# Posts Tagged scalar field

## Recent Postings from scalar field

### An exactly solvable inflationary model

We discuss a model of gravity coupled to a scalar field that admits exact cosmological solutions displaying an inflationary behavior at early times and a power-law expansion at late times.

### One-loop Modified Gravity in de Sitter Universe, Quantum Corrected Inflation, and its Confrontation with the Planck Result

Motivated by issues on inflation, a generalized modified gravity model is investigated, where the model Lagrangian is described by a smooth function $f(R, K, \phi)$ of the Ricci scalar $R$, the kinetic term $K$ of a scalar field $\phi$. In particular, the one-loop effective action in the de Sitter background is examined on-shell as well as off-shell in the Landau gauge. In addition, the on-shell quantum equivalence of $f(R)$ gravity in the Jordan and Einstein frames is explicitly demonstrated. Furthermore, we present applications related to the stability of the de Sitter solutions and the one-loop quantum correction to inflation in quantum-corrected $R^2$ gravity. It is shown that for a certain range of parameters, the spectral index of the curvature perturbations can be consistent with the Planck analysis, but the tensor-to-scalar ratio is smaller than the minimum value within the 1 $\sigma$ error range of the BICEP2 result.

### One-loop Modified Gravity in de Sitter Universe, Quantum Corrected Inflation, and its Confrontation with the Planck Result [Cross-Listing]

Motivated by issues on inflation, a generalized modified gravity model is investigated, where the model Lagrangian is described by a smooth function $f(R, K, \phi)$ of the Ricci scalar $R$, the kinetic term $K$ of a scalar field $\phi$. In particular, the one-loop effective action in the de Sitter background is examined on-shell as well as off-shell in the Landau gauge. In addition, the on-shell quantum equivalence of $f(R)$ gravity in the Jordan and Einstein frames is explicitly demonstrated. Furthermore, we present applications related to the stability of the de Sitter solutions and the one-loop quantum correction to inflation in quantum-corrected $R^2$ gravity. It is shown that for a certain range of parameters, the spectral index of the curvature perturbations can be consistent with the Planck analysis, but the tensor-to-scalar ratio is smaller than the minimum value within the 1 $\sigma$ error range of the BICEP2 result.

### One-loop Modified Gravity in de Sitter Universe, Quantum Corrected Inflation, and its Confrontation with the Planck Result [Cross-Listing]

Motivated by issues on inflation, a generalized modified gravity model is investigated, where the model Lagrangian is described by a smooth function $f(R, K, \phi)$ of the Ricci scalar $R$, the kinetic term $K$ of a scalar field $\phi$. In particular, the one-loop effective action in the de Sitter background is examined on-shell as well as off-shell in the Landau gauge. In addition, the on-shell quantum equivalence of $f(R)$ gravity in the Jordan and Einstein frames is explicitly demonstrated. Furthermore, we present applications related to the stability of the de Sitter solutions and the one-loop quantum correction to inflation in quantum-corrected $R^2$ gravity. It is shown that for a certain range of parameters, the spectral index of the curvature perturbations can be consistent with the Planck analysis, but the tensor-to-scalar ratio is smaller than the minimum value within the 1 $\sigma$ error range of the BICEP2 result.

### One-loop Modified Gravity in de Sitter Universe, Quantum Corrected Inflation, and its Confrontation with the Planck Result [Cross-Listing]

Motivated by issues on inflation, a generalized modified gravity model is investigated, where the model Lagrangian is described by a smooth function $f(R, K, \phi)$ of the Ricci scalar $R$, the kinetic term $K$ of a scalar field $\phi$. In particular, the one-loop effective action in the de Sitter background is examined on-shell as well as off-shell in the Landau gauge. In addition, the on-shell quantum equivalence of $f(R)$ gravity in the Jordan and Einstein frames is explicitly demonstrated. Furthermore, we present applications related to the stability of the de Sitter solutions and the one-loop quantum correction to inflation in quantum-corrected $R^2$ gravity. It is shown that for a certain range of parameters, the spectral index of the curvature perturbations can be consistent with the Planck analysis, but the tensor-to-scalar ratio is smaller than the minimum value within the 1 $\sigma$ error range of the BICEP2 result.

### Late-time cosmology of scalar-tensor theory with a universal coupling between the scalar field and the matter Lagrangian

We investigate the late-time cosmological behaviour of scalar-tensor theories with a universal multiplicative coupling between the scalar field and the matter Lagrangian in the matter era. This class of theory encompasses the case of the massless string dilaton (see Damour and Polyakov, General Relativity and Gravitation, 26, 1171) as well as a theory with an intrinsic decoupling mechanism in the solar system (see Minazzoli and Hees, Phys. Rev. D 88, 041504). The cosmological evolution is studied in the General Relativity limit justified by solar system constraints on the gravitation theory. The behaviour of these cosmological evolutions are then compared to two types of observations: the constraints on temporal variations of the constants of Nature and the distance-luminosity measurements. In particular, the non-minimal coupling implies that the distance-luminosity relation is modified compared to General Relativity. Theories producing a cosmological behaviour in agreement with these observations are identified.

### Dark Energy and Tachyon Field in Bianchi Type-V Space-time

In this paper, we consider Bianchi type-V space-time and study a cosmological model of dark energy based on Tachyon scalar field. We assumed three different kinds of matter without possibility of interaction with scalar dark energy. Assuming power law Hubble parameter in terms of scale factor we obtain evolution of scalar field, scalar potential and equation of state parameter.

### Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity [Replacement]

We present a turnkey solution, ready for implementation in numerical codes, for the study of linear structure formation in general scalar-tensor models involving a single universally coupled scalar field. We show that the totality of cosmological information on the gravitational sector can be compressed – without any redundancy – into five independent and arbitrary functions of time only and one constant. These describe physical properties of the universe: the observable background expansion history, fractional matter density today, and four functions of time describing the properties of the dark energy. We show that two of those dark-energy property functions control the existence of anisotropic stress, the other two – dark-energy clustering, both of which are can be scale-dependent. All these properties can in principle be measured, but no information on the underlying theory of acceleration beyond this can be obtained. We present a translation between popular models of late-time acceleration (e.g. perfect fluids, f (R), kinetic gravity braiding, galileons), as well as the effective field theory framework, and our formulation. In this way, implementing this formulation numerically would give a single tool which could consistently test the majority of models of late-time acceleration heretofore proposed.

### Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity [Cross-Listing]

We present a turnkey solution, ready for implementation in numerical codes, for the study of linear structure formation in general scalar-tensor models involving a single universally coupled scalar field. We show that the totality of cosmological information on the gravitational sector can be compressed – without any redundancy – into five independent and arbitrary functions of time only and one constant. These describe physical properties of the universe: the observable background expansion history, fractional matter density today, and four functions of time describing the properties of the dark energy. We show that two of those dark-energy property functions control the existence of anisotropic stress, the other two – dark-energy clustering, both of which are can be scale-dependent. All these properties can in principle be measured, but no information on the underlying theory of acceleration beyond this can be obtained. We present a translation between popular models of late-time acceleration (e.g. perfect fluids, f (R), kinetic gravity braiding, galileons), as well as the effective field theory framework, and our formulation. In this way, implementing this formulation numerically would give a single tool which could consistently test the majority of models of late-time acceleration heretofore proposed.

### Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity

We present a turnkey solution, ready for implementation in numerical codes, for the study of linear structure formation in general scalar-tensor models involving a single universally coupled scalar field. We show that the totality of cosmological information on the gravitational sector can be compressed – without any redundancy – into five independent and arbitrary functions of time only and one constant. These describe physical properties of the universe: the observable background expansion history, fractional matter density today, and four functions of time describing the properties of the dark energy. We show that two of those dark-energy property functions control the existence of anisotropic stress, the other two – dark-energy clustering, both of which are can be scale-dependent. All these properties can in principle be measured, but no information on the underlying theory of acceleration beyond this can be obtained. We present a translation between popular models of late-time acceleration (e.g. perfect fluids, f (R), kinetic gravity braiding, galileons), as well as the effective field theory framework, and our formulation. In this way, implementing this formulation numerically would give a single tool which could consistently test the majority of models of late-time acceleration heretofore proposed.

### Imaginary mass lens space determinants

Functional determinants for a single scalar field with negative mass squared are evaluated on homogeneous lens spaces. For example, on even order spaces, the Hartle–Hawking wave function oscillates about its zeros with increasing amplitude as the (imaginary) mass increases. I also present results for the binary tetrahedral, octahedral and icosahedral factors of the three–sphere. The final answer is given as a quadrature and some graphs are drawn. In the technical evaluation of the infinite sums, the explicit form of the degeneracies is not needed.

### Evolution of a dwarf satellite galaxy embedded in a scalar field dark matter halo

In the standard cold dark matter (CDM) model there are still two major unsolved issues, simulations predict that the number of satellites around the Milky Way is higher than the current observed population, additionally high resolution observations in dwarf galaxies show that central densities are more consistent with constant density profiles (core profiles) in disagreement with CDM simulations. An alternative explanation that has been widely discussed is that the dark matter is a scalar field of a small mass, this is known as the scalar field dark matter (SFDM) model. The model can potentially solve the overabundance issue and successfully fit the density distribution found in dwarf galaxies. In fact, one of the attractive features of the model is the prediction of core profiles for the dark halos. Thus, in this paper we conduct N-Body simulations to explore the influence of tidal forces over a stellar distribution embedded in a SFDM halo orbiting a SFDM host halo that has a baryonic disk possessing parameters similar to the Milky Way. We found that galaxies in halos with core profiles and high central densities can survive for 10 Gyrs similar to the CDM subhalos, the same happens for galaxies in low density halos that are far from the host disk interaction, whereas satellites in low density dark matter halos and with tight orbits can be fully stripped of stars and eventually be dissolved. Therefore, we conclude that core profiles and small initial masses could be an alternative solution to the missing satellite problem present in CDM simulations.

### Evolution of a dwarf satellite galaxy embedded in a scalar field dark matter halo [Cross-Listing]

In the standard cold dark matter (CDM) model there are still two major unsolved issues, simulations predict that the number of satellites around the Milky Way is higher than the current observed population, additionally high resolution observations in dwarf galaxies show that central densities are more consistent with constant density profiles (core profiles) in disagreement with CDM simulations. An alternative explanation that has been widely discussed is that the dark matter is a scalar field of a small mass, this is known as the scalar field dark matter (SFDM) model. The model can potentially solve the overabundance issue and successfully fit the density distribution found in dwarf galaxies. In fact, one of the attractive features of the model is the prediction of core profiles for the dark halos. Thus, in this paper we conduct N-Body simulations to explore the influence of tidal forces over a stellar distribution embedded in a SFDM halo orbiting a SFDM host halo that has a baryonic disk possessing parameters similar to the Milky Way. We found that galaxies in halos with core profiles and high central densities can survive for 10 Gyrs similar to the CDM subhalos, the same happens for galaxies in low density halos that are far from the host disk interaction, whereas satellites in low density dark matter halos and with tight orbits can be fully stripped of stars and eventually be dissolved. Therefore, we conclude that core profiles and small initial masses could be an alternative solution to the missing satellite problem present in CDM simulations.

### Investigation of Q-tubes stability using the piecewise parabolic potential [Cross-Listing]

We analyse the classical stability of Q-tubes – charged extended objects in (2+1)-dimensional theory of complex scalar field. Explicit solutions were found analytically in the piecewise parabolic potential. Our choice of potential allows to construct a powerful method of the stability investigation. We checked that in the case of the zero winding number $n=0$ the previously known stability condition $\partial^2E/\partial Q^2<0$ for Q-balls fulfils. However, in the case $n\geq 1$ we found continuous family of instabilities. Our result has an analogy with the theory of superconductivity of the second type, in which the vortex with $n\geq 1$ becomes unstable towards the decay into the $n$ vortices with the single winding number.

### Investigation of Q-tubes stability using the piecewise parabolic potential

We analyse the classical stability of Q-tubes – charged extended objects in (2+1)-dimensional theory of complex scalar field. Explicit solutions were found analytically in the piecewise parabolic potential. Our choice of potential allows to construct a powerful method of the stability investigation. We checked that in the case of the zero winding number $n=0$ the previously known stability condition $\partial^2E/\partial Q^2<0$ for Q-balls fulfils. However, in the case $n\geq 1$ we found continuous family of instabilities. Our result has an analogy with the theory of superconductivity of the second type, in which the vortex with $n\geq 1$ becomes unstable towards the decay into the $n$ vortices with the single winding number.

### Weyl-invariant SU(N) Einstein-Yang-Mills theory and related symmetry breaking mechanism

We construct a noncompact Weyl-Einstein-Yang-Mills model on a generic 4-dimensional scale-invariant curved background. Here the Weyl scalar field, that supplies the scale symmetry, is constructed from the modulus of the complex scalar field, which also brings on a Weyl-invariant extension of Higgs-type Inflation. The model has no dimensionful parameter, hence the vacuum expectation value (VEV) of the Higgs-type field is generated via spontaneous breaking of the noncompact Weyl non-Abelian gauge symmetry in (Anti)-de Sitter vacua. We obtain almost infinite values of VEV and mass of the Higgs-type field. To get a VEV in the order of GeV in analogy with the usual Higgs field, one needs to either tune the Newton constant, which inevitably causes gravity to drop dramatically into TeV scale, or to modify scale-invariant Higgs-type potential which does not require any change in gravity.

### Weyl-invariant SU(N) Einstein-Yang-Mills theory and spontaneous generation of vacuum expectation value for Higgs-type field [Replacement]

We construct a noncompact Weyl-Einstein-Yang-Mills model on a generic 4-dimensional curved background. Here the Weyl scalar field, that supplies scale symmetry, is constructed from modulus of the complex scalar field, which also brings on a Weyl-invariant extension of Higgs-type Inflation. The model has no dimensionful parameter, hence the vacuum expectation value (VEV) of the Higgs-type field is generated via spontaneous breaking of the noncompact Weyl non-Abelian gauge symmetry in (Anti)-de Sitter vacua. The obtained values for VEV and mass of the Higgs-type field are at the Planck-mass level. To get a VEV in the order of GeV in analogy with the usual Higgs field, one needs to either tune the Newton constant, which inevitably causes gravity to drop dramatically into TeV scale, or to modify scale-invariant Higgs-type potential which does not require any change in gravity.

### Weyl-invariant SU(N) Einstein-Yang-Mills theory and spontaneous generation of vacuum expectation value for Higgs-type field [Replacement]

We construct a noncompact Weyl-Einstein-Yang-Mills model on a generic 4-dimensional curved background. Here the Weyl scalar field, that supplies scale symmetry, is constructed from modulus of the complex scalar field, which also brings on a Weyl-invariant extension of Higgs-type Inflation. The model has no dimensionful parameter, hence the vacuum expectation value (VEV) of the Higgs-type field is generated via spontaneous breaking of the noncompact Weyl non-Abelian gauge symmetry in (Anti)-de Sitter vacua. The obtained values for VEV and mass of the Higgs-type field are at the Planck-mass level. To get a VEV in the order of GeV in analogy with the usual Higgs field, one needs to either tune the Newton constant, which inevitably causes gravity to drop dramatically into TeV scale, or to modify scale-invariant Higgs-type potential which does not require any change in gravity.

### Weyl-invariant SU(N) Einstein-Yang-Mills theory and related symmetry breaking mechanism [Cross-Listing]

We construct a noncompact Weyl-Einstein-Yang-Mills model on a generic 4-dimensional scale-invariant curved background. Here the Weyl scalar field, that supplies the scale symmetry, is constructed from the modulus of the complex scalar field, which also brings on a Weyl-invariant extension of Higgs-type Inflation. The model has no dimensionful parameter, hence the vacuum expectation value (VEV) of the Higgs-type field is generated via spontaneous breaking of the noncompact Weyl non-Abelian gauge symmetry in (Anti)-de Sitter vacua. We obtain almost infinite values of VEV and mass of the Higgs-type field. To get a VEV in the order of GeV in analogy with the usual Higgs field, one needs to either tune the Newton constant, which inevitably causes gravity to drop dramatically into TeV scale, or to modify scale-invariant Higgs-type potential which does not require any change in gravity.

### Brane structure and metastable graviton in five-dimensional model with (non)canonical scalar field

The appearance of inner brane structure is an interesting issue in domain wall {brane model}. Because such structure usually leads to quasilocalized modes of various kinds of bulk fields. In this paper, we construct a domain wall brane model by using a scalar field $\phi$, which couples to its kinetic term. The inner brane structure emerges as the scalar-kinetic coupling increases. With such brane structure, we show that it is possible to obtain gravity resonant modes in both tensor and scalar sectors. The number of the resonant modes depends on the vacuum expectation value of $\phi$ and the form of scalar-kinetic coupling. The correspondence between our model and the canonical one is also discussed. The noncanonical and canonical background scalar fields are connected by an integral equation, while the warp factor remains the same. Via this correspondence, the canonical and noncanonical models share the same linear perturbation spectrum. So the gravity resonances {obtained} in the noncanonical frame can also be obtained in the standard model. However, due to the inequivalence between the corresponding background scalar solutions, the localization condition for the left-chiral fermion zero mode can be largely different in different frames. Our estimate shows that the magnitude of the Yukawa coupling in the noncanonical frame might be hundreds times larger than the one in the canonical frame, if one demands the localization of the left-chiral fermion zero mode as well as the appearance of a few gravity resonance modes.

### Brane structure and metastable graviton in five-dimensional model with (non)canonical scalar field [Cross-Listing]

The appearance of inner brane structure is an interesting issue in domain wall {brane model}. Because such structure usually leads to quasilocalized modes of various kinds of bulk fields. In this paper, we construct a domain wall brane model by using a scalar field $\phi$, which couples to its kinetic term. The inner brane structure emerges as the scalar-kinetic coupling increases. With such brane structure, we show that it is possible to obtain gravity resonant modes in both tensor and scalar sectors. The number of the resonant modes depends on the vacuum expectation value of $\phi$ and the form of scalar-kinetic coupling. The correspondence between our model and the canonical one is also discussed. The noncanonical and canonical background scalar fields are connected by an integral equation, while the warp factor remains the same. Via this correspondence, the canonical and noncanonical models share the same linear perturbation spectrum. So the gravity resonances {obtained} in the noncanonical frame can also be obtained in the standard model. However, due to the inequivalence between the corresponding background scalar solutions, the localization condition for the left-chiral fermion zero mode can be largely different in different frames. Our estimate shows that the magnitude of the Yukawa coupling in the noncanonical frame might be hundreds times larger than the one in the canonical frame, if one demands the localization of the left-chiral fermion zero mode as well as the appearance of a few gravity resonance modes.

### Compact Structures in Standard Field Theory [Replacement]

We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential equations and illustrate how to find compact structures in models engendering standard kinematics. In particular, we study linear stability and show that all the static solutions we have found are linearly stable.

### Compact Structures in Standard Field Theory

We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential equations and illustrate how to find compact structures in models engendering standard kinematics. In particular, we study linear stability and show that all the static solutions we have found are linearly stable.

### Generalized Holographic Superconductors with Higher Derivative Couplings

We introduce and study generalized holographic superconductors with higher derivative couplings between the field strength tensor and a complex scalar field, in four dimensional AdS black hole backgrounds. We study this theory in the probe limit, as well as with backreaction. There are multiple tuning parameters in the theory, and with two non-zero parameters, we show that the theory has a rich phase structure, and in particular, the transition from the normal to the superconducting phase can be tuned to be of first order or of second order within a window of one of these. This is established numerically as well as by computing the free energy of the boundary theory. We further present analytical results for the critical temperature of the model, and compare these with numerical analysis. Optical properties of this system are also studied numerically in the probe limit, and our results show evidence for negative refraction at low frequencies.

### Quark-Hadron Phase Transition in DGP Brane Gravity with Bulk Scalar Field

A DGP brane-world framework is picked out to study quark-hadron phase transition problem. The model also includes a bulk scalar field in agreement with string theory prediction. The work is performed utilizing two formalisms as: smooth crossover approach and first order approach. General behavior of temperature is the same in these two approaches and it decrease by passing time and expanding Universe. Phase transition occurs at about micro-second after the big bang. The results show that transition time depends on brane tension value in which larger brane tension comes to earlier transition time.

### B mode polarization {\it \a la} BICEP2 and relic gravity waves produced during quintessential inflation [Cross-Listing]

We focus on general features of quintessential inflation which is an effort to unify inflation and dark energy using a single scalar field. These models essentially lead to relic gravity waves with blue spectrum. We describe a class of models of quintessential inflation which can give rise to the tensor to scalar ratio of perturbations consistent with recent measurement of B mode polarization spectrum. The scale of inflation in the model is around the GUT scale consistent with BICEP2 findings.

### B mode polarization {\it \a la} BICEP2 and relic gravity waves produced during quintessential inflation

We focus on general features of quintessential inflation which is an effort to unify inflation and dark energy using a single scalar field. These models essentially lead to relic gravity waves with blue spectrum. We describe a class of models of quintessential inflation which can give rise to the tensor to scalar ratio of perturbations consistent with recent measurement of B mode polarization spectrum. The scale of inflation in the model is around the GUT scale consistent with BICEP2 findings.

### Phase space analysis of the F (X) - V (\phi) scalar field Lagrangian and scaling solutions in flat cosmology [Cross-Listing]

We review a system of autonomous differential equations developed in our previous work [1] describing a flat cosmology filled with a barotropic fluid and a scalar field with a modified kinetic term of the form L=F(X)-V(phi). We analyze the critical points and summarize the conditions to obtain scaling solutions. We consider a set of transformations and show that they leave invariant the equations of motion for the systems in which the scaling solution is obtained, allowing to reduce the number of degrees of freedom.

### Phase space analysis of the F (X) - V (\phi) scalar field Lagrangian and scaling solutions in flat cosmology

We review a system of autonomous differential equations developed in our previous work [1] describing a flat cosmology filled with a barotropic fluid and a scalar field with a modified kinetic term of the form L=F(X)-V(phi). We analyze the critical points and summarize the conditions to obtain scaling solutions. We consider a set of transformations and show that they leave invariant the equations of motion for the systems in which the scaling solution is obtained, allowing to reduce the number of degrees of freedom.

### Black hole kinematics: the "in"-vacuum energy density and flux for different observers [Cross-Listing]

We have investigated the local invariant scalar observables – energy density and flux – which explicitly depend on the kinematics of the concerned observers in the Vaidya gravitational collapse geometry. The use of globally defined null coordinates allows for the definition of a unique in-vacuum for the scalar field propagating in this background. Computing the stress-energy tensor for this scalar field, we work out the energy density and flux for the static observers outside the horizon and then consider the radially in-falling observers who fall in from some specified initial radius all the way through the horizon and inside to the eventual singularity. Our results confirm the thermal Tolman-shifted energy density and fluxes for the static observers which diverge at the horizon. For the in-falling observer starting from far off, both the quantities — energy density and flux at the horizon crossing are \emph{regular and finite}. For example, the flux at the horizon for the in-falling observer from infinity is approximately 24 times the flux for the observer at infinity. Compared with the static observers in the near-horizon region, this is quite small. Both the quantities grow as the in-fall progresses inside the horizon and diverge at the singularity.

### Black hole kinematics: the "in"-vacuum energy density and flux for different observers

We have investigated the local invariant scalar observables – energy density and flux – which explicitly depend on the kinematics of the concerned observers in the Vaidya gravitational collapse geometry. The use of globally defined null coordinates allows for the definition of a unique in-vacuum for the scalar field propagating in this background. Computing the stress-energy tensor for this scalar field, we work out the energy density and flux for the static observers outside the horizon and then consider the radially in-falling observers who fall in from some specified initial radius all the way through the horizon and inside to the eventual singularity. Our results confirm the thermal Tolman-shifted energy density and fluxes for the static observers which diverge at the horizon. For the in-falling observer starting from far off, both the quantities — energy density and flux at the horizon crossing are \emph{regular and finite}. For example, the flux at the horizon for the in-falling observer from infinity is approximately 24 times the flux for the observer at infinity. Compared with the static observers in the near-horizon region, this is quite small. Both the quantities grow as the in-fall progresses inside the horizon and diverge at the singularity.

### A scenario for critical scalar field collapse in $AdS_3$

We present a family of exact solutions, depending on two parameters $\alpha$ and $b$ (related to the scalar field strength), to the three-dimensional Einstein-scalar field equations with negative cosmological constant $\Lambda$. For $b=0$ these solutions reduce to the static BTZ family of vacuum solutions, with mass $M = -\alpha$. For $b\neq0$, the solutions become dynamical and develop a strong spacelike central singularity. The $\alpha<0$ solutions are black-hole like, with a global structure topologically similar to that of the BTZ black holes, and a finite effective mass. We show that the near-singularity behavior of the solutions with $\alpha>0$ agrees qualitatively with that observed in numerical simulations of subcritical collapse. We analyze the linear perturbations of the threshold solution, $\alpha=0$, in the $\Lambda=0$ approximation, and find that it has only one unstable growing mode, which qualifies it as a candidate critical solution for scalar field collapse.

### A scenario for critical scalar field collapse in $AdS_3$ [Cross-Listing]

We present a family of exact solutions, depending on two parameters $\alpha$ and $b$ (related to the scalar field strength), to the three-dimensional Einstein-scalar field equations with negative cosmological constant $\Lambda$. For $b=0$ these solutions reduce to the static BTZ family of vacuum solutions, with mass $M = -\alpha$. For $b\neq0$, the solutions become dynamical and develop a strong spacelike central singularity. The $\alpha<0$ solutions are black-hole like, with a global structure topologically similar to that of the BTZ black holes, and a finite effective mass. We show that the near-singularity behavior of the solutions with $\alpha>0$ agrees qualitatively with that observed in numerical simulations of subcritical collapse. We analyze the linear perturbations of the threshold solution, $\alpha=0$, in the $\Lambda=0$ approximation, and find that it has only one unstable growing mode, which qualifies it as a candidate critical solution for scalar field collapse.

### Production of non-gaussianities in a bouncing phase

We compute the level of non-gaussianities produced by a cosmological bouncing phase in the minimal non-singular setup that lies within the context of General Relativity when the matter content consists of a simple scalar field with a standard kinetic term. Such a bouncing phase is obtained by requiring that the spatial sections of the background spacetime be positively curved. We restrict attention to the close vicinity of the bounce by Taylor expanding the scale factor, the scalar field and its potential in powers of the conformal time around the bounce. We find that possibly large non-gaussianities are generically produced at the bounce itself and also discuss which shapes of non-gaussianities are mostly likely to be produced.

### Production of non-gaussianities in a bouncing phase [Cross-Listing]

We compute the level of non-gaussianities produced by a cosmological bouncing phase in the minimal non-singular setup that lies within the context of General Relativity when the matter content consists of a simple scalar field with a standard kinetic term. Such a bouncing phase is obtained by requiring that the spatial sections of the background spacetime be positively curved. We restrict attention to the close vicinity of the bounce by Taylor expanding the scale factor, the scalar field and its potential in powers of the conformal time around the bounce. We find that possibly large non-gaussianities are generically produced at the bounce itself and also discuss which shapes of non-gaussianities are mostly likely to be produced.

### Production of non-gaussianities in a bouncing phase [Cross-Listing]

We compute the level of non-gaussianities produced by a cosmological bouncing phase in the minimal non-singular setup that lies within the context of General Relativity when the matter content consists of a simple scalar field with a standard kinetic term. Such a bouncing phase is obtained by requiring that the spatial sections of the background spacetime be positively curved. We restrict attention to the close vicinity of the bounce by Taylor expanding the scale factor, the scalar field and its potential in powers of the conformal time around the bounce. We find that possibly large non-gaussianities are generically produced at the bounce itself and also discuss which shapes of non-gaussianities are mostly likely to be produced.

### Higgs mass in Noncommutative Geometry [Replacement]

In the noncommutative geometry approach to the standard model, an extra scalar field – initially suggested by particle physicist to stabilize the electroweak vacuum – makes the computation of the Higgs mass compatible with the 126 GeV experimental value. We give a brief account on how to generate this field from the Majorana mass of the neutrino, following the principles of noncommutative geometry.

### Higgs mass in Noncommutative Geometry

In the noncommutative geometry approach to the standard model, an extra scalar field – initially suggested by particle physicist to stabilize the electroweak vacuum – makes the computation of the Higgs mass compatible with the 126 GeV experimental value. We give a brief account on how to generate this field from the Majorana mass of the neutrino, following the principles of noncommutative geometry.

### Higgs mass in Noncommutative Geometry [Replacement]

In the noncommutative geometry approach to the standard model, an extra scalar field – initially suggested by particle physicist to stabilize the electroweak vacuum – makes the computation of the Higgs mass compatible with the 126 GeV experimental value. We give a brief account on how to generate this field from the Majorana mass of the neutrino, following the principles of noncommutative geometry.

### Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2 [Replacement]

The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential \propto \phi^n: n \simeq 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R + R^2 model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N=1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focussing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

### Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2 [Replacement]

The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential \propto \phi^n: n \simeq 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R + R^2 model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N=1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focussing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

### Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2 [Replacement]

The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential \propto \phi^n: n \simeq 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R + R^2 model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N=1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focussing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

### Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2 [Replacement]

The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential \propto \phi^n: n \simeq 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R + R^2 model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N=1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focussing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

### Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2 [Cross-Listing]

The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential \propto \phi^n: n \simeq 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R + R^2 model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N=1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focussing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

### Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2 [Cross-Listing]

The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential \propto \phi^n: n \simeq 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R + R^2 model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N=1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focussing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

### Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2

The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential \propto \phi^n: n \simeq 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R + R^2 model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N=1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focussing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

### Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2 [Cross-Listing]

The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential \propto \phi^n: n \simeq 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R + R^2 model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N=1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focussing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

### Superradiant instability of the charged scalar field in stringy black hole mirror system

It has been shown that the mass of the scalar field in the charged stringy black hole is never able to generate a potential well outside the event horizon to trap the superradiant modes. This is to say that the charged stringy black hole is stable against the massive charged scalar perturbation. In this paper we will study the superradiant instability of the massless scalar field in the background of charged stringy black hole due to a mirror-like boundary condition. The analytical expression of the unstable superradiant modes is derived by using the asymptotic matching method. It is also pointed out that the black hole mirror system becomes extremely unstable for a large charge $q$ of scalar field and the small mirror radius $r_m$.

### Stable static structures in models with galileon-like dynamics [Replacement]

We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space-time. We study models in which the scalar field engenders galileon-like dynamics and spontaneous symmetry breaking, inducing the presence of domain walls. The galileon-like behavior keeps to equation of motion second-order differential equation, so we focus on the presence of first-order equation that solves the equation of motion and very much help us to investigate stability on general grounds. We then illustrate the investigation with some specific examples, showing that the domain wall may become compact and that the zero mode may split. Moreover, if the model is further generalized to include k-field behavior, it may contribute to split the static structure.

### Stable static structures in models with galileon-like dynamics

We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space-time. We study models in which the scalar field engenders galileon-like dynamics and spontaneous symmetry breaking, inducing the presence of domain walls. The galileon-like behavior keeps to equation of motion second-order differential equation, so we focus on the presence of first-order equation that solves the equation of motion and very much help us to investigate stability on general grounds. We then illustrate the investigation with some specific examples, showing that the domain wall may become compact and that the zero mode may split. Moreover, if the model is further generalized to include k-field behavior, it may contribute to split the static structure.