$, and thereby find the order $\epsilon$ corrections to the Starobinsky-Yokoyama result. This PDF can then be used to calculate e.g. various $n-$point functions of the (self-interacting) scalar field, which are valid at late times in arbitrary accelerating space-times with $\epsilon=$ constant.

### Electrodynamics on Cosmological Scales [Cross-Listing]

Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero net charge Maxwell's equations always fail regardless of the spacetime symmetry and the charge distribution. The two paradoxes indicate that Maxwell's equations need to be modified to be applicable to the universe as a whole. We consider two types of modified Maxwell equations, both of which can address the paradoxes. One is the Proca-type equation, which contains a photon mass term, i.e., a term proportional to the vector potential of the electromagnetic field. We show that this term can naturally arise if the electromagnetic field is coupled to a complex scalar field. If the complex scalar field is interpreted as describing charged pion particles, the mean mass density of charged pions in the universe gives rise to an effective photon mass with a Compton wavelength comparable to the Hubble radius of the universe. The other type of modified Maxwell equations contains a term with the electromagnetic field potential vector coupled to the spacetime curvature tensor. We show that this term can naturally arise if the Maxwell equation in a flat spacetime is written in terms of a symmetric tensor instead of the anti-symmetric tensor and then extended to a curved spacetime through the "minimal substitution rule". Some consequences of the modified Maxwell equations are investigated. The results show that for reasonable parameters the modification does not affect existing experiments and observations. However, we argue that, the modified equations may be testable in appropriate astrophysical and cosmological environments.

### Scalar mass stability bound in a simple Yukawa-theory from renormalisation group equations

Functional Renormalisation Group equations are constructed for a simple fermion-scalar Yukawa-model with discrete chiral symmetry, including also the effect of a nonzero composite fermion background beyond the conventional scalar condensate. Two approximate versions consistent with the scale dependent equations of motion are solved, taking into account also field renormalisation. The lower bound for the mass of the scalar field is determined requiring the stability of effective potential in the full momentum range, from the cutoff down to vanishing momentum. Close agreement is demonstrated with the results of previous studies done exclusively in presence of scalar condensate. A semiquantitative explanation is provided both for the negligible effect of the wave-function renormalisation and the narrow dispersion in the scalar mass bounds found from different approximation schemes.

### Scalar mass stability bound in a simple Yukawa-theory from renormalisation group equations [Cross-Listing]

Functional Renormalisation Group equations are constructed for a simple fermion-scalar Yukawa-model with discrete chiral symmetry, including also the effect of a nonzero composite fermion background beyond the conventional scalar condensate. Two approximate versions consistent with the scale dependent equations of motion are solved, taking into account also field renormalisation. The lower bound for the mass of the scalar field is determined requiring the stability of effective potential in the full momentum range, from the cutoff down to vanishing momentum. Close agreement is demonstrated with the results of previous studies done exclusively in presence of scalar condensate. A semiquantitative explanation is provided both for the negligible effect of the wave-function renormalisation and the narrow dispersion in the scalar mass bounds found from different approximation schemes.

### Teleparallel quintessence with a non-minimal coupling to a boundary term [Cross-Listing]

We propose a new model in the teleparallel framework where we consider a scalar field non-minimally coupled to both the torsion $T$ and a boundary term given by the divergence of the torsion vector $B=\frac{2}{e}\partial_\mu (eT^\mu)$. This is inspired by the relation $R=-T+B$ between the Ricci scalar of general relativity and the torsion of teleparallel gravity. This theory in suitable limits incorporates both the non-minimal coupling of a scalar field to torsion, and the non-minimal coupling of a scalar field to the Ricci scalar. We analyse the cosmology of such models, and we perform a dynamical systems analysis on the case when we have only a pure coupling to the boundary term. It is found that the system generically evolves to a late time accelerating attractor solution without requiring any fine tuning of the parameters. A dynamical crossing of the phantom barrier is also shown to be possible.

### Curvature Perturbation and Domain Wall Formation with Pseudo Scaling Scalar Dynamics [Cross-Listing]

Cosmological dynamics of scalar field with a monomial potential $\phi^{n}$ with a general background equation of state is revisited. It is known that if $n$ is smaller than a critical value, the scalar field exhibits a coherent oscillation and if $n$ is larger it obeys a scaling solution without oscillation. We study in detail the case where $n$ is equal to the critical value, and find a peculiar scalar dynamics which is neither oscillating nor scaling solution, and we call it a pseudo scaling solution. We also discuss cosmological implications of a pseudo scaling scalar dynamics, such as the curvature perturbation and the domain wall problem.

### Curvature Perturbation and Domain Wall Formation with Pseudo Scaling Scalar Dynamics [Cross-Listing]

Cosmological dynamics of scalar field with a monomial potential $\phi^{n}$ with a general background equation of state is revisited. It is known that if $n$ is smaller than a critical value, the scalar field exhibits a coherent oscillation and if $n$ is larger it obeys a scaling solution without oscillation. We study in detail the case where $n$ is equal to the critical value, and find a peculiar scalar dynamics which is neither oscillating nor scaling solution, and we call it a pseudo scaling solution. We also discuss cosmological implications of a pseudo scaling scalar dynamics, such as the curvature perturbation and the domain wall problem.

### Scalar field cosmology modified by the Generalized Uncertainty Principle [Cross-Listing]

We consider quintessence scalar field cosmology in which the Lagrangian of the scalar field is modified by the Generalized Uncertainty Principle. We show that the perturbation terms which arise from the deformed algebra are equivalent with the existence of a second scalar field, where the two fields interact in the kinetic part. Moreover, we consider a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime (FLRW), and we derive the gravitational field equations. We show that the modified equation of state parameter $w_{GUP}$ can cross the phantom divide line; that is $w_{GUP}<-1$. Furthermore, we derive the field equations in the dimensionless parameters, the dynamical system which arises is a singular perturbation system in which we study the existence of the fixed points in the slow manifold. Finally, we perform numerical simulations for some well known models and we show that for these models with the specific initial conditions, the parameter $w_{GUP}$ crosses the phantom barrier.

### Scalar field cosmology modified by the Generalized Uncertainty Principle [Cross-Listing]

We consider quintessence scalar field cosmology in which the Lagrangian of the scalar field is modified by the Generalized Uncertainty Principle. We show that the perturbation terms which arise from the deformed algebra are equivalent with the existence of a second scalar field, where the two fields interact in the kinetic part. Moreover, we consider a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime (FLRW), and we derive the gravitational field equations. We show that the modified equation of state parameter $w_{GUP}$ can cross the phantom divide line; that is $w_{GUP}<-1$. Furthermore, we derive the field equations in the dimensionless parameters, the dynamical system which arises is a singular perturbation system in which we study the existence of the fixed points in the slow manifold. Finally, we perform numerical simulations for some well known models and we show that for these models with the specific initial conditions, the parameter $w_{GUP}$ crosses the phantom barrier.

### Entanglement Dynamics of Detectors in an Einstein Cylinder [Cross-Listing]

We investigate how nontrivial topology affects the entanglement dynamics between a detector and a quantum field and between two detectors mediated by a quantum field. Nontrivial topology refers to both that of the base space and that of the bundle. Using a derivative-coupling Unruh-DeWitt-like detector model interacting with a quantum scalar field in an Einstein cylinder S1 (space) x R1 (time), we see the beating behaviors in the dynamics of the detector-field entanglement and the detector-detector entanglement, which distinguish from the results in the non-compact (1+1) dimensional Minkowski space. The beat patterns of entanglement dynamics in an untwisted and twisted fields with the same parameter values are different simply because of different spectrum of the eigen-modes. In terms of the physically measurable momentum of the detectors, we find that the contribution by the zero mode in a normal field to entanglement dynamics has no qualitative difference from those by the nonzero modes.

### Oscillons and oscillating kinks in the Abelian-Higgs model

We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear Schr\"{o}dinger equation for the gauge field, and a linear equation for the scalar field containing the gauge field as a nonlinear source. This equation is used to predict the existence of oscillons and oscillating kinks for certain regimes of the ratio of the Higgs to the gauge field masses. Results of numerical simulations are found to be in very good agreement with the analytical findings, and show that the oscillons are robust, while kinks are unstable. It is also demonstrated that oscillons emerge spontaneously as a result of the onset of the modulational instability of plane wave solutions of the model. Connections of the obtained solutions with the phenomenology of superconductors is discussed.

### Effects of local features of the inflaton potential on the spectrum and bispectrum of primordial perturbations

We study the effects of a class of features of the potential of slow-roll inflationary models corresponding to a step symmetrically dumped by an even power negative exponential factor. We compute the effects on the background evolution and on the scalar and tensor perturbations. This class of features differs from other branch-type features considered previously because the potential is only affected in a limited range of the scalar field value, and is symmetric respect to the location of the feature. As a consequence this type of features only affects the spectrum and bispectrum in a narrow range of scales which leave the horizon during the time interval corresponding to the modification of the potential, contrary to branch-type features which have effects on all the perturbation modes leaving the horizon when the field value is within the interval defining the branch. When the scalar field enters the range affected by the feature the slow-roll conditions are temporarily violated, but once the field leaves the interval affected by the feature the slow roll regime is re-established. The tensor-to-scalar ration, the spectrum and bispectrum of primordial curvature perturbations are affected by oscillations around the scale $k_0$ exiting the horizon at the time $\tau_0$ of the feature. The amplitude of the oscillations depends on the parameters defining the feature, and the effects are larger when the potential has a steeper change, since in this case the slow-roll violation is also stronger. Due to the local nature of their effects these type of features could be used to model local glitches of the power spectrum without affecting other scales.

### Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations [Replacement]

Spherically symmetric perturbations in AdS-scalar field systems of small amplitude epsilon approximately periodic on time scales of order 1/epsilon^2 (in the sense that no significant transfer of energy between the AdS normal modes occurs) have played an important role in considerations of AdS stability. They are seen as anchors of stability islands where collapse of small perturbations to black holes does not occur. (This collapse, if it happens, typically develops on time scales of the order 1/epsilon^2.) We construct an analytic treatment of the frequency spectra of such quasiperiodic perturbations, paying special attention to the large frequency asymptotics. For the case of a self-interacting phi^4 scalar field in a non-dynamical AdS background, we arrive at a fairly complete analytic picture involving quasiperiodic spectra with an exponential suppression modulated by a power law at large mode numbers. For the case of dynamical gravity, the structure of the large frequency asymptotics is more complicated. We give analytic explanations for the general qualitative features of quasiperiodic solutions localized around a single mode, in close parallel to our discussion of the probe scalar field, and find numerical evidence for logarithmic modulations in the gravitational quasiperiodic spectra existing on top of the formulas previously reported in the literature.

### Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations [Cross-Listing]

Spherically symmetric perturbations in AdS-scalar field systems of small amplitude epsilon approximately periodic on time scales of order 1/epsilon^2 (in the sense that no significant transfer of energy between the AdS normal modes occurs) have played an important role in considerations of AdS stability. They are seen as anchors of stability islands where collapse of small perturbations to black holes does not occur. (This collapse, if it happens, typically develops on time scales of the order 1/epsilon^2.) We construct an analytic treatment of the frequency spectra of such quasiperiodic perturbations, paying special attention to the large frequency asymptotics. For the case of a self-interacting phi^4 scalar field in a non-dynamical AdS background, we arrive at a fairly complete analytic picture involving quasiperiodic spectra with an exponential suppression modulated by a power law at large mode numbers. For the case of dynamical gravity, the structure of the large frequency asymptotics is more complicated. We give analytic explanations for the general qualitative features of quasiperiodic solutions localized around a single mode, in close parallel to our discussion of the probe scalar field, and find numerical evidence for logarithmic modulations in the gravitational quasiperiodic spectra existing on top of the formulas previously reported in the literature.

### Large N limit of supersymmetric Chern-Simons-matter model: breakdown of superconformal symmetry [Replacement]

In this work we study some properties of the three dimensional $U(N)$ SUSY Chern-Simons coupled to a scalar field in the fundamental representation in the large $N$ limit. For large $N$ we show that the theory has two phases, one which is conformally invariant, and other where the superconformal symmetry is broken and masses for the matter fields are generated.

### Large N limit of supersymmetric Chern-Simons-matter model: breakdown of superconformal symmetry

In this work we study some properties of the three dimensional $U(N)$ SUSY Chern-Simons coupled to a scalar field in the fundamental representation in the large $N$ limit. For large $N$ we show that the theory has two phases, one which is conformally invariant, and other where the superconformal symmetry is broken and masses for the matter fields are generated.

### Dark matter relic density in scalar-tensor gravity revisited

We revisit the calculation of dark matter relic abundances in scalar-tensor gravity using a generic form $A(\varphi_*) = e^{\beta\varphi_*^2/2}$ for the coupling between the scalar field $\varphi_*$ and the metric, for which detailed Big Bang Nucleosynthesis constraints are available. We find that BBN constraints restrict the modified expansion rate in these models to be almost degenerate with the standard expansion history at the time of dark matter decoupling. In this case the maximum level of enhancement of the dark matter relic density was found to be a factor of $\sim 3$, several orders of magnitude below that found in previous investigations.