# Posts Tagged scalar field

## Recent Postings from scalar field

### Black holes in a cubic Galileon universe

We find and study the properties of black hole solutions for a subclass of Horndeski theory including the cubic Galileon term. The theory under study has shift symmetry but not reflection symmetry for the scalar field. The Galileon is assumed to have linear time dependence characterized by a velocity parameter. We give analytic 3-dimensional solutions that are akin to the BTZ solutions but with a non-trivial scalar field that modifies the effective cosmological constant. We then study the 4-dimensional asymptotically flat and de Sitter solutions. The latter present three different branches according to their effective cosmological constant. For two of these branches, we find families of black hole solutions, parametrized by the velocity of the scalar field. These spherically symmetric solutions, obtained numerically, are different from GR solutions close to the black hole event horizon, while they have the same de-Sitter asymptotic behavior. The velocity parameter represents black hole primary hair.

### Shear Viscosity to Entropy Density Ratio in Higher Derivative Gravity with Momentum Dissipation

Recently, it has been suggested that there is a new bound for the shear viscosity to entropy density ratio that reads $\eta/s\gtrsim (T/\Delta)^2$ as $T/\Delta\to 0$, where $\Delta$ is a scale present in the zero temperature IR theory. In this paper, we investigate $\eta/s$ in linear scalar fields modified Gauss-Bonnet theory that breaks translation invariance. We first calculate $\eta/s$ both analytically and numerically and show its relationship with temperature in log-log plot. Our results are in good agreement with the new viscosity bound above. The causality is also considered in this work. We then find that there will be no causality violation if the linear scalar field is added and hence the constraint for the Gauss-Bonnet coupling $\lambda$ vanishes.

### Boson Stars in a Theory of Complex Scalar Fields coupled to $U(1)$ Gauge Field and Gravity [Cross-Listing]

We study boson shells and boson stars in a theory of complex scalar field coupled to the $U(1)$ gauge field $A_{\mu}$ and Einstein gravity with the potential: $V(|\Phi|) := \frac{1}{2} m^{2} \left(|\Phi|+ a \right)^2$. This could be considered either as a theory of massive complex scalar field coupled to electromagnetic field and gravity in a conical potential or as a theory in the presence of a potential which is an overlap of a parabolic and a conical potential. Our theory has a positive cosmological constant $(\Lambda := 4 \pi G m^2 a^2)$. Boson stars are found to come in two types, having either ball-like or shell-like charge density. We have studied the properties of these solutions and have also determined their domains of existence for some specific values of the parameters of the theory. Similar solutions have also been obtained by Kleihaus, Kunz, Laemmerzahl and List, in a V-shaped scalar potential.

### Boson Stars in a Theory of Complex Scalar Fields coupled to $U(1)$ Gauge Field and Gravity

We study boson shells and boson stars in a theory of complex scalar field coupled to the $U(1)$ gauge field $A_{\mu}$ and Einstein gravity with the potential: $V(|\Phi|) := \frac{1}{2} m^{2} \left(|\Phi|+ a \right)^2$. This could be considered either as a theory of massive complex scalar field coupled to electromagnetic field and gravity in a conical potential or as a theory in the presence of a potential which is an overlap of a parabolic and a conical potential. Our theory has a positive cosmological constant $(\Lambda := 4 \pi G m^2 a^2)$. Boson stars are found to come in two types, having either ball-like or shell-like charge density. We have studied the properties of these solutions and have also determined their domains of existence for some specific values of the parameters of the theory. Similar solutions have also been obtained by Kleihaus, Kunz, Laemmerzahl and List, in a V-shaped scalar potential.

### Invariant slow-roll parameters in scalar-tensor theories

A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan frames using quantities that are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field. By comparing spectral indices, calculated up to second order, we find that the frames are equivalent up to this order, due to the underlying assumptions.

### Boson Stars in a Theory of Complex Scalar Field coupled to Gravity

We study boson stars in a theory of complex scalar field coupled to Einstein gravity with the potential: $V(|\Phi|) := m^{2} |\Phi|^2 +2 \lambda |\Phi|$ (where $m^2$ and $\lambda$ are positive constant parameters). This could be considered either as a theory of massive complex scalar field coupled to gravity in a conical potential or as a theory in the presence of a potential which is an overlap of a parabolic and a conical potential. We study our theory with positive as well as negative values of the cosmological constant $\Lambda$. Boson stars are found to come in two types, having either ball-like or shell-like charge density. We have studied the properties of these solutions and have also determined their domains of existence for some specific values of the parameters of the theory. Similar solutions have also been obtained by Hartmann, Kleihaus, Kunz, and Schaffer, in a V-shaped scalar potential.

### Boson Stars in a Theory of Complex Scalar Field coupled to Gravity [Cross-Listing]

We study boson stars in a theory of complex scalar field coupled to Einstein gravity with the potential: $V(|\Phi|) := m^{2} |\Phi|^2 +2 \lambda |\Phi|$ (where $m^2$ and $\lambda$ are positive constant parameters). This could be considered either as a theory of massive complex scalar field coupled to gravity in a conical potential or as a theory in the presence of a potential which is an overlap of a parabolic and a conical potential. We study our theory with positive as well as negative values of the cosmological constant $\Lambda$. Boson stars are found to come in two types, having either ball-like or shell-like charge density. We have studied the properties of these solutions and have also determined their domains of existence for some specific values of the parameters of the theory. Similar solutions have also been obtained by Hartmann, Kleihaus, Kunz, and Schaffer, in a V-shaped scalar potential.

### Non-local form factors for curved-space antisymmetric fields

In the recent paper Buchbinder, Kirillova and Pletnev presented formal arguments concerning quantum equivalence of free massive antisymmetric tensor fields of second and third rank to the free Proca theory and massive scalar field with minimal coupling to gravity, respectively. We confirm this result using explicit covariant calculations of non-local form factors based on the heart-kernel technique, and discuss the discontinuity of quantum contributions in the massless limit.

### Collapsing objects with the same gravitational trajectory can radiate away different amount of energy [Cross-Listing]

We study radiation emitted during the gravitational collapse from two different types of shells. We assume that one shell is made of dark matter and is completely transparent to the test scalar (for simplicity) field which belongs to the standard model, while the other shell is made of the standard model particles and is totally reflecting to the scalar field. These two shells have exactly the same mass, charge and angular momentum (though we set the charge and angular momentum to zero), and therefore follow the same geodesic trajectory. However, we demonstrate that they radiate away different amount of energy during the collapse. This difference can in principle be used by an asymptotic observer to reconstruct the physical properties of the initial collapsing object other than mass, charge and angular momentum. This result has implications for the information paradox and expands the list of the type of information which can be released from a collapsing object.

### Collapsing objects with the same gravitational trajectory can radiate away different amount of energy [Cross-Listing]

We study radiation emitted during the gravitational collapse from two different types of shells. We assume that one shell is made of dark matter and is completely transparent to the test scalar (for simplicity) field which belongs to the standard model, while the other shell is made of the standard model particles and is totally reflecting to the scalar field. These two shells have exactly the same mass, charge and angular momentum (though we set the charge and angular momentum to zero), and therefore follow the same geodesic trajectory. However, we demonstrate that they radiate away different amount of energy during the collapse. This difference can in principle be used by an asymptotic observer to reconstruct the physical properties of the initial collapsing object other than mass, charge and angular momentum. This result has implications for the information paradox and expands the list of the type of information which can be released from a collapsing object.

### Collapsing objects with the same gravitational trajectory can radiate away different amount of energy

We study radiation emitted during the gravitational collapse from two different types of shells. We assume that one shell is made of dark matter and is completely transparent to the test scalar (for simplicity) field which belongs to the standard model, while the other shell is made of the standard model particles and is totally reflecting to the scalar field. These two shells have exactly the same mass, charge and angular momentum (though we set the charge and angular momentum to zero), and therefore follow the same geodesic trajectory. However, we demonstrate that they radiate away different amount of energy during the collapse. This difference can in principle be used by an asymptotic observer to reconstruct the physical properties of the initial collapsing object other than mass, charge and angular momentum. This result has implications for the information paradox and expands the list of the type of information which can be released from a collapsing object.

### A Study on the Expanding Universe Based on a Model of the Time Variation of its Matter Content in the Framework of Brans-Dicke Theory

A theoretical model of cosmic expansion has been formulated on an assumption of inter-conversion of matter and dark energy, in the framework of Brans-Dicke theory. An empirical scale factor has been used, which generates a signature flip of the deceleration parameter with time. To account for the non-conservation of matter, a function of time f(t) is incorporated into the equation representing the density of matter. Its value at any instant of time is proportional to the matter content of the universe. The functional form of f(t) has been determined from the field equations by using an empirical scalar field parameter expressed in terms of the scale factor. It is found to decrease with time almost monotonically, implying a conversion of matter into dark energy. Using this function f(t), the time variation of the density of matter has been determined and also the expressions regarding the proportions of matter and dark energy of the universe have been formulated. Time variation of gravitational constant, its fractional rate of change and the Brans-Dicke dimensionless parameter has been analyzed. The dependence of Brans-Dicke parameter upon the scalar field has been determined. The present study enables us to correlate the change of matter content with the change of deceleration parameter and gravitational constant without using any specific mechanism of interaction between matter and scalar field.

### Primordial fluctuations from inflation in dRGT bimetric theory of gravity [Cross-Listing]

We investigate primordial gravitational waves and curvature perturbations in de Rham-Gabadadze-Tolley (dRGT) bimetric gravity. We evaluate the power-spectra in the leading order in slow roll. Taking into account the decay of massive graviton, we find that the action up to the second order reduces to the Einstein theory with a non-minimally coupled scalar field, which is simplified to a minimally coupled model by conformal transformation. We also find that the tensor to scalar ratio for large field inflation with power law potential is larger than the general relativity counterpart for any choice of parameters in dRGT bimetric gravity. In addition, we confirm that the usual consistency relation holds and we have a steeper spectrum for the gravitational waves.

### Primordial fluctuations from inflation in dRGT bimetric theory of gravity

We investigate primordial gravitational waves and curvature perturbations in de Rham-Gabadadze-Tolley (dRGT) bimetric gravity. We evaluate the power-spectra in the leading order in slow roll. Taking into account the decay of massive graviton, we find that the action up to the second order reduces to the Einstein theory with a non-minimally coupled scalar field, which is simplified to a minimally coupled model by conformal transformation. We also find that the tensor to scalar ratio for large field inflation with power law potential is larger than the general relativity counterpart for any choice of parameters in dRGT bimetric gravity. In addition, we confirm that the usual consistency relation holds and we have a steeper spectrum for the gravitational waves.

### Primordial fluctuations from inflation in dRGT bimetric theory of gravity [Cross-Listing]

We investigate primordial gravitational waves and curvature perturbations in de Rham-Gabadadze-Tolley (dRGT) bimetric gravity. We evaluate the power-spectra in the leading order in slow roll. Taking into account the decay of massive graviton, we find that the action up to the second order reduces to the Einstein theory with a non-minimally coupled scalar field, which is simplified to a minimally coupled model by conformal transformation. We also find that the tensor to scalar ratio for large field inflation with power law potential is larger than the general relativity counterpart for any choice of parameters in dRGT bimetric gravity. In addition, we confirm that the usual consistency relation holds and we have a steeper spectrum for the gravitational waves.

### The scalar-scalar-tensor inflationary three-point function in the axion monodromy model

The axion monodromy model involves a canonical scalar field that is governed by a linear potential with superimposed modulations. The modulations in the potential are responsible for a resonant behavior which gives rise to persisting oscillations in the scalar and, to a smaller extent, in the tensor power spectra. Interestingly, such spectra have been shown to lead to an improved fit to the cosmological data than the more conventional, nearly scale invariant, primordial power spectra. The scalar bi-spectrum in the model too exhibits continued modulations and the resonance is known to boost the amplitude of the scalar non-Gaussianity parameter to rather large values. An analytical expression for the scalar bi-spectrum had been arrived at earlier which, in fact, has been used to compare the model with the cosmic microwave background anisotropies at the level of three-point functions involving scalars. In this work, with future applications in mind, we arrive at a similar analytical template for the scalar-scalar-tensor cross-correlation. We also analytically establish the consistency relation (in the squeezed limit) for this three-point function. We conclude with a summary of the main results obtained.

### The scalar-scalar-tensor inflationary three-point function in the axion monodromy model [Cross-Listing]

The axion monodromy model involves a canonical scalar field that is governed by a linear potential with superimposed modulations. The modulations in the potential are responsible for a resonant behavior which gives rise to persisting oscillations in the scalar and, to a smaller extent, in the tensor power spectra. Interestingly, such spectra have been shown to lead to an improved fit to the cosmological data than the more conventional, nearly scale invariant, primordial power spectra. The scalar bi-spectrum in the model too exhibits continued modulations and the resonance is known to boost the amplitude of the scalar non-Gaussianity parameter to rather large values. An analytical expression for the scalar bi-spectrum had been arrived at earlier which, in fact, has been used to compare the model with the cosmic microwave background anisotropies at the level of three-point functions involving scalars. In this work, with future applications in mind, we arrive at a similar analytical template for the scalar-scalar-tensor cross-correlation. We also analytically establish the consistency relation (in the squeezed limit) for this three-point function. We conclude with a summary of the main results obtained.

### The scalar-scalar-tensor inflationary three-point function in the axion monodromy model [Cross-Listing]

The axion monodromy model involves a canonical scalar field that is governed by a linear potential with superimposed modulations. The modulations in the potential are responsible for a resonant behavior which gives rise to persisting oscillations in the scalar and, to a smaller extent, in the tensor power spectra. Interestingly, such spectra have been shown to lead to an improved fit to the cosmological data than the more conventional, nearly scale invariant, primordial power spectra. The scalar bi-spectrum in the model too exhibits continued modulations and the resonance is known to boost the amplitude of the scalar non-Gaussianity parameter to rather large values. An analytical expression for the scalar bi-spectrum had been arrived at earlier which, in fact, has been used to compare the model with the cosmic microwave background anisotropies at the level of three-point functions involving scalars. In this work, with future applications in mind, we arrive at a similar analytical template for the scalar-scalar-tensor cross-correlation. We also analytically establish the consistency relation (in the squeezed limit) for this three-point function. We conclude with a summary of the main results obtained.

### Diphoton resonance confronts dark matter [Replacement]

As an interpretation of the 750 GeV diphoton excesses recently reported by both ATLAS and CMS collaborations, we consider a simple extension of the Standard Model with a Dirac fermion dark matter where a singlet complex scalar field mediates between dark matter and SM particles via effective couplings to SM gauge bosons and/or Higgs-portal. In this model, we can accommodate the diphoton events through the direct and/or cascade decays of pseudo-scalar and real scalar partners of the complex scalar field. We show that mono-jet searches and gamma-ray observations are complementary in constraining the region where the width of the diphoton resonance can be enhanced due to the couplings of the resonance to dark matter and the correct relic density is obtained. In the case of cascade decay of the resonance, the effective couplings of singlet scalars can be smaller, but the model is still testable by the future discrimination between single photon and photon-jet at the LHC as well as the gamma-ray searches for the cascade annihilation of dark matter.

### Diphoton resonance confronts dark matter

As an interpretation of the 750 GeV diphoton excesses recently reported by both ATLAS and CMS collaborations, we consider a simple extension of the Standard Model with a Dirac fermion dark matter where a singlet complex scalar field mediates between dark matter and SM particles via effective couplings to SM gauge bosons and/or Higgs-portal. In this model, we can accommodate the diphoton events through the direct and/or cascade decays of pseudo-scalar and real scalar partners of the complex scalar field. We show that mono-jet searches and gamma-ray observations are complementary in constraining the region where the width of the diphoton resonance can be enhanced due to the couplings of the resonance to dark matter and the correct relic density is obtained. In the case of cascade decay of the resonance, the effective couplings of singlet scalars can be smaller, but the model is still testable by the future discrimination between single photon and photon-jet at the LHC as well as the gamma-ray searches for the cascade annihilation of dark matter.

### A fresh view of cosmological models describing very early Universe: general solution of the dynamical equations

The dynamics of any spherical cosmology with a scalar field (scalaron') coupling to gravity is described by the nonlinear second-order differential equations for two metric functions and the scalaron depending on the time' parameter. The equations depend on the scalaron potential and on arbitrary gauge function that describes time parameterizations. This dynamical system can be integrated for flat, isotropic models with very special potentials. But, somewhat unexpectedly, replacing the independent variable $t$ by one of the metric functions allows us to completely integrate the general spherical theory in any gauge and with arbitrary potentials. In this approach, inflationary solutions can be easily identified, explicitly derived, and compared to the standard approximate expressions. This approach is also applicable to intrinsically anisotropic models with a massive vector field (vecton') as well as to some non-inflationary models.

### A fresh view of cosmological models describing very early Universe: general solution of the dynamical equations [Cross-Listing]

The dynamics of any spherical cosmology with a scalar field (scalaron') coupling to gravity is described by the nonlinear second-order differential equations for two metric functions and the scalaron depending on the time' parameter. The equations depend on the scalaron potential and on arbitrary gauge function that describes time parameterizations. This dynamical system can be integrated for flat, isotropic models with very special potentials. But, somewhat unexpectedly, replacing the independent variable $t$ by one of the metric functions allows us to completely integrate the general spherical theory in any gauge and with arbitrary potentials. In this approach, inflationary solutions can be easily identified, explicitly derived, and compared to the standard approximate expressions. This approach is also applicable to intrinsically anisotropic models with a massive vector field (vecton') as well as to some non-inflationary models.

### Geometry of the Scalar Sector

The $S$-matrix of a quantum field theory is unchanged by field redefinitions, and so only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold ${\mathcal M}$ is flat. We explicitly compute the one-loop correction to scalar scattering in the SM written in non-linear Callan-Coleman-Wess-Zumino (CCWZ) form, where it has an infinite series of higher dimensional operators, and show that the $S$-matrix is finite. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved ${\mathcal M}$, since they parametrize deviations from the flat SM case. We show that the HEFT Lagrangian can be written in SMEFT form if and only if ${\cal M}$ has a $SU(2)_L \times U(1)_Y$ invariant fixed point. Experimental observables in HEFT depend on local geometric invariants of ${\mathcal M}$ such as sectional curvatures, which are of order $1/\Lambda^2$, where $\Lambda$ is the EFT scale. We give explicit expressions for these quantities in terms of the structure constants for a general $\mathcal G \to \mathcal H$ symmetry breaking pattern. (Full abstract in pdf)

### Vacuum Cherenkov radiation and bremsstrahlung from disformal couplings [Cross-Listing]

The simplest way to modify gravity is to extend the gravitational sector to include an additional scalar degree of freedom. The most general metric that can be built in such a theory includes disformal terms, so that standard model fields move on a metric which is the sum of the space time metric and a tensor constructed from first derivatives of the scalar. In such a theory gravitational waves and photons can propagate at different speeds, and these can in turn be different from the maximum speed limit for matter particles. In this work we show that disformal couplings can cause charged particles to emit Cherenkov radiation and bremsstrahlung apparently in vacuum, depending on the background evolution of the scalar field. We discuss the implications of this for observations of cosmic rays, and the constraints that arise for models of dark energy with disformal couplings.

### Vacuum Cherenkov radiation and bremsstrahlung from disformal couplings [Cross-Listing]

The simplest way to modify gravity is to extend the gravitational sector to include an additional scalar degree of freedom. The most general metric that can be built in such a theory includes disformal terms, so that standard model fields move on a metric which is the sum of the space time metric and a tensor constructed from first derivatives of the scalar. In such a theory gravitational waves and photons can propagate at different speeds, and these can in turn be different from the maximum speed limit for matter particles. In this work we show that disformal couplings can cause charged particles to emit Cherenkov radiation and bremsstrahlung apparently in vacuum, depending on the background evolution of the scalar field. We discuss the implications of this for observations of cosmic rays, and the constraints that arise for models of dark energy with disformal couplings.

### Vacuum Cherenkov radiation and bremsstrahlung from disformal couplings [Cross-Listing]

The simplest way to modify gravity is to extend the gravitational sector to include an additional scalar degree of freedom. The most general metric that can be built in such a theory includes disformal terms, so that standard model fields move on a metric which is the sum of the space time metric and a tensor constructed from first derivatives of the scalar. In such a theory gravitational waves and photons can propagate at different speeds, and these can in turn be different from the maximum speed limit for matter particles. In this work we show that disformal couplings can cause charged particles to emit Cherenkov radiation and bremsstrahlung apparently in vacuum, depending on the background evolution of the scalar field. We discuss the implications of this for observations of cosmic rays, and the constraints that arise for models of dark energy with disformal couplings.

### Vacuum Cherenkov radiation and bremsstrahlung from disformal couplings

The simplest way to modify gravity is to extend the gravitational sector to include an additional scalar degree of freedom. The most general metric that can be built in such a theory includes disformal terms, so that standard model fields move on a metric which is the sum of the space time metric and a tensor constructed from first derivatives of the scalar. In such a theory gravitational waves and photons can propagate at different speeds, and these can in turn be different from the maximum speed limit for matter particles. In this work we show that disformal couplings can cause charged particles to emit Cherenkov radiation and bremsstrahlung apparently in vacuum, depending on the background evolution of the scalar field. We discuss the implications of this for observations of cosmic rays, and the constraints that arise for models of dark energy with disformal couplings.

### $K$-essence model from the mechanical approach point of view: coupled scalar field and the late cosmic acceleration

In this paper, we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, we can consider the Universe to be filled with dust-like matter in the form of discretely distributed galaxies, a $K$-essence scalar field, playing the role of dark energy, and radiation as matter sources. We investigate such a Universe in the mechanical approach. This means that the peculiar velocities of the inhomogeneities (in the form of galaxies) as well as the fluctuations of the other perfect fluids are non-relativistic. Such fluids are designated as coupled because they are concentrated around the inhomogeneities. In the present paper, we investigate the conditions under which the $K$-essence scalar field with the most general form for its action can become coupled. We investigate at the background level three particular examples of the $K$-essence models: (i) the pure kinetic $K$-essence field, (ii) a $K$-essence with a constant speed of sound and (iii) the $K$-essence model with the Lagrangian $bX+cX^2-V(\phi)$. We demonstrate that if the $K$-essence is coupled, all these $K$-essence models take the form of multicomponent perfect fluids where one of the component is the cosmological constant. Therefore, they can provide the late-time cosmic acceleration and be simultaneously compatible with the mechanical approach.

### Ultra-local models of modified gravity without kinetic term [Cross-Listing]

We present a class of modified-gravity theories which we call ultra-local models. We add a scalar field, with negligible kinetic terms, to the Einstein-Hilbert action. We also introduce a conformal coupling to matter. This gives rise to a new screening mechanism which is not entirely due to the non-linearity of the scalar field potential or the coupling function but to the absence of the kinetic term. As a result this removes any fifth force between isolated objects in vacuum. The predictions of these models only depend on a single free function, as the potential and the coupling function are degenerate, with an amplitude given by a parameter $\alpha \lesssim 10^{-6}$, whose magnitude springs from requiring a small modification of Newton's potential astrophysically and cosmologically. This singles out a redshift $z_{\alpha} \sim \alpha^{-1/3} \gtrsim 100$ where the fifth force is the greatest. The cosmological background follows the $\Lambda$-CDM history within a $10^{-6}$ accuracy, while cosmological perturbations are significantly enhanced (or damped) on small scales, $k \gtrsim 2 h {\rm Mpc}^{-1}$ at $z=0$. The spherical collapse and the halo mass function are modified in the same manner. We find that the modifications of gravity are greater for galactic or sub-galactic structures. We also present a thermodynamic analysis of the non-linear and inhomogeneous fifth-force regime where we find that the Universe is not made more inhomogeneous before $z_\alpha$ when the fifth force dominates, and does not lead to the existence of clumped matter on extra small scales inside halos for large masses while this possibility exists for masses $M\lesssim 10^{11} M_\odot$ where the phenomenology of ultra-local models would be most different from $\Lambda$-CDM.

### Ultra-local models of modified gravity without kinetic term [Replacement]

We present a class of modified-gravity theories which we call ultra-local models. We add a scalar field, with negligible kinetic terms, to the Einstein-Hilbert action. We also introduce a conformal coupling to matter. This gives rise to a new screening mechanism which is not entirely due to the non-linearity of the scalar field potential or the coupling function but to the absence of the kinetic term. As a result this removes any fifth force between isolated objects in vacuum. The predictions of these models only depend on a single free function, as the potential and the coupling function are degenerate, with an amplitude given by a parameter $\alpha \lesssim 10^{-6}$, whose magnitude springs from requiring a small modification of Newton's potential astrophysically and cosmologically. This singles out a redshift $z_{\alpha} \sim \alpha^{-1/3} \gtrsim 100$ where the fifth force is the greatest. The cosmological background follows the $\Lambda$-CDM history within a $10^{-6}$ accuracy, while cosmological perturbations are significantly enhanced (or damped) on small scales, $k \gtrsim 2 h {\rm Mpc}^{-1}$ at $z=0$. The spherical collapse and the halo mass function are modified in the same manner. We find that the modifications of gravity are greater for galactic or sub-galactic structures. We also present a thermodynamic analysis of the non-linear and inhomogeneous fifth-force regime where we find that the Universe is not made more inhomogeneous before $z_\alpha$ when the fifth force dominates, and does not lead to the existence of clumped matter on extra small scales inside halos for large masses while this possibility exists for masses $M\lesssim 10^{11} M_\odot$ where the phenomenology of ultra-local models would be most different from $\Lambda$-CDM.

### Ultra-local models of modified gravity without kinetic term [Replacement]

We present a class of modified-gravity theories which we call ultra-local models. We add a scalar field, with negligible kinetic terms, to the Einstein-Hilbert action. We also introduce a conformal coupling to matter. This gives rise to a new screening mechanism which is not entirely due to the non-linearity of the scalar field potential or the coupling function but to the absence of the kinetic term. As a result this removes any fifth force between isolated objects in vacuum. The predictions of these models only depend on a single free function, as the potential and the coupling function are degenerate, with an amplitude given by a parameter $\alpha \lesssim 10^{-6}$, whose magnitude springs from requiring a small modification of Newton's potential astrophysically and cosmologically. This singles out a redshift $z_{\alpha} \sim \alpha^{-1/3} \gtrsim 100$ where the fifth force is the greatest. The cosmological background follows the $\Lambda$-CDM history within a $10^{-6}$ accuracy, while cosmological perturbations are significantly enhanced (or damped) on small scales, $k \gtrsim 2 h {\rm Mpc}^{-1}$ at $z=0$. The spherical collapse and the halo mass function are modified in the same manner. We find that the modifications of gravity are greater for galactic or sub-galactic structures. We also present a thermodynamic analysis of the non-linear and inhomogeneous fifth-force regime where we find that the Universe is not made more inhomogeneous before $z_\alpha$ when the fifth force dominates, and does not lead to the existence of clumped matter on extra small scales inside halos for large masses while this possibility exists for masses $M\lesssim 10^{11} M_\odot$ where the phenomenology of ultra-local models would be most different from $\Lambda$-CDM.

### Ultra-local models of modified gravity without kinetic term

We present a class of modified-gravity theories which we call ultra-local models. We add a scalar field, with negligible kinetic terms, to the Einstein-Hilbert action. We also introduce a conformal coupling to matter. This gives rise to a new screening mechanism which is not entirely due to the non-linearity of the scalar field potential or the coupling function but to the absence of the kinetic term. As a result this removes any fifth force between isolated objects in vacuum. The predictions of these models only depend on a single free function, as the potential and the coupling function are degenerate, with an amplitude given by a parameter $\alpha \lesssim 10^{-6}$, whose magnitude springs from requiring a small modification of Newton's potential astrophysically and cosmologically. This singles out a redshift $z_{\alpha} \sim \alpha^{-1/3} \gtrsim 100$ where the fifth force is the greatest. The cosmological background follows the $\Lambda$-CDM history within a $10^{-6}$ accuracy, while cosmological perturbations are significantly enhanced (or damped) on small scales, $k \gtrsim 2 h {\rm Mpc}^{-1}$ at $z=0$. The spherical collapse and the halo mass function are modified in the same manner. We find that the modifications of gravity are greater for galactic or sub-galactic structures. We also present a thermodynamic analysis of the non-linear and inhomogeneous fifth-force regime where we find that the Universe is not made more inhomogeneous before $z_\alpha$ when the fifth force dominates, and does not lead to the existence of clumped matter on extra small scales inside halos for large masses while this possibility exists for masses $M\lesssim 10^{11} M_\odot$ where the phenomenology of ultra-local models would be most different from $\Lambda$-CDM.

### K-essence in Horndeski models

In this paper, we investigate a simple class of Horndeski models where the scalar field plays the role of a k-essence fluid. We present several solutions for early-time universe, namely inflation and cosmological bounce, by making use of some reconstruction technique. Moreover, we furnish the formalism to calculate perturbations in FRW space-time and we compute the spectral index and the tensor-to-scalar ratio during inflation.

### Quest for potentials in the quintessence scenario

The time variation of the equation of state $w$ for quintessence scenario with a scalar field as dark energy is studied up to the third derivative ($d^3w/da^3$) with respect to the scale factor $a$, in order to predict the future observations and specify the scalar potential parameters with the observables. The third derivative of $w$ for general potential $V$ is derived and applied to several types of potentials. They are the inverse power-law ($V=M^{4+\alpha}/Q^{\alpha}$), the exponential ($V=M^4\exp{(\beta M/Q)}$), the cosine ($V=M^4(\cos (Q/f)+1)$) and the Gaussian types ($V=M^4\exp(-Q^2/\sigma^2)$), which are prototypical potentials for the freezing and thawing models. If the parameter number for a potential form is $n$, it is necessary to find at least for $n+2$ independent observations to identify the potential form and the evolution of the scalar field ($Q$ and $\dot{Q}$). Such observations would be the values of $\Omega_Q, w, dw/da. \cdots$, and $dw^n/da^n$. Since four of the above mentioned potentials have two parameters, it is necessary to calculate the third derivative of $w$ for them to estimate the predict values. If they are tested observationally, it will be understood whether the dark energy could be described by the scalar field with this potential. Numerical analysis for $d^3w/da^3$ are made under some specified parameters in the investigated potentials. It becomes possible to distinguish the freezing and thawing modes by the accurate observing $dw/da$ and $d^2w/da^2$ in some parameters.

### Asymptotic cosmological regimes in scalar-torsion gravity with a perfect fluid

We consider cosmological dynamics of nonminimally coupled scalar field in the scalar-torsion gravity in the presence of a hydrodynamical matter. Potential of the scalar field have been chosen as power-law with negative index, this type of potentials is usually used in quintessence scenarios. We identify several asymptotic regimes, including de Sitter, kinetic dominance, kinetic tracker and tracker solution and study conditions for their existence and stability. We show that for each combination of coupling constant and potential power index one of regimes studied in the present paper is stable to the future.

### Scaling solutions for Dilaton Quantum Gravity

Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale $k$ is varied. In the Einstein frame the quantum effective action corresponding to the scaling solutions becomes independent of $k$. The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity.

### Scaling solutions for Dilaton Quantum Gravity [Cross-Listing]

Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale $k$ is varied. In the Einstein frame the quantum effective action corresponding to the scaling solutions becomes independent of $k$. The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity.

### Local vs. global temperature under a positive curvature condition [Cross-Listing]

For a massless free scalar field in a globally hyperbolic space-time we compare the global temperature T, defined for the KMS states $\omega^T$, with the local temperature $T_{\omega}(x)$ introduced by Buchholz and Schlemmer. We prove the following claims: (1) Whenever $T_{\omega^T}(x)$ is defined, it is a continuous, monotonically increasing function of T at every point x. (2) $T_{\omega}(x)$ is defined when the space-time is ultra-static with compact Cauchy surface and non-trivial scalar curvature $R\ge 0$, $\omega$ is stationary and a few other assumptions are satisfied. Our proof of (2) relies on the positive mass theorem. We discuss the necessity of its assumptions, providing counter-examples in an ultra-static space-time with non-compact Cauchy surface and R<0 somewhere. We interpret the result in terms of a violation of the weak energy condition in the background space-time.

### Testing a Two Field Inflation Beyond the Slow-Roll Approximation [Cross-Listing]

We consider a model of two-field inflation, containing an ordinary scalar field and a DBI field. We work beyond the slow-roll approximation, but we assume a separable Hubble parameter. We then derive the form of potential in this framework and study the spectrum of the primordial perturbations in details. We also study the amplitude of the non-Gaussianity of the primordial perturbations both in equilateral and orthogonal configurations in this setup. We test the model with recent observational data and find some constraints on the model parameters. Our study shows that for some ranges of the DBI parameter, the model is consistent with observation and it is also possible to have large non-Gaussianity which would be observable by future improvements in experiments.

### Testing a Two Field Inflation Beyond the Slow-Roll Approximation

We consider a model of two-field inflation, containing an ordinary scalar field and a DBI field. We work beyond the slow-roll approximation, but we assume a separable Hubble parameter. We then derive the form of potential in this framework and study the spectrum of the primordial perturbations in details. We also study the amplitude of the non-Gaussianity of the primordial perturbations both in equilateral and orthogonal configurations in this setup. We test the model with recent observational data and find some constraints on the model parameters. Our study shows that for some ranges of the DBI parameter, the model is consistent with observation and it is also possible to have large non-Gaussianity which would be observable by future improvements in experiments.

### Testing a Two Field Inflation Beyond the Slow-Roll Approximation [Cross-Listing]

We consider a model of two-field inflation, containing an ordinary scalar field and a DBI field. We work beyond the slow-roll approximation, but we assume a separable Hubble parameter. We then derive the form of potential in this framework and study the spectrum of the primordial perturbations in details. We also study the amplitude of the non-Gaussianity of the primordial perturbations both in equilateral and orthogonal configurations in this setup. We test the model with recent observational data and find some constraints on the model parameters. Our study shows that for some ranges of the DBI parameter, the model is consistent with observation and it is also possible to have large non-Gaussianity which would be observable by future improvements in experiments.

### Cosmological Aspects of Spontaneous Baryogenesis [Cross-Listing]

We investigate cosmological aspects of spontaneous baryogenesis driven by a scalar field, and present general constraints that are independent of the particle physics model. The relevant constraints are obtained by studying the backreaction of the produced baryons on the scalar field, the cosmological expansion history after baryogenesis, and the baryon isocurvature perturbations. We show that cosmological considerations alone provide powerful constraints, especially for the minimal scenario with a quadratic scalar potential. Intriguingly, we find that for a given inflation scale, the other parameters including the reheat temperature, decoupling temperature of the baryon violating interactions, and the mass and decay constant of the scalar are restricted to lie within ranges of at most a few orders of magnitude. We also discuss possible extensions to the minimal setup, and propose two ideas for evading constraints on isocurvature perturbations: one is to suppress the baryon isocurvature with nonquadratic scalar potentials, another is to compensate the baryon isocurvature with CDM isocurvature by making the scalar survive until the present.

### Cosmological Aspects of Spontaneous Baryogenesis [Cross-Listing]

We investigate cosmological aspects of spontaneous baryogenesis driven by a scalar field, and present general constraints that are independent of the particle physics model. The relevant constraints are obtained by studying the backreaction of the produced baryons on the scalar field, the cosmological expansion history after baryogenesis, and the baryon isocurvature perturbations. We show that cosmological considerations alone provide powerful constraints, especially for the minimal scenario with a quadratic scalar potential. Intriguingly, we find that for a given inflation scale, the other parameters including the reheat temperature, decoupling temperature of the baryon violating interactions, and the mass and decay constant of the scalar are restricted to lie within ranges of at most a few orders of magnitude. We also discuss possible extensions to the minimal setup, and propose two ideas for evading constraints on isocurvature perturbations: one is to suppress the baryon isocurvature with nonquadratic scalar potentials, another is to compensate the baryon isocurvature with CDM isocurvature by making the scalar survive until the present.

### Cosmological Aspects of Spontaneous Baryogenesis

We investigate cosmological aspects of spontaneous baryogenesis driven by a scalar field, and present general constraints that are independent of the particle physics model. The relevant constraints are obtained by studying the backreaction of the produced baryons on the scalar field, the cosmological expansion history after baryogenesis, and the baryon isocurvature perturbations. We show that cosmological considerations alone provide powerful constraints, especially for the minimal scenario with a quadratic scalar potential. Intriguingly, we find that for a given inflation scale, the other parameters including the reheat temperature, decoupling temperature of the baryon violating interactions, and the mass and decay constant of the scalar are restricted to lie within ranges of at most a few orders of magnitude. We also discuss possible extensions to the minimal setup, and propose two ideas for evading constraints on isocurvature perturbations: one is to suppress the baryon isocurvature with nonquadratic scalar potentials, another is to compensate the baryon isocurvature with CDM isocurvature by making the scalar survive until the present.

### Nonlinearly charged dilatonic black holes and their Brans-Dicke counterpart: Energy dependent spacetime

Regarding the wide applications of dilaton gravity in the presence of electrodynamics, we introduce a suitable Lagrangian for the coupling of dilaton with gauge field. There are various Lagrangians which show the coupling between scalar fields and electrodynamics with correct special situations. In this paper, taking into account conformal transformation of Brans-Dick theory with an electrodynamics Lagrangian, we show that how the scalar field should couple with electrodynamics in dilaton gravity. In other words, in order to introduce a correct Lagrangian of dilaton gravity, one should check at least two requirements: compatibility with Brans-Dick theory and appropriate special situations. Finally, we apply the mentioned method to obtain analytical solutions of dilaton-Born-Infeld and Brans-Dicke-Born-Infeld theories with energy dependent spacetime.

### Compact Q-balls

In this work we deal with non-topological solutions of the Q-ball type in two space-time dimensions, in models described by a single complex scalar field that engenders global symmetry. The main novelty is the presence of stable Q-balls solutions that live in a compact interval of the real line and appear from a family of models controlled by two distinct parameters. We find analytical solutions and study their charge and energy, and show how to control the parameters to make the Q-balls classically and quantum mechanically stable.

### Compact Q-balls [Replacement]

In this work we deal with non-topological solutions of the Q-ball type in two space-time dimensions, in models described by a single complex scalar field that engenders global symmetry. The main novelty is the presence of stable Q-balls solutions that live in a compact interval of the real line and appear from a family of models controlled by two distinct parameters. We find analytical solutions and study their charge and energy, and show how to control the parameters to make the Q-balls classically and quantum mechanically stable.

### Holographic Quenches with a Gap

In order to holographically model quenches with a gapped final hamiltonian, we consider a gravity-scalar theory in anti-de Sitter space with an infrared hard wall. We allow a time dependent profile for the scalar field at the wall. This induces an energy exchange between bulk and wall and generates an oscillating scalar pulse. We argue that such backgrounds are the counterpart of quantum revivals in the dual field theory. We perform a qualitative comparison with the quench dynamics of the massive Schwinger model, which has been recently analyzed using tensor network techniques. Agreement is found provided the width of the oscillating scalar pulse is inversely linked to the energy density communicated by the quench. We propose this to be a general feature of holographic quenches.

### Searching for an oscillating massive scalar field as a dark matter candidate using atomic hyperfine frequency comparisons

We use six years of accurate hyperfine frequency comparison data of the dual Rubidium and Caesium cold atom fountain FO2 at LNE-SYRTE to search for a massive scalar dark matter candidate. Such a scalar field can induce harmonic variations of the fine structure constant, of the mass of fermions and of the quantum chromodynamic mass scale, which will directly impact the Rubidium/Caesium hyperfine transition frequency ratio. We find no signal consistent with a scalar dark matter candidate but provide improved constraints on the coupling of the putative scalar field to standard matter. Our limits are complementary to previous results that were only sensitive to the fine-structure constant, and improve them by more than an order of magnitude when only a coupling to electromagnetism is assumed.

### Searching for an oscillating massive scalar field as a dark matter candidate using atomic hyperfine frequency comparisons [Cross-Listing]

We use six years of accurate hyperfine frequency comparison data of the dual Rubidium and Caesium cold atom fountain FO2 at LNE-SYRTE to search for a massive scalar dark matter candidate. Such a scalar field can induce harmonic variations of the fine structure constant, of the mass of fermions and of the quantum chromodynamic mass scale, which will directly impact the Rubidium/Caesium hyperfine transition frequency ratio. We find no signal consistent with a scalar dark matter candidate but provide improved constraints on the coupling of the putative scalar field to standard matter. Our limits are complementary to previous results that were only sensitive to the fine-structure constant, and improve them by more than an order of magnitude when only a coupling to electromagnetism is assumed.

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