# Posts Tagged scalar field

## Recent Postings from scalar field

### Self tuning scalar tensor black holes

Studying a certain sub class of higher order Horndeski (scalar-tensor) theories we discuss a method discovered recently permitting analytic black hole solutions with a non trivial and regular scalar field. One of the solutions found has de Sitter asymptotics and self tunes the bulk cosmological constant. Using the aforementioned method we find and analyse new black hole solutions which can also have de Sitter asymptotics. By looking at small deviations of the integration constant responsible for self tuning we discuss the robustness of the self tuning mechanism. We find that neighboring solutions to the one previously found present also self tuning properties with unaltered effective cosmological constant.

### Self tuning scalar tensor black holes [Cross-Listing]

Studying a certain sub class of higher order Horndeski (scalar-tensor) theories we discuss a method discovered recently permitting analytic black hole solutions with a non trivial and regular scalar field. One of the solutions found has de Sitter asymptotics and self tunes the bulk cosmological constant. Using the aforementioned method we find and analyse new black hole solutions which can also have de Sitter asymptotics. By looking at small deviations of the integration constant responsible for self tuning we discuss the robustness of the self tuning mechanism. We find that neighboring solutions to the one previously found present also self tuning properties with unaltered effective cosmological constant.

### Dynamical system analysis for DBI dark energy interacting with dark matter

A dynamical system analysis related to Dirac Born Infeld (DBI) cosmological model has been investigated in this present work. For spatially flat FRW space time, the Einstein field equation for DBI scenario has been used to study the dynamics of DBI dark energy interacting with dark matter. The DBI dark energy model is considered as a scalar field with a nonstandard kinetic energy term. An interaction between the DBI dark energy and dark matter is considered through a phenomenological interaction between DBI scalar field and the dark matter fluid. The field equations are reduced to an autonomous dynamical system by a suitable redefinition of the basic variables. The potential of the DBI scalar field is assumed to be exponential. Finally, critical points are determined, their nature have been analyzed and corresponding cosmological scenario has been discussed.

### Construction and physical properties of Kerr black holes with scalar hair [Cross-Listing]

Kerr black holes with scalar hair are solutions of the Einstein-Klein-Gordon field equations describing regular (on and outside an event horizon), asymptotically flat black holes with scalar hair (arXiv:1403.2757). These black holes interpolate continuously between the Kerr solution and rotating boson stars in D=4 spacetime dimensions. Here we provide details on their construction, discussing properties of the ansatz, the field equations, the boundary conditions and the numerical strategy. Then, we present an overview of the parameter space of the solutions, and describe in detail the space-time structure of the black holes exterior geometry and of the scalar field for a sample of reference solutions. Phenomenological properties of potential astrophysical interest are also discussed, and the stability properties and possible generalizations are commented on. As supplementary material to this paper we make available numerical data files for the sample of reference solutions discussed, for public use.

### Construction and physical properties of Kerr black holes with scalar hair

Kerr black holes with scalar hair are solutions of the Einstein-Klein-Gordon field equations describing regular (on and outside an event horizon), asymptotically flat black holes with scalar hair (arXiv:1403.2757). These black holes interpolate continuously between the Kerr solution and rotating boson stars in D=4 spacetime dimensions. Here we provide details on their construction, discussing properties of the ansatz, the field equations, the boundary conditions and the numerical strategy. Then, we present an overview of the parameter space of the solutions, and describe in detail the space-time structure of the black holes exterior geometry and of the scalar field for a sample of reference solutions. Phenomenological properties of potential astrophysical interest are also discussed, and the stability properties and possible generalizations are commented on. As supplementary material to this paper we make available numerical data files for the sample of reference solutions discussed, for public use.

### Construction and physical properties of Kerr black holes with scalar hair [Cross-Listing]

Kerr black holes with scalar hair are solutions of the Einstein-Klein-Gordon field equations describing regular (on and outside an event horizon), asymptotically flat black holes with scalar hair (arXiv:1403.2757). These black holes interpolate continuously between the Kerr solution and rotating boson stars in D=4 spacetime dimensions. Here we provide details on their construction, discussing properties of the ansatz, the field equations, the boundary conditions and the numerical strategy. Then, we present an overview of the parameter space of the solutions, and describe in detail the space-time structure of the black holes exterior geometry and of the scalar field for a sample of reference solutions. Phenomenological properties of potential astrophysical interest are also discussed, and the stability properties and possible generalizations are commented on. As supplementary material to this paper we make available numerical data files for the sample of reference solutions discussed, for public use.

### Singular Inflation [Cross-Listing]

We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, $V(\phi)=A\phi ^{n}$, with $0<n<1$ and $A>0$ always develops a finite-time singularity at which the Hubble rate and its first derivative are finite, but its second derivative diverges. These are the first examples of cosmological models with realistic matter sources that possess weak singularities of ‘sudden’ type. We also show that a large class of models with even weaker singularities exist for non-integer $n>1$. More precisely, if $k<n<k+1$ where $k$ is a positive integer then the first divergence of the Hubble rate occurs with its ($k+2)$th derivative. At early times these models behave like standard large-field inflation models but they encounter a singular end-state when inflation ends. We term this singular inflation.

### Singular Inflation [Cross-Listing]

We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, $V(\phi)=A\phi ^{n}$, with $0<n<1$ and $A>0$ always develops a finite-time singularity at which the Hubble rate and its first derivative are finite, but its second derivative diverges. These are the first examples of cosmological models with realistic matter sources that possess weak singularities of ‘sudden’ type. We also show that a large class of models with even weaker singularities exist for non-integer $n>1$. More precisely, if $k<n<k+1$ where $k$ is a positive integer then the first divergence of the Hubble rate occurs with its ($k+2)$th derivative. At early times these models behave like standard large-field inflation models but they encounter a singular end-state when inflation ends. We term this singular inflation.

### Singular Inflation

We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, $V(\phi)=A\phi ^{n}$, with $0<n<1$ and $A>0$ always develops a finite-time singularity at which the Hubble rate and its first derivative are finite, but its second derivative diverges. These are the first examples of cosmological models with realistic matter sources that possess weak singularities of ‘sudden’ type. We also show that a large class of models with even weaker singularities exist for non-integer $n>1$. More precisely, if $k<n<k+1$ where $k$ is a positive integer then the first divergence of the Hubble rate occurs with its ($k+2)$th derivative. At early times these models behave like standard large-field inflation models but they encounter a singular end-state when inflation ends. We term this singular inflation.

### $Om$ diagnostic applied to scalar field models and slowing down of cosmic acceleration

We apply the $Om$ diagnostic to models for dark energy based on scalar fields. In case of the power law potentials, we demonstrate the possibility of slowing down the expansion of the Universe around the present epoch for a specific range in the parameter space. For these models, we also examine the issues concerning the age of Universe. We use the $Om$ diagnostic to distinguish the $\Lambda$CDM model from non minimally coupled scalar field, phantom field and generic quintessence models. Our study shows that the $Om$ has zero, positive and negative curvatures for $\Lambda$CDM, phantom and quintessence models respectively. We use an integrated data base (SN+Hubble+BAO+CMB) for bservational analysis and demonstrate that $Om$ is a useful diagnostic to apply to observational data.

### $Om$ diagnostic applied to scalar field models and slowing down of cosmic acceleration [Cross-Listing]

We apply the $Om$ diagnostic to models for dark energy based on scalar fields. In case of the power law potentials, we demonstrate the possibility of slowing down the expansion of the Universe around the present epoch for a specific range in the parameter space. For these models, we also examine the issues concerning the age of Universe. We use the $Om$ diagnostic to distinguish the $\Lambda$CDM model from non minimally coupled scalar field, phantom field and generic quintessence models. Our study shows that the $Om$ has zero, positive and negative curvatures for $\Lambda$CDM, phantom and quintessence models respectively. We use an integrated data base (SN+Hubble+BAO+CMB) for bservational analysis and demonstrate that $Om$ is a useful diagnostic to apply to observational data.

### Strategy to Construct Exact Solutions in Einstein-Scalar Gravities

In this article we propose a new efficient strategy to construct exact solutions of Einstein gravities with a minimally coupled self-interacting scalar field. The strategy is to use the symmetry of the equations of motion (EOMs) to give a proper ansatz for scalar field first, then derive the metric and the corresponding scalar potential later. Using this strategy we give a simple example of constructing exact circular solutions in three dimensional gravities, these solutions contain the HMTZ black holes as a special case and some other new solutions. We also talk about thermodynamics of these exact solutions. This strategy also works for other metrics and in higher dimensional spacetime if their EOMs admit a scalar invariance.

### Reconstructing thawing quintessence with multiple datasets

In this work we model the quintessence potential in a Taylor series expansion, up to second order, around the present-day value of the scalar field. The field is evolved in a thawing regime assuming zero initial velocity. We use the latest data from the Planck satellite, baryonic acoustic oscillations observations from the Sloan Digital Sky Survey, and Supernovae luminosity distance information from Union$2.1$ to constrain our models parameters, and also include perturbation growth data from WiggleZ. We show explicitly that the growth data does not perform as well as the other datasets in constraining the dark energy parameters we introduce. We also show that the constraints we obtain for our model parameters, when compared to previous works of nearly a decade ago, have not improved significantly. This is indicative of how little dark energy constraints, overall, have improved in the last decade, even when we add new growth of structure data to previous existent types of data.

### Chaotic inflation in higher derivative gravity theories

In this paper, we investigate chaotic inflation from scalar field subjected to potential in the framework of $f(R^2, P, Q)$-gravity, where we add a correction to Einstein’s gravity based on a function of the square of the Ricci scalar $R^2$, the contraction of the Ricci tensor $P$, and the contraction of the Riemann tensor $Q$. The Gauss-Bonnet case is also discussed. We give the general formalism of inflation, deriving the slow-roll parameters, the $e$-folds number, and the spectral indexes. Several explicit examples are furnished, namely we will consider the cases of massive scalar field and scalar field with quartic potential and some power-law function of the curvature invariants under investigation in the gravitational action of the theory. Viable inflation according with observations is analyzed.

### Dynamics of a scalar field, with a double exponential potential, interacting with dark matter [Replacement]

We study the interaction between dark matter and dark energy, with dark energy described by a scalar field having a double exponential effective potential. We discover conditions under which such a scalar field driven solution is a late time attractor. We observe a realistic cosmological evolution which consists of sequential stages of dominance of radiation, matter and dark energy, respectively.

### Dynamics of a scalar field, with a double exponential potential, interacting with dark matter [Replacement]

We study the interaction between dark matter and dark energy, with dark energy described by a scalar field having a double exponential effective potential. We discover conditions under which such a scalar field driven solution is a late time attractor. We observe a realistic cosmological evolution which consists of sequential stages of dominance of radiation, matter and dark energy, respectively.

### Dynamics of a scalar field, with a double exponential potential, interacting with dark matter [Cross-Listing]

We study the interaction between dark matter and dark energy, with dark energy described by a scalar field having a double exponential effective potential. We discover conditions under which such a scalar field driven solution is a late time attractor. We observe a realistic cosmological evolution which consists of sequential stages of dominance of radiation, matter and dark energy, respectively.

### Dynamics of a scalar field, with a double exponential potential, interacting with dark matter

We study the interaction between dark matter and dark energy, with dark energy described by a scalar field having a double exponential effective potential. We discover conditions under which such a scalar field driven solution is a late time attractor. We observe a realistic cosmological evolution which consists of sequential stages of dominance of radiation, matter and dark energy, respectively.

### Cosmology of a Lorentz violating Galileon theory

We modify the scalar Einstein-aether theory by breaking the Lorentz invariance of a gravitational theory coupled to a Galileon type scalar field. This is done by introducing a Lagrange multiplier term into the action, thus ensuring that the gradient of the scalar field is time-like, with unit norm. The resulting theory is then generally invariant at the level of action, breaking the Lorentz invariance at the level of equations of motion. The theory can also be considered as an extension to the mimetic dark matter theory, by adding some derivative self interactions to the action, which keeps the equations of motion at most second order in time derivatives. The cosmological implications of the model are discussed in detail. In particular, we show that a matter dominated (dust) universe experiences a late time acceleration. The cosmological implications of a special coupling between the scalar field and the trace of the energy-momentum tensor are also explored.

### Cosmology of a Lorentz violating Galileon theory [Cross-Listing]

We modify the scalar Einstein-aether theory by breaking the Lorentz invariance of a gravitational theory coupled to a Galileon type scalar field. This is done by introducing a Lagrange multiplier term into the action, thus ensuring that the gradient of the scalar field is time-like, with unit norm. The resulting theory is then generally invariant at the level of action, breaking the Lorentz invariance at the level of equations of motion. The theory can also be considered as an extension to the mimetic dark matter theory, by adding some derivative self interactions to the action, which keeps the equations of motion at most second order in time derivatives. The cosmological implications of the model are discussed in detail. In particular, we show that a matter dominated (dust) universe experiences a late time acceleration. The cosmological implications of a special coupling between the scalar field and the trace of the energy-momentum tensor are also explored.

### Self-Gravitating Spherically Symmetric Solutions in Scalar-Torsion Theories

We studied spherically symmetric solutions in scalar-torsion gravity theories in which a scalar field is coupled to torsion with a derivative coupling. We obtained the general field equations from which we extracted a decoupled master equation, the solution of which leads to the specification of all other unknown functions. We first obtained an exact solution which represents a new wormhole-like solution dressed with a regular scalar field. Then, we found large distance linearized spherically symmetric solutions in which the space asymptotically is AdS.

### Self-Gravitating Spherically Symmetric Solutions in Scalar-Torsion Theories [Cross-Listing]

We studied spherically symmetric solutions in scalar-torsion gravity theories in which a scalar field is coupled to torsion with a derivative coupling. We obtained the general field equations from which we extracted a decoupled master equation, the solution of which leads to the specification of all other unknown functions. We first obtained an exact solution which represents a new wormhole-like solution dressed with a regular scalar field. Then, we found large distance linearized spherically symmetric solutions in which the space asymptotically is AdS.

### Gravity localization in sine-Gordon braneworlds

In this work we study two types of five-dimensional braneworld models given by sine-Gordon potentials. In both scenarios, the thick brane is generated by a real scalar field coupled to gravity. We focus our investigation on the localization of graviton field and the behaviour of the massive spectrum. In particular, we analyse the localization of massive modes by means of a relative probability method in a Quantum Mechanics context. Initially, considering a scalar field sine-Gordon potential, we find a resonance to the graviton at zero mode. However, when we consider a double sine-Gordon potential, the brane structure is changed allowing the existence of massless and massive resonant states. The new results show how the existence of an internal structure can aid in the emergence of massive resonant modes on the brane.

### On coupling between Galileon and massive gravity with composite metrics [Cross-Listing]

We investigate the coupling between a Galileon scalar field and massive gravity through composite metrics. We derive the full set of equations of motion for a flat FRW background, and study linear perturbations around it. Generally, the nonminimal coupling with the composite metric will excite all six degrees of freedom of the spatial metric perturbations, one of which may correspond to the BD ghost.

### On coupling between Galileon and massive gravity with composite metrics

We investigate the coupling between a Galileon scalar field and massive gravity through composite metrics. We derive the full set of equations of motion for a flat FRW background, and study linear perturbations around it. Generally, the nonminimal coupling with the composite metric will excite all six degrees of freedom of the spatial metric perturbations, one of which may correspond to the BD ghost.

### Statistical Physics of 3D Hairy Black Holes

We investigate the statistical behaviors of 3D hairy black holes in the presence of a scalar field. The present study is made in terms of two relevant parameters: rotation parameter a and B parameter related to the scalar field. More precisely, we compute various statistical quantities including the partition function for non-charged and charged black hole solutions. Using a partition function calculation, we show that the probability is independent of a and B parameters.

### Quasi-stationary solutions of self-gravitating scalar fields around black holes

Recent perturbative studies have shown the existence of long-lived, quasi-stationary configurations of scalar fields around black holes. In particular, such configurations have been found to survive for cosmological timescales, which is a requirement for viable dark matter halo models in galaxies based on such type of structures. In this paper we perform a series of numerical relativity simulations of dynamical non-rotating black holes surrounded by self-gravitating scalar fields. We solve numerically the coupled system of equations formed by the Einstein and the Klein-Gordon equations under the assumption of spherical symmetry using spherical coordinates. Our results confirm the existence of oscillating, long-lived, self-gravitating scalar fields configurations around non-rotating black holes in highly dynamical spacetimes with a rich scalar field environment. Our numerical simulations are long-term stable and allow for the extraction of the resonant frequencies to make a direct comparison with results obtained in the linearized regime. A byproduct of our simulations is the existence of a degeneracy in plausible long-lived solutions of Einstein equations that would induce the same motion of test particles, either with or without the existence of quasi-bound states.

### Confinement and stability in presence of scalar fields and perturbation in the bulk

In this paper we have considered a five-dimensional warped product spacetime with spacelike extra dimension and with a scalar field source in the bulk. We have studied the dynamics of the scalar field under different types of potential in an effort to explain the confinement of particles in the five-dimensional spacetime. The behaviour of the system is determined from the nature of damping force on the system. We have also examined the nature of the effective potential under different circumstances. Lastly we have studied the system to determine whether or not the system attains asymptotically stable condition for both unperturbed and perturbed condition.

### Confinement and stability in presence of scalar fields and perturbation in the bulk [Cross-Listing]

In this paper we have considered a five-dimensional warped product spacetime with spacelike extra dimension and with a scalar field source in the bulk. We have studied the dynamics of the scalar field under different types of potential in an effort to explain the confinement of particles in the five-dimensional spacetime. The behaviour of the system is determined from the nature of damping force on the system. We have also examined the nature of the effective potential under different circumstances. Lastly we have studied the system to determine whether or not the system attains asymptotically stable condition for both unperturbed and perturbed condition.

### Warm Dark Matter in Two Higgs Doublet Models [Cross-Listing]

We show that a neutral scalar field, \sigma, of two Higgs doublet extensions of the Standard Model incorporating the seesaw mechanism for neutrino masses can be identified as a consistent {\it warm} dark matter candidate with a mass of order keV. The relic density of $\sigma$ is correctly reproduced by virtue of the late decay of a right-handed neutrino N participating in the seesaw mechanism. Constraints from cosmology determine the mass and lifetime of N to be M_N = 25 GeV – 20 TeV and \tau_N = (10^{-4} – 1) sec. These models can also explain the 3.5 keV X-ray anomaly in the extra-galactic spectrum that has been recently reported in terms of the decay \sigma \to \gamma \gamma. Future tests of these models at colliders and in astrophysical settings are outlined.

### Warm Dark Matter in Two Higgs Doublet Models

We show that a neutral scalar field, \sigma, of two Higgs doublet extensions of the Standard Model incorporating the seesaw mechanism for neutrino masses can be identified as a consistent {\it warm} dark matter candidate with a mass of order keV. The relic density of $\sigma$ is correctly reproduced by virtue of the late decay of a right-handed neutrino N participating in the seesaw mechanism. Constraints from cosmology determine the mass and lifetime of N to be M_N = 25 GeV – 20 TeV and \tau_N = (10^{-4} – 1) sec. These models can also explain the 3.5 keV X-ray anomaly in the extra-galactic spectrum that has been recently reported in terms of the decay \sigma \to \gamma \gamma. Future tests of these models at colliders and in astrophysical settings are outlined.

### Relaxed superconductors

Momentum relaxation can be built into many holographic models without sacrificing homogeneity of the bulk solution. In this paper we study two such models: one in which translational invariance is broken in the dual theory by spatially-dependent sources for massless scalar fields and another that features an additional neutral scalar field. We turn on a charged scalar field in order to explore the condensation of a charged scalar operator in the dual theories. After demonstrating that the relaxed superconductors we construct are thermodynamically relevant, we find that the finite DC electrical conductivity of the normal phase is replaced by a superfluid pole in the broken phase. Moreover, when the normal phase possesses a Drude behaviour at low frequencies, the optical conductivity of the broken phase at low frequencies can be described by a two-fluid model that is a sum of a Drude peak and a superfluid pole, as was found recently for inhomogeneous holographic superconductors. We also study cases in which this low-frequency behavior does not hold. We find that the Drude description is accurate when the retarded current-current correlator has a purely-dissipative pole that is well-separated from the rest of the excitations.

### 3.55 keV line in Minimal Decaying Dark Matter scenarios

We investigate the possibility of reproducing the recently reported $3.55\,\mbox{keV}$ line in some simple decaying dark matter scenarios. In all cases a keV scale decaying DM is coupled with a scalar field charged under SM gauge interactions and thus capable of pair production at the LHC. We will investigate how the demand of a DM lifetime compatible with the observed signal, combined with the requirement of the correct DM relic density through the freeze-in mechanism, impacts the prospects of observation at the LHC of the decays of the scalar field.

### Unimodular Theory of Gravity and Inflation

We study inflation and its scalar perturbations in the unimodular theory of gravity. When the unimodular parameter is $\xi=6$, the classical picture of inflation such as the slow-roll parameters, the number of $e$-foldings and the scale of the scalar field, can be reproduced in the unimodular theory because it recovers the background equations of the standard theory of general relativity. Considering the scalar perturbation, the unimodular gravity constrains the gauge degree of freedom, but the perturbation equations are similar to those in general relativity. For $\xi \neq 6$, we derived the power spectrum and the spectral index, and obtain the unimodular correction to the tensor-to-scalar ratio. Depending on the value of $\xi$, the correction can either raise or lower the value of the tensor-to-scalar ratio.

### Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space [Cross-Listing]

We consider a massive scalar field with quartic self-interaction $\lambda/4!\,\phi^4$ in de~Sitter spacetime and present a diagrammatic expansion that describes the field as driven by stochastic noise. This is compared with the Feynman diagrams in the Keldysh basis of the Amphichronous (Closed-Time-Path) Field Theoretical formalism. For all orders in the expansion, we find that the diagrams agree when evaluated in the leading infrared approximation, i.e. to leading order in $m^2/H^2$, where $m$ is the mass of the scalar field and $H$ is the Hubble rate. As a consequence, the correlation functions computed in both approaches also agree to leading infrared order. This perturbative correspondence shows that the stochastic Theory is exactly equivalent to the Field Theory in the infrared. The former can then offer a non-perturbative resummation of the Field Theoretical Feynman diagram expansion, including fields with $0\leq m^2\ll\sqrt \lambda H^2$ for which the perturbation expansion fails at late times.

### Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space [Cross-Listing]

We consider a massive scalar field with quartic self-interaction $\lambda/4!\,\phi^4$ in de~Sitter spacetime and present a diagrammatic expansion that describes the field as driven by stochastic noise. This is compared with the Feynman diagrams in the Keldysh basis of the Amphichronous (Closed-Time-Path) Field Theoretical formalism. For all orders in the expansion, we find that the diagrams agree when evaluated in the leading infrared approximation, i.e. to leading order in $m^2/H^2$, where $m$ is the mass of the scalar field and $H$ is the Hubble rate. As a consequence, the correlation functions computed in both approaches also agree to leading infrared order. This perturbative correspondence shows that the stochastic Theory is exactly equivalent to the Field Theory in the infrared. The former can then offer a non-perturbative resummation of the Field Theoretical Feynman diagram expansion, including fields with $0\leq m^2\ll\sqrt \lambda H^2$ for which the perturbation expansion fails at late times.

### Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space [Cross-Listing]

We consider a massive scalar field with quartic self-interaction $\lambda/4!\,\phi^4$ in de~Sitter spacetime and present a diagrammatic expansion that describes the field as driven by stochastic noise. This is compared with the Feynman diagrams in the Keldysh basis of the Amphichronous (Closed-Time-Path) Field Theoretical formalism. For all orders in the expansion, we find that the diagrams agree when evaluated in the leading infrared approximation, i.e. to leading order in $m^2/H^2$, where $m$ is the mass of the scalar field and $H$ is the Hubble rate. As a consequence, the correlation functions computed in both approaches also agree to leading infrared order. This perturbative correspondence shows that the stochastic Theory is exactly equivalent to the Field Theory in the infrared. The former can then offer a non-perturbative resummation of the Field Theoretical Feynman diagram expansion, including fields with $0\leq m^2\ll\sqrt \lambda H^2$ for which the perturbation expansion fails at late times.

### Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space

We consider a massive scalar field with quartic self-interaction $\lambda/4!\,\phi^4$ in de~Sitter spacetime and present a diagrammatic expansion that describes the field as driven by stochastic noise. This is compared with the Feynman diagrams in the Keldysh basis of the Amphichronous (Closed-Time-Path) Field Theoretical formalism. For all orders in the expansion, we find that the diagrams agree when evaluated in the leading infrared approximation, i.e. to leading order in $m^2/H^2$, where $m$ is the mass of the scalar field and $H$ is the Hubble rate. As a consequence, the correlation functions computed in both approaches also agree to leading infrared order. This perturbative correspondence shows that the stochastic Theory is exactly equivalent to the Field Theory in the infrared. The former can then offer a non-perturbative resummation of the Field Theoretical Feynman diagram expansion, including fields with $0\leq m^2\ll\sqrt \lambda H^2$ for which the perturbation expansion fails at late times.

### ADM with Massless Scalar Field as Internal Time and Wheeler-Dewitt Equation for 4D Supermetric

We study the ADM split with respect to the scalar massless field serving as internal time. The four dimensional hyper-surfaces $\Sigma_{\phi = const}$ span the five dimensional space with the scalar field being the fifth coordinate. As a result we obtain the analog of the Wheeler-DeWitt equation for the 4-dimensional supermetric. We compare the ADM action with the non-compactified Kaluza-Klein action for the same physical space and obtain the equation for the extrinsic curvature and the scalar massless field.

### ADM with Massless Scalar Field as Internal Time and Wheeler-DeWitt Equation for 4D Supermetric [Replacement]

We study the ADM split with respect to the scalar massless field serving as internal time. The four dimensional hyper-surfaces $\Sigma_{\phi = const}$ span the five dimensional space with the scalar field being the fifth coordinate. As a result we obtain the analog of the Wheeler-DeWitt equation for the 4-dimensional supermetric. We compare the ADM action with the non-compactified Kaluza-Klein action for the same physical space and obtain the equation for the extrinsic curvature and the scalar massless field.

### Cosmology in GSG [Cross-Listing]

We describe what cosmology looks like in the context of the geometric theory of gravity (GSG) based on a single scalar field. There are two distinct classes of cosmological solutions. An interesting feature is the possibility of having a bounce without invoking exotic equations of state for the cosmic fluid. We also discuss cosmological perturbation and present the basis of structure formation by gravitational instability in the framework of the geometric scalar gravity.

### Cosmology in GSG

We describe what cosmology looks like in the context of the geometric theory of gravity (GSG) based on a single scalar field. There are two distinct classes of cosmological solutions. An interesting feature is the possibility of having a bounce without invoking exotic equations of state for the cosmic fluid. We also discuss cosmological perturbation and present the basis of structure formation by gravitational instability in the framework of the geometric scalar gravity.

### Einstein-Maxwell gravity coupled to a scalar field in 2+1-dimensions

We consider Einstein-Maxwell-self-interacting scalar field theory described by a potential $V\left( \phi \right)$ in $2+1-$dimensions. The self-interaction potential is chosen to be a highly non-linear double-Liouville type. Exact solutions, including chargeless black holes and singularity-free non-black hole solutions are obtained in this model.

### Stationary axisymmetric spacetimes with a conformally coupled scalar field

Solution generating techniques for general relativity with a conformally (and minimally) coupled scalar field are pushed forward to build a wide class of asymptotically flat, axisymmetric and stationary spacetimes continuously connected to Kerr. This family contains, amongst other things, rotating extensions of the BBMB black hole and also its angular and mass multipolar generalisations. Further addition of NUT charge is also discussed.

### Stationary axisymmetric spacetimes with a conformally coupled scalar field [Cross-Listing]

Solution generating techniques for general relativity with a conformally (and minimally) coupled scalar field are pushed forward to build a wide class of asymptotically flat, axisymmetric and stationary spacetimes continuously connected to Kerr. This family contains, amongst other things, rotating extensions of the BBMB black hole and also its angular and mass multipolar generalisations. Further addition of NUT charge is also discussed.

### Monochromatic neutrinos generated by dark matter and the see-saw mechanism [Cross-Listing]

We study a minimal extension of the Standard Model where a scalar field is coupled to the right handed neutrino responsible for the see-saw mechanism for neutrino masses. In the absence of other couplings, the scalar $A$ has a unique decay mode $A \rightarrow \nu \nu$, $\nu$ being the physical observed light neutrino state. Imposing constraints on neutrino masses $m_\nu$ from atmospheric and solar experiments implies a long lifetime for $A$, much larger than the age of the Universe, making it a natural dark matter candidate. Its lifetime can be as large as $10^{29}$ seconds, and its signature would be a clear monochromatic neutrino signal, which can be observed by IceCube. Under certain conditions, the scalar $A$ may be viewed as a Goldstone mode of a complex scalar field whose vacuum expectation value generates the Majorana mass for $\nu_R$. In this case, we expect the dark matter scalar to have a mass $\lesssim 10$ GeV.

### Monochromatic neutrinos generated by dark matter and the see-saw mechanism

We study a minimal extension of the Standard Model where a scalar field is coupled to the right handed neutrino responsible for the see-saw mechanism for neutrino masses. In the absence of other couplings, the scalar $A$ has a unique decay mode $A \rightarrow \nu \nu$, $\nu$ being the physical observed light neutrino state. Imposing constraints on neutrino masses $m_\nu$ from atmospheric and solar experiments implies a long lifetime for $A$, much larger than the age of the Universe, making it a natural dark matter candidate. Its lifetime can be as large as $10^{29}$ seconds, and its signature would be a clear monochromatic neutrino signal, which can be observed by IceCube. Under certain conditions, the scalar $A$ may be viewed as a Goldstone mode of a complex scalar field whose vacuum expectation value generates the Majorana mass for $\nu_R$. In this case, we expect the dark matter scalar to have a mass $\lesssim 10$ GeV.

### Renormalization, averaging, conservation laws and AdS (in)stability [Replacement]

We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.

### Renormalization, averaging, conservation laws and AdS (in)stability [Replacement]

We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the obvious energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.

### Renormalization, averaging, conservation laws and AdS (in)stability

We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the obvious energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.

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