# Posts Tagged scalar field

## Recent Postings from scalar field

### Building a Holographic Superconductor with a Scalar Field Coupled Kinematically to Einstein Tensor

We study the holographic dual description of a superconductor in which the gravity sector consists of a Maxwell field and a charged scalar field which except its minimal coupling to gravity it is also coupled kinematically to Einstein tensor. As the strength of the new coupling is increased, the critical temperature below which the scalar field condenses is lowering, the condensation gap decreases faster than the temperature, the width of the condensation gap is not proportional to the size of the condensate and at low temperatures the condensation gap tends to zero for the strong coupling. These effects which are the result of the presence of the coupling of the scalar field to the Einstein tensor in the gravity bulk, provide a dual description of impurities concentration in a superconducting state on the boundary.

### Building a Holographic Superconductor with a Scalar Field Coupled Kinematically to Einstein Tensor [Replacement]

We study the holographic dual description of a superconductor in which the gravity sector consists of a Maxwell field and a charged scalar field which except its minimal coupling to gravity it is also coupled kinematically to Einstein tensor. As the strength of the new coupling is increased, the critical temperature below which the scalar field condenses is lowering, the condensation gap decreases faster than the temperature, the width of the condensation gap is not proportional to the size of the condensate and at low temperatures the condensation gap tends to zero for the strong coupling. These effects which are the result of the presence of the coupling of the scalar field to the Einstein tensor in the gravity bulk, provide a dual description of impurities concentration in a superconducting state on the boundary.

### Building a Holographic Superconductor with a Scalar Field Coupled Kinematically to Einstein Tensor [Replacement]

We study the holographic dual description of a superconductor in which the gravity sector consists of a Maxwell field and a charged scalar field which except its minimal coupling to gravity it is also coupled kinematically to Einstein tensor. As the strength of the new coupling is increased, the critical temperature below which the scalar field condenses is lowering, the condensation gap decreases faster than the temperature, the width of the condensation gap is not proportional to the size of the condensate and at low temperatures the condensation gap tends to zero for the strong coupling. These effects which are the result of the presence of the coupling of the scalar field to the Einstein tensor in the gravity bulk, provide a dual description of impurities concentration in a superconducting state on the boundary.

### Building a Holographic Superconductor with a Scalar Field Coupled Kinematically to Einstein Tensor [Cross-Listing]

We study the holographic dual description of a superconductor in which the gravity sector consists of a Maxwell field and a charged scalar field which except its minimal coupling to gravity it is also coupled kinematically to Einstein tensor. As the strength of the new coupling is increased, the critical temperature below which the scalar field condenses is lowering, the condensation gap decreases faster than the temperature, the width of the condensation gap is not proportional to the size of the condensate and at low temperatures the condensation gap tends to zero for the strong coupling. These effects which are the result of the presence of the coupling of the scalar field to the Einstein tensor in the gravity bulk, provide a dual description of impurities concentration in a superconducting state on the boundary.

### Scalar field dark energy with a minimal coupling in a spherically symmetric background [Cross-Listing]

Dark energy models and modified gravity theories have been actively studied and the behaviors in the solar system have been also carefully investigated in a part of the models. However, the behaviors of the scalar field in an isotropic space-time under the simple models of dark energy, e.g. quintessence model without matter coupling, have not been well investigated. One of the reason of it would be the nonlinearity of the field equation. In this paper, the theoretical analysises are carried out by using the appropriate values of the parameters and taking some limit for the field. As a result, it is shown that there is a model that can naturally pass the solar system tests and there is also a model that would not be valid.

### Scalar field dark energy with a minimal coupling in a spherically symmetric background [Replacement]

Dark energy models and modified gravity theories have been actively studied and the behaviors in the solar system have been also carefully investigated in a part of the models. However, the behaviors of the scalar field in an isotropic space-time under the simple models of dark energy, e.g. quintessence model without matter coupling, have not been well investigated. One of the reason of it would be the nonlinearity of the field equation. In this paper, the theoretical analyses are carried out by using the appropriate values of the parameters and taking some limit for the field. As a result, it is shown that there is a model that can naturally pass the solar system tests and there is also a model that would not be valid.

### Scalar field dark energy with a minimal coupling in a spherically symmetric background

Dark energy models and modified gravity theories have been actively studied and the behaviors in the solar system have been also carefully investigated in a part of the models. However, the behaviors of the scalar field in an isotropic space-time under the simple models of dark energy, e.g. quintessence model without matter coupling, have not been well investigated. One of the reason of it would be the nonlinearity of the field equation. In this paper, the theoretical analysises are carried out by using the appropriate values of the parameters and taking some limit for the field. As a result, it is shown that there is a model that can naturally pass the solar system tests and there is also a model that would not be valid.

### Scalar field dark energy with a minimal coupling in a spherically symmetric background [Replacement]

Dark energy models and modified gravity theories have been actively studied and the behaviors in the solar system have been also carefully investigated in a part of the models. However, the behaviors of the scalar field in an isotropic space-time under the simple models of dark energy, e.g. quintessence model without matter coupling, have not been well investigated. One of the reason of it would be the nonlinearity of the field equation. In this paper, the theoretical analyses are carried out by using the appropriate values of the parameters and taking some limit for the field. As a result, it is shown that there is a model that can naturally pass the solar system tests and there is also a model that would not be valid.

### Scalar field dark energy with a minimal coupling in a spherically symmetric background [Cross-Listing]

Dark energy models and modified gravity theories have been actively studied and the behaviors in the solar system have been also carefully investigated in a part of the models. However, the behaviors of the scalar field in an isotropic space-time under the simple models of dark energy, e.g. quintessence model without matter coupling, have not been well investigated. One of the reason of it would be the nonlinearity of the field equation. In this paper, the theoretical analysises are carried out by using the appropriate values of the parameters and taking some limit for the field. As a result, it is shown that there is a model that can naturally pass the solar system tests and there is also a model that would not be valid.

### Scalar field dark energy with a minimal coupling in a spherically symmetric background [Replacement]

Dark energy models and modified gravity theories have been actively studied and the behaviors in the solar system have been also carefully investigated in a part of the models. However, the behaviors of the scalar field in an isotropic space-time under the simple models of dark energy, e.g. quintessence model without matter coupling, have not been well investigated. One of the reason of it would be the nonlinearity of the field equation. In this paper, the theoretical analyses are carried out by using the appropriate values of the parameters and taking some limit for the field. As a result, it is shown that there is a model that can naturally pass the solar system tests and there is also a model that would not be valid.

### Polymer-Fourier quantization of the scalar field revisited

The Polymer Quantization of the Fourier modes of the real scalar field is studied within algebraic scheme. We replace the positive linear functional of the standard Poincar\'e invariant quantization by a singular one. This singular positive linear functional is constructed as mimicking the singular limit of the complex structure of the Poincar\'e invariant Fock quantization. The resulting symmetry group of such Polymer Quantization is the subgroup $\mbox{SDiff}(\mathbb{R}^4)$ which is a subgroup of $\mbox{Diff}(\mathbb{R}^4)$ formed by spatial volume preserving diffeomorphisms. In consequence, this yields an entirely different irreducible representation of the Canonical Commutation Relations, non-unitary equivalent to the standard Fock representation. We also compared the Poincar\'e invariant Fock vacuum with the Polymer Fourier vacuum.

### Full linear perturbations and localization of gravity on $f(R,T)$ brane [Cross-Listing]

We study the thick brane world system constructed in the recently proposed $f(R,T)$ theories of gravity, with $R$ the Ricci scalar and $T$ the trace of the energy-momentum tensor. The analytic solution with a kink scalar field is obtained in a specific model, thus a domain wall configuration is constructed. We also discuss the full linear perturbations, especially the scalar perturbations. It is found that no tachyon state exists in this model and only the massless tensor mode can be localized on the brane, which recovers the effective four-dimensional gravity. These conclusions hold provided that two constraints on the original formalism of the action are satisfied.

### Full linear perturbations and localization of gravity on $f(R,T)$ brane

We study the thick brane world system constructed in the recently proposed $f(R,T)$ theories of gravity, with $R$ the Ricci scalar and $T$ the trace of the energy-momentum tensor. The analytic solution with a kink scalar field is obtained in a specific model, thus a domain wall configuration is constructed. We also discuss the full linear perturbations, especially the scalar perturbations. It is found that no tachyon state exists in this model and only the massless tensor mode can be localized on the brane, which recovers the effective four-dimensional gravity. These conclusions hold provided that two constraints on the original formalism of the action are satisfied.

### Static, spherically symmetric solutions with a scalar field in Rastall gravity [Cross-Listing]

Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except in a very special case. When a canonical scalar field is coupled to the gravity sector in this theory, new exact solutions appear for some values of the Rastall parameter $a$. Some of these solutions describe the same space-time geometry as the recently found solutions in the $k$-essence theory with a power function for the kinetic term of the scalar field. There is a large class of solutions (in particular, those describing wormholes and regular black holes) whose geometry coincides with that of solutions of GR coupled to scalar fields with nontrivial self-interaction potentials; the form of these potentials, however, depends on the Rastall parameter $a$. We also note that all solutions of GR with a zero trace of the energy-momentum tensor, including black-hole and wormhole ones, may be re-interpreted as solutions of Rastall's theory.

### Static, spherically symmetric solutions with a scalar field in Rastall gravity

Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except in a very special case. When a canonical scalar field is coupled to the gravity sector in this theory, new exact solutions appear for some values of the Rastall parameter $a$. Some of these solutions describe the same space-time geometry as the recently found solutions in the $k$-essence theory with a power function for the kinetic term of the scalar field. There is a large class of solutions (in particular, those describing wormholes and regular black holes) whose geometry coincides with that of solutions of GR coupled to scalar fields with nontrivial self-interaction potentials; the form of these potentials, however, depends on the Rastall parameter $a$. We also note that all solutions of GR with a zero trace of the energy-momentum tensor, including black-hole and wormhole ones, may be re-interpreted as solutions of Rastall's theory.

### Decoherence and disentanglement of qubits detecting scalar fields in an expanded universe

We consider Unruh-Wald qubit detector model adopted for the far future region of an exactly solvable 1+1 dimensional scalar field theory in a Robertson-Walker expanding spacetime. It is shown that the expansion of the universe in its history enhances the decoherence of the qubit coupled with a scalar field. Moreover, we consider two entangled qubits, each locally coupled a scalar field. The expansion of the universe in its history degrades the entanglement between the qubits, and can lead to entanglement sudden death if the initial entanglement is small enough. The details depend on the parameters characterizing the expansion of the universe. This work, albeit on a toy model, suggests that the history of the universe might be probed through the coherent and entanglement behavior of future detectors of quantum fields.

### Complete Hamiltonian analysis of cosmological perturbations at all orders II: Non-canonical scalar field [Cross-Listing]

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.

### Complete Hamiltonian analysis of cosmological perturbations at all orders II: Non-canonical scalar field [Replacement]

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.

### Complete Hamiltonian analysis of cosmological perturbations at all orders II: Non-canonical scalar field

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.

### Complete Hamiltonian analysis of cosmological perturbations at all orders II: Non-canonical scalar field [Replacement]

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.

### Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Kerr Black Hole

In this article we will discuss a Lorentzian sector calculation of the entropy of a minimally coupled scalar field in the Kerr black hole background. We will use the brick wall model of t' Hooft. In the Kerr black hole, complications arise due to the absence of a global timelike Killing field and the presence of the ergosphere. Nevertheless, it is possible to calculate the entropy of a thin shell of matter field in the near-horizon region using the brick wall model. The corresponding leading order entropy of the nonsuperradiant modes is found to be proportional to the area of the horizon and is logarithmically divergent. Thus, the entropy of a three dimensional system in the near-horizon region is proportional to the boundary surface. This is similar to that of the black hole entropy itself. The corresponding internal energy remains finite if the entropy is chosen to be of the order of the black hole entropy itself. The leading order entropy is found to be half of the corresponding term in the Schwarzschild black hole. This is expected due to the preferential emission of particles in the Kerr black hole with azimuthal angular momentum in the same direction as that of the black hole itself.

### Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Kerr Black Hole [Replacement]

In this article we will discuss a Lorentzian sector calculation of the entropy of a minimally coupled scalar field in the Kerr black hole background. We will use the brick wall model of t' Hooft. In the Kerr black hole, complications arise due to the absence of a global timelike Killing field and the presence of the ergosphere. Nevertheless, it is possible to calculate the entropy of a thin shell of matter field in the near-horizon region using the brick wall model. The corresponding leading order entropy of the nonsuperradiant modes is found to be proportional to the area of the horizon and is logarithmically divergent. Thus, the entropy of a three dimensional system in the near-horizon region is proportional to the boundary surface. This is similar to that of the black hole entropy itself. The corresponding internal energy remains finite if the entropy is chosen to be of the order of the black hole entropy itself. For a fixed value of the brick wall cut-off, the leading order entropy in the Kerr black hole is found to be half of the corresponding term in the Schwarzschild black hole. This is consistent with the preferential emission of particles in the Kerr black hole with azimuthal angular momentum in the same direction as that of the black hole itself. However, we can obtain the Schwarzschild case expression by including a subleading term and taking the appropriate limit.

### Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Kerr Black Hole [Replacement]

In this article we will discuss a Lorentzian sector calculation of the entropy of a minimally coupled scalar field in the Kerr black hole background. We will use the brick wall model of t' Hooft. In the Kerr black hole, complications arise due to the absence of a global timelike Killing field and the presence of the ergosphere. Nevertheless, it is possible to calculate the entropy of a thin shell of matter field in the near-horizon region using the brick wall model. The corresponding leading order entropy of the nonsuperradiant modes is found to be proportional to the area of the horizon and is logarithmically divergent. Thus, the entropy of a three dimensional system in the near-horizon region is proportional to the boundary surface. This is similar to that of the black hole entropy itself. The corresponding internal energy remains finite if the entropy is chosen to be of the order of the black hole entropy itself. The leading order entropy is found to be half of the corresponding term in the Schwarzschild black hole. This is expected due to the preferential emission of particles in the Kerr black hole with azimuthal angular momentum in the same direction as that of the black hole itself.

### Quantum probes of timelike naked singularity with scalar hair

We study the curvature singularity resolution via quantum fields on a fixed background based on Klein--Gordon and Dirac equations for a static spacetime with a scalar field producing a timelike naked singularity. We show that both Klein--Gordon and Dirac quantum fields see this singularity. Subsequently we check the results by applying the maximal acceleration existence in Covariant Loop Quantum Gravity described recently and obtain the resolution of singularity. In the process we study the geodesics in the spacetime.

### Quantum probes of timelike naked singularity with scalar hair [Cross-Listing]

We study the curvature singularity resolution via quantum fields on a fixed background based on Klein--Gordon and Dirac equations for a static spacetime with a scalar field producing a timelike naked singularity. We show that both Klein--Gordon and Dirac quantum fields see this singularity. Subsequently we check the results by applying the maximal acceleration existence in Covariant Loop Quantum Gravity described recently and obtain the resolution of singularity. In the process we study the geodesics in the spacetime.

### Quasistationary solutions of scalar fields around accreting black holes

Massive scalar fields can form long-lived configurations around black holes. These configurations, dubbed quasi-bound states, have been studied both in the linear and nonlinear regimes. In this paper we show that quasi-bound states can form in a dynamical scenario in which the mass of the black hole grows significantly due to the capture of infalling matter. We solve the Klein-Gordon equation numerically in spherical symmetry, mimicking the evolution of the spacetime through a sequence of analytic Schwarzschild black hole solutions of increasing mass. It is found that the frequency of oscillation of the quasi-bound states decreases as the mass of the black hole increases. In addition, accretion leads to a significative increase of the exponential decay of the scalar field energy due to the presence of terms of order higher than linear in the exponent. We compare the black hole mass growth rates used in our study with estimates from observational surveys and extrapolate our results to values of the scalar field masses consistent with models that propose scalar fields as dark matter in the universe. We show that even for unrealistically large mass accretion rates, quasi-bound states around accreting black holes can survive for cosmological timescales. Our results provide further support to the intriguing possibility of the existence of dark matter halos based on (ultra-light) scalar fields surrounding supermassive black holes in galactic centers.

### Ring wormholes via duality rotations

We apply duality rotations and complex transformations to the Schwarzschild metric to obtain wormhole geometries with two asymptotically flat regions connected by a throat. In the simplest case these are the well-known wormholes supported by phantom scalar field. Further duality rotations remove the scalar field to yield less well known vacuum metrics of the oblate Zipoy-Voorhees-Weyl class, which describe ring wormholes. The ring encircles the wormhole throat and can have any radius, whereas its tension is always negative and should be less than $-c^4/4G$. If the tension reaches the maximal value, the geometry becomes exactly flat, but the topology remains non-trivial and corresponds to two copies of Minkowski space glued together along the disk encircled by the ring. The geodesics are straight lines, and those which traverse the ring get to the other universe. The ring therefore literally produces a whole in space. Such wormholes could perhaps be created by negative energies concentrated in toroidal volumes, for example by vacuum fluctuations.

### Ring wormholes via duality rotations [Cross-Listing]

We apply duality rotations and complex transformations to the Schwarzschild metric to obtain wormhole geometries with two asymptotically flat regions connected by a throat. In the simplest case these are the well-known wormholes supported by phantom scalar field. Further duality rotations remove the scalar field to yield less well known vacuum metrics of the oblate Zipoy-Voorhees-Weyl class, which describe ring wormholes. The ring encircles the wormhole throat and can have any radius, whereas its tension is always negative and should be less than $-c^4/4G$. If the tension reaches the maximal value, the geometry becomes exactly flat, but the topology remains non-trivial and corresponds to two copies of Minkowski space glued together along the disk encircled by the ring. The geodesics are straight lines, and those which traverse the ring get to the other universe. The ring therefore literally produces a whole in space. Such wormholes could perhaps be created by negative energies concentrated in toroidal volumes, for example by vacuum fluctuations.

### Exact solutions for the biadjoint scalar field [Cross-Listing]

Biadjoint scalar theories are novel field theories that arise in the study of non-abelian gauge and gravity amplitudes. In this short paper, we present exact nonperturbative solutions of the field equations, and compare their properties with monopole-like solutions in non-abelian gauge theory. Our results may pave the way for nonperturbative studies of the double copy.

### Exact solutions for the biadjoint scalar field

Biadjoint scalar theories are novel field theories that arise in the study of non-abelian gauge and gravity amplitudes. In this short paper, we present exact nonperturbative solutions of the field equations, and compare their properties with monopole-like solutions in non-abelian gauge theory. Our results may pave the way for nonperturbative studies of the double copy.

### Parametrized post Newtonian approximation in teleparallel model with a scalar field coupled to torsion and boundary term

We study the parameterized post Newtonian approximation in teleparallel model of gravity with a scalar field. The scalar field is non-minimally coupled to the scalar torsion as well as to the boundary term introduced in [1]. We show that, in contrast to the case where the scalar field is only coupled to the scalar torsion, the presence of the new coupling affects the parameterized post Newtonian parameters. These parameters for different situations are obtained and discussed.

### Integrable cosmological models in the Einstein and in the Jordan frames and Bianchi - I cosmology [Cross-Listing]

We study the integrable models with a minimally and a non-minimally coupled scalar field and the correspondence between their general solutions. Using the model with a minimally coupled scalar field and a constant potential as an example, we demonstrate the way to obtain the general solutions of the corresponding models in the Einstein and Jordan frames.

### Integrable cosmological models in the Einstein and in the Jordan frames and Bianchi - I cosmology

We study the integrable models with a minimally and a non-minimally coupled scalar field and the correspondence between their general solutions. Using the model with a minimally coupled scalar field and a constant potential as an example, we demonstrate the way to obtain the general solutions of the corresponding models in the Einstein and Jordan frames.

### Localization of scalar massless excitations in self-gravitating $SO(10)$ kinks

Three self-gravitating $SO(10)$ kinks inducing asymptotically the breaking pattern $SO(10)\rightarrow SU(5)$ are determined which can be distinguished by the unbroken group on each of them: $SO(10)$ for the first kink and $SO(6)\times SU(2)\times U(1)$ and $SU(4)\times SO(2)\times U(1)$ for the second and third kink respectively. The scenarios are perturbed by considering small excitations on the fields; in particular, the metric fluctuations are parameterized in terms of tensor, vector and scalar modes. All these modes as well as the perturbations of the scalar field are rewritten as gauge-invariant variables. With regarding the tensor and vector fluctuations, for a four dimensional observer, the standard results are obtained: while the massless graviton is localized on the wall the graviphotons propagate freely in the bulk. On the other hand, for the scalar excitations in correspondence with the symmetry on the kink, both along the broken generators and along the some unbroken generators, normalizable zero modes in the four dimensional sector of the scenario are found.

### The superradiant instability regime of the spinning Kerr black hole [Cross-Listing]

Spinning Kerr black holes are known to be superradiantly unstable to massive scalar perturbations. We here prove that the instability regime of the composed Kerr-black-hole-massive-scalar-field system is bounded from above by the dimensionless inequality $M\mu < m \cdot \sqrt{{{2(1+\gamma) (1-\sqrt{1-\gamma^2}) - \gamma^2} \over {4\gamma^2}}}$, where $\{\mu,m\}$ are respectively the proper mass and azimuthal harmonic index of the scalar field and $\gamma\equiv r_-/r_+$ is the dimensionless ratio between the horizon radii of the black hole. It is further shown that this {\it analytically} derived upper bound on the superradiant instability regime of the spinning Kerr black hole agrees with recent {\it numerical} computations of the instability resonance spectrum.

### The superradiant instability regime of the spinning Kerr black hole

Spinning Kerr black holes are known to be superradiantly unstable to massive scalar perturbations. We here prove that the instability regime of the composed Kerr-black-hole-massive-scalar-field system is bounded from above by the dimensionless inequality $M\mu < m \cdot \sqrt{{{2(1+\gamma) (1-\sqrt{1-\gamma^2}) - \gamma^2} \over {4\gamma^2}}}$, where $\{\mu,m\}$ are respectively the proper mass and azimuthal harmonic index of the scalar field and $\gamma\equiv r_-/r_+$ is the dimensionless ratio between the horizon radii of the black hole. It is further shown that this {\it analytically} derived upper bound on the superradiant instability regime of the spinning Kerr black hole agrees with recent {\it numerical} computations of the instability resonance spectrum.

### The superradiant instability regime of the spinning Kerr black hole [Cross-Listing]

Spinning Kerr black holes are known to be superradiantly unstable to massive scalar perturbations. We here prove that the instability regime of the composed Kerr-black-hole-massive-scalar-field system is bounded from above by the dimensionless inequality $M\mu < m \cdot \sqrt{{{2(1+\gamma) (1-\sqrt{1-\gamma^2}) - \gamma^2} \over {4\gamma^2}}}$, where $\{\mu,m\}$ are respectively the proper mass and azimuthal harmonic index of the scalar field and $\gamma\equiv r_-/r_+$ is the dimensionless ratio between the horizon radii of the black hole. It is further shown that this {\it analytically} derived upper bound on the superradiant instability regime of the spinning Kerr black hole agrees with recent {\it numerical} computations of the instability resonance spectrum.

### Consistent Quantization of Weyl-Invariant Gravity Coupled to Stueckelberg Photon

The background field method is used to linearize the Weyl invariant scalar-tensor gravity,coupled with a Stueckelberg photon. For a generic background metric, this action is found to be not invariant, under both diffeomorphism and generalized Weyl symmetry, the latter being a combination of gauge and Weyl transformations. Interestingly, the quadratic Lagrangian, emerging from a background of Minkowski metric, respects both the transformations, independently. Becchi-Rouet-Stora-Tyutin (BRST) quantization of scalar-tensor gravity coupled with Stueckelberg photon, possessing diffeomorphism and generalized Weyl symmetry, reveals that in both the cases, negative norm states with unphysical degrees of freedom do exist. We then show that, combining diffeomorphism and generalized Weyl symmetries decouples all the ghost states, thereby removing the unphysical redundancies of the theory. During this quantization process, the scalar field does not represent any physical mode, yet modifies the usual harmonic gauge condition through non-minimal coupling with gravity.

### Consistent Quantization of Weyl-Invariant Gravity Coupled to Stueckelberg Photon [Cross-Listing]

The background field method is used to linearize the Weyl invariant scalar-tensor gravity,coupled with a Stueckelberg photon. For a generic background metric, this action is found to be not invariant, under both diffeomorphism and generalized Weyl symmetry, the latter being a combination of gauge and Weyl transformations. Interestingly, the quadratic Lagrangian, emerging from a background of Minkowski metric, respects both the transformations, independently. Becchi-Rouet-Stora-Tyutin (BRST) quantization of scalar-tensor gravity coupled with Stueckelberg photon, possessing diffeomorphism and generalized Weyl symmetry, reveals that in both the cases, negative norm states with unphysical degrees of freedom do exist. We then show that, combining diffeomorphism and generalized Weyl symmetries decouples all the ghost states, thereby removing the unphysical redundancies of the theory. During this quantization process, the scalar field does not represent any physical mode, yet modifies the usual harmonic gauge condition through non-minimal coupling with gravity.

### Constraining Curvatonic Reheating

We derive the first systematic observational constraints on reheating in models of inflation where an additional light scalar field contributes to primordial density perturbations and affects the expansion history during reheating. This encompasses the original curvaton model but also covers a larger class of scenarios. We find that, compared to the single-field case, lower values of the energy density at the end of inflation and of the reheating temperature are preferred when an additional scalar field is introduced. For instance, if inflation is driven by a quartic potential, which is one of the most favoured models when a light scalar field is added, the upper bound $T_{\mathrm{reh}}<5\times 10^{4}\,\mathrm{GeV}$ on the reheating temperature $T_{\mathrm{reh}}$ is derived, and the implications of this value on post-inflationary physics are discussed. The information gained about reheating is also quantified and it is found that it remains modest in plateau inflation (though still larger than in the single-field version of the model) but can become substantial in quartic inflation. The role played by the vev of the additional scalar field at the end of inflation is highlighted, and opens interesting possibilities for exploring stochastic inflation effects that could determine its distribution.

### Constraining Curvatonic Reheating [Cross-Listing]

We derive the first systematic observational constraints on reheating in models of inflation where an additional light scalar field contributes to primordial density perturbations and affects the expansion history during reheating. This encompasses the original curvaton model but also covers a larger class of scenarios. We find that, compared to the single-field case, lower values of the energy density at the end of inflation and of the reheating temperature are preferred when an additional scalar field is introduced. For instance, if inflation is driven by a quartic potential, which is one of the most favoured models when a light scalar field is added, the upper bound $T_{\mathrm{reh}}<5\times 10^{4}\,\mathrm{GeV}$ on the reheating temperature $T_{\mathrm{reh}}$ is derived, and the implications of this value on post-inflationary physics are discussed. The information gained about reheating is also quantified and it is found that it remains modest in plateau inflation (though still larger than in the single-field version of the model) but can become substantial in quartic inflation. The role played by the vev of the additional scalar field at the end of inflation is highlighted, and opens interesting possibilities for exploring stochastic inflation effects that could determine its distribution.

### Constraining Curvatonic Reheating [Cross-Listing]

We derive the first systematic observational constraints on reheating in models of inflation where an additional light scalar field contributes to primordial density perturbations and affects the expansion history during reheating. This encompasses the original curvaton model but also covers a larger class of scenarios. We find that, compared to the single-field case, lower values of the energy density at the end of inflation and of the reheating temperature are preferred when an additional scalar field is introduced. For instance, if inflation is driven by a quartic potential, which is one of the most favoured models when a light scalar field is added, the upper bound $T_{\mathrm{reh}}<5\times 10^{4}\,\mathrm{GeV}$ on the reheating temperature $T_{\mathrm{reh}}$ is derived, and the implications of this value on post-inflationary physics are discussed. The information gained about reheating is also quantified and it is found that it remains modest in plateau inflation (though still larger than in the single-field version of the model) but can become substantial in quartic inflation. The role played by the vev of the additional scalar field at the end of inflation is highlighted, and opens interesting possibilities for exploring stochastic inflation effects that could determine its distribution.

### Quantum and classical aspects of scalar and vector fields around black holes

This thesis presents recent studies on test scalar and vector fields around black holes. It is separated in two parts according to the asymptotic properties of the spacetime under study. In the first part, we investigate scalar and Proca fields on an asymptotically flat background. For the Proca field, we obtain a complete set of equations of motion in higher dimensional spherically symmetric backgrounds. These equations are solved numerically, both to compute Hawking radiation spectra and quasi-bound states. In the former case, we carry out a precise study of the longitudinal degrees of freedom induced by the field mass. This can be used to improve the model in the black hole event generators currently used at the Large Hadron Collider. Regarding quasi-bound states, we find arbitrarily long lived modes for a charged Proca field, as well as for a charged scalar field, in a Reissner-Nordstr\"om black hole. The second part of this thesis presents research on superradiant instabilities of scalar and Maxwell fields on an asymptotically anti-de Sitter background. For the scalar case, we introduce a charge coupling between the field and the background, and show that superradiant instabilities do exist for all $\ell$ modes, in higher dimensions. For the Maxwell case, we first propose a general prescription to impose boundary conditions on the Kerr-anti-de Sitter spacetime, and obtain two Robin boundary conditions. Then these two conditions are implemented to study superradiant unstable modes and vector clouds. In particular, we find that the new branch of quasinormal modes may be unstable in a larger parameter space. Furthermore, the existence of vector clouds indicates that one may find a vector hairy black hole solution for the Einstein-Maxwell-anti-de Sitter system at the nonlinear level, which implies that, in such system, the Kerr-Newman-anti-de Sitter black hole is not a unique solution.

### $k$-essence non-minimally coupled with Gauss-Bonnet invariant for inflation

In this paper, we investigated inflationary solutions for a subclass of Horndeski models where a scalar field is non-minimally coupled with the Gauss-Bonnet invariant. Examples of canonical scalar field and $k$-essence to support the early-time acceleration are considered. The formalism to calculate the perturbations in FRW universe and to derive the spectral index and the tensor-to-scalar ratio is furnished.

### The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field [Cross-Listing]

The well-known superradiant amplification mechanism allows a charged scalar field of proper mass $\mu$ and electric charge $q$ to extract the Coulomb energy of a charged Reissner-Nordstr\"om black hole. The rate of energy extraction can grow exponentially in time if the system is placed inside a reflecting cavity which prevents the charged scalar field from escaping to infinity. This composed black-hole-charged-scalar-field-mirror system is known as the {\it charged black-hole bomb}. Previous numerical studies of this composed physical system have shown that, in the linearized regime, the inequality $q/\mu>1$ provides a necessary condition for the development of the superradiant instability. In the present paper we use analytical techniques to study the instability properties of the charged black-hole bomb in the regime of linearized scalar fields. In particular, we prove that the lower bound ${{q}\over{\mu}}>\sqrt{{{r_{\text{m}}/r_--1}\over{r_{\text{m}}/r_+-1}}}$ provides a necessary condition for the development of the superradiant instability in this composed physical system (here $r_{\pm}$ are the horizon radii of the charged Reissner-Nordstr\"om black hole and $r_{\text{m}}$ is the radius of the confining mirror). This {\it analytically} derived lower bound on the superradiant instability regime of the composed black-hole-charged-scalar-field-mirror system is shown to agree with direct {\it numerical} computations of the instability spectrum.

### The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field [Cross-Listing]

The well-known superradiant amplification mechanism allows a charged scalar field of proper mass $\mu$ and electric charge $q$ to extract the Coulomb energy of a charged Reissner-Nordstr\"om black hole. The rate of energy extraction can grow exponentially in time if the system is placed inside a reflecting cavity which prevents the charged scalar field from escaping to infinity. This composed black-hole-charged-scalar-field-mirror system is known as the {\it charged black-hole bomb}. Previous numerical studies of this composed physical system have shown that, in the linearized regime, the inequality $q/\mu>1$ provides a necessary condition for the development of the superradiant instability. In the present paper we use analytical techniques to study the instability properties of the charged black-hole bomb in the regime of linearized scalar fields. In particular, we prove that the lower bound ${{q}\over{\mu}}>\sqrt{{{r_{\text{m}}/r_--1}\over{r_{\text{m}}/r_+-1}}}$ provides a necessary condition for the development of the superradiant instability in this composed physical system (here $r_{\pm}$ are the horizon radii of the charged Reissner-Nordstr\"om black hole and $r_{\text{m}}$ is the radius of the confining mirror). This {\it analytically} derived lower bound on the superradiant instability regime of the composed black-hole-charged-scalar-field-mirror system is shown to agree with direct {\it numerical} computations of the instability spectrum.

### The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field

The well-known superradiant amplification mechanism allows a charged scalar field of proper mass $\mu$ and electric charge $q$ to extract the Coulomb energy of a charged Reissner-Nordstr\"om black hole. The rate of energy extraction can grow exponentially in time if the system is placed inside a reflecting cavity which prevents the charged scalar field from escaping to infinity. This composed black-hole-charged-scalar-field-mirror system is known as the {\it charged black-hole bomb}. Previous numerical studies of this composed physical system have shown that, in the linearized regime, the inequality $q/\mu>1$ provides a necessary condition for the development of the superradiant instability. In the present paper we use analytical techniques to study the instability properties of the charged black-hole bomb in the regime of linearized scalar fields. In particular, we prove that the lower bound ${{q}\over{\mu}}>\sqrt{{{r_{\text{m}}/r_--1}\over{r_{\text{m}}/r_+-1}}}$ provides a necessary condition for the development of the superradiant instability in this composed physical system (here $r_{\pm}$ are the horizon radii of the charged Reissner-Nordstr\"om black hole and $r_{\text{m}}$ is the radius of the confining mirror). This {\it analytically} derived lower bound on the superradiant instability regime of the composed black-hole-charged-scalar-field-mirror system is shown to agree with direct {\it numerical} computations of the instability spectrum.

We discuss a class of models for gravity based on a scalar field. The models include and generalize the old approach by Nordstr\"om which predated and in some way inspired General Relativity. The class include also a model that we have recently introduced and discussed in its cosmological aspects (GSG). We present here a complete characterisation of the Schwarschild geometry as a vacuum solution of GSG and sketch a discussion of the first Post-Newtonian approximation.

### Entanglement Entropy of A Simple Non-minimal Coupling Model [Replacement]

In this article, we evaluate the entanglement entropy of a non-minimal coupling Einstein-scalar theory with two approaches under the conical singularity method with replica trick in classical Euclidean gravity. We focus on the static spacetime which is the solution of the Einstein-scalar theory. By analysing the equation of motion, we find that the gravity sector gives the minimal surface restriction to the entangled surface, while the solution of the equation of motion of scalar field is the product of Bessel function and solution depending on the entangled surface. After that we derived the entanglement entropy formula directly from the standard procedure of the conical singularity regularization approach. On the other hand, by extracting the geometric quantities of the conical singularity, we can also obtain the same result as the former one. The reduced geometric approach can be easily generalized to linear combinations of the known reduced geometric quantities with non-minimal coupling to scalar fields.

### Entanglement Entropy of A Simple Non-minimal Coupling Model

In this article, we evaluate the entanglement entropy of a non-minimal coupling Einstein-scalar theory with two approaches under the conical singularity method with replica trick in classical Euclidean gravity. We focus on the static spacetime which is the solution of the Einstein-scalar theory. By analysing the equation of motion, we find that the gravity sector gives the minimal surface restriction to the entangled surface, while the solution of the equation of motion of scalar field is the product of Bessel function and solution depending on the entangled surface. After that we derived the entanglement entropy formula directly from the standard procedure of the conical singularity regularization approach. On the other hand, by extracting the geometric quantities of the conical singularity, we can also obtain the same result as the former one. The reduced geometric approach can be easily generalized to linear combinations of the known reduced geometric quantities with non-minimal coupling to scalar fields.