# Posts Tagged scalar field

## Recent Postings from scalar field

### Renormalization group approach to scalar quantum electrodynamics on de Sitter [Cross-Listing]

We consider the quantum loop effects in scalar electrodynamics on de Sitter space by making use of the functional renormalization group approach. We first integrate out the photon field, which can be done exactly to leading (zeroth) order in the gradients of the scalar field, thereby making this method suitable for investigating the dynamics of the infrared sector of the theory. Assuming that the scalar remains light we then apply the functional renormalization group methods to the resulting effective scalar theory and focus on investigating the effective potential, which is the leading order contribution in the gradient expansion of the effective action. We find symmetry restoration at a critical renormalization scale $\kappa=\kappa_{\rm cr}$ much below the Hubble scale $H$. When compared with the results of Serreau and Guilleux [arXiv:1306.3846 [hep-th], arXiv:1506.06183 [hep-th]] we find that the photon facilitates symmetry restoration such that it occurs at an RG scale $\kappa_{\rm cr}$ that is higher than in the case of a pure scalar theory. The true effective potential is recovered when $\kappa\rightarrow 0$ and in that limit one obtains the results that agree with those of stochastic inflation, provided one interprets it in the sense as advocated by Lazzari and Prokopec [arXiv:1304.0404 [hep-th]].

### Universality in generalized models of inflation [Cross-Listing]

We show that the cosmological evolution of a scalar field with non standard kinetic term can be described in terms of a Renormalization Group Equation. In this framework inflation corresponds to the slow evolution in a neighborhood of a fixed point and universality classes for inflationary models can be naturally introduced. Using some examples we show the application of the formalism. The predicted values for the speed of sound $c_s$ and for the amount of non-Gaussianities produced in these models are discussed. In particular, we show that it is possible to introduce models with $c_s^2 \neq 1$ that can be in agreement with present cosmological observations.

### Reconstructions of the dark-energy equation of state and the inflationary potential

We use a new mathematical approach to reconstruct the equation of state and the inflationary potential for the inflaton field from the spectral indices for the density perturbations $n_{s}$ and the tensor to scalar ratio $r$. According to the astronomical data, the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that $n_{s}-1=h\left( r\right)$. For the function $h\left( r\right)$, we consider three cases, where $h\left( r\right)$ is constant, linear and quadratic, respectively. From this, we derive second-order equations whose solutions provide us with the explicit forms for the expansion scale-factor, the scalar-field potential, and the effective equation of state for the scalar field. Finally, we show that for there exist mappings which transform one cosmological solution to another and allow new solutions to be generated from existing ones.

### O($N$) Invariance of the Multi-Field Bounce [Cross-Listing]

In his 1977 paper on vacuum decay in field theory: The Fate of the False Vacuum, Coleman considered the problem of a single scalar field and assumed that the minimum action tunnelling field configuration, the bounce, is invariant under O(4) rotations in Euclidean space. A proof of the O(4) invariance of the bounce was provided later that year by Coleman, Glaser, and Martin, who further extended the proof to $N$ Euclidean dimensions. Their proof holds for $N>2$ and was again restricted non-trivially to the case of a single scalar field. As far as we know a proof of O($N$) invariance of the bounce for the tunnelling problem with multiple scalar fields has not been reported, even though it was assumed in many works since, being of phenomenological interest. In the current paper we provide such proof. More precisely, we show that if a non-trivial minimum action solution of the Euclidean field equations exists, then it is O($N$) symmetric.

### Stealths on $(1+1)$-dimensional dilatonic gravity

We study gravitational stealth configurations emerging on a charged dilatonic $(1+1)$-D black hole spacetime. We accomplish this by considering the coupling of a non-minimally scalar field $\phi$ and a self-interacting scalar field $\Psi$ living in a $(1+1)$-D charged black hole background. In addition, the self-interacting potential for $\Psi$ is obtained which exhibits transitions for some specific values of the non-minimal parameter. Atypically, we found that the solutions for these stealth scalar fields do not have a dependence on the temporal coordinate.

### Casimir effect for Elko spinor field

The Casimir effect for the Elko spinor field in $3+1$ dimension is obtained using Dirichlet boundary conditions. It is shown the existence of a repulsive force four times greater than the case of the scalar field. The precise reason for such differences are highlighted and interpreted, as well as the right parallel of the Casimir effect due to scalar and fermionic fields.

### Weakly dynamic dark energy via metric-scalar couplings with torsion

We study the dynamical aspects of dark energy in the context of a non-minimally coupled scalar field with curvature and torsion. Whereas the scalar field acts as the source of the trace mode of torsion, a suitable constraint on the pseudo-trace of the latter provides a mass term for the scalar field in the effective action. In the equivalent scalar-tensor framework, we find explicit cosmological solutions suitable for describing dark energy in both Einstein and Jordan frames. We demand the dynamical evolution of the dark energy to be weak enough, so that the present-day values of the cosmological parameters could be estimated keeping them within the confidence limits set for the standard $\L$CDM model from recent observations. For such estimates, we examine the variations of the effective matter density and the dark energy equation of state over different redshift ranges. In spite of being weakly dynamic, the dark energy component here differs significantly from the cosmological constant, both in characteristics and features, for e.g. it interacts with the cosmological (dust) fluid in the Einstein frame, and crosses the phantom barrier in the Jordan frame. We also obtain the upper bounds on the torsion mode parameters and the lower bound on the effective Brans-Dicke parameter. The latter turns out to be fairly large, and in agreement with the local gravity constraints, which therefore come in support of our analysis.

### Exact solutions for scalar field cosmology in f(R) gravity

We look for exact solutions in scalar field cosmology. To achieve this we use $f(R)$ modified gravity with a scalar field and do not specify the the form of the $f(R)$ function. In particular, we study Friedmann universe assuming that acceleration of the scalar curvature is negligible. We first present solutions for special cases and then the general solution. Using initial conditions which represent the universe at the present epoch, we evaluated the constants of integration. This allows for the comparison of the scale factor in the new solutions with that of the $\Lambda CDM$ solution, thereby affecting the age of the universe in $f(R)$ gravity.

### Delta isobars in relativistic mean-field models with $\sigma$-scaled hadron masses and couplings

We extend the relativistic mean-field models with hadron masses and meson-baryon coupling constants dependent on the scalar $\sigma$ field, studied previously to incorporate $\Delta(1232)$ baryons. Available empirical information is analyzed to put constraints on the couplings of $\Delta$s with meson fields. Conditions for the appearance of $\Delta$s are studied. We demonstrate that with inclusion of the $\Delta$s our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars, the direct Urca and the gravitational-baryon mass ratio constraints.

### Delta isobars in relativistic mean-field models with $\sigma$-scaled hadron masses and couplings [Cross-Listing]

We extend the relativistic mean-field models with hadron masses and meson-baryon coupling constants dependent on the scalar $\sigma$ field, studied previously to incorporate $\Delta(1232)$ baryons. Available empirical information is analyzed to put constraints on the couplings of $\Delta$s with meson fields. Conditions for the appearance of $\Delta$s are studied. We demonstrate that with inclusion of the $\Delta$s our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars, the direct Urca and the gravitational-baryon mass ratio constraints.

### Spherically symmetric solution of the Weyl-Dirac theory of gravitation and possible influence of dark matter on the interplanetary spacecraft motion

The Poincare and Poincare-Weyl gauge theories of gravitation with Lagrangians quadratic on curvature and torsion in post-Riemannian spaces with the Dirac scalar field is discussed in a historical aspect. The various hypothesizes concerning the models of a dark matter with the help of a scalar field are considered. The new conformal Weyl-Dirac theory of gravitation is proposed, which is a gravitational theory in Cartan-Weyl space-time with the Dirac scalar field representing the dark matter model. A static spherically symmetric solution of the field equations in vacuum for a central compact mass is obtained as the metrics conformal to the Yilmaz-Rosen metrics. On the base of this solution one considers a radial movement of an interplanetary spacecraft starting from the Earth. Using the Newton approximation one obtains that the asymptotic line-of-sight velocity in this case depends from the parameters of the solution, and therefore one can obtain on basis of the observable data the values of these parameters.

### Black hole hair formation in shift-symmetric generalised scalar-tensor gravity [Cross-Listing]

A linear coupling between a scalar field and the Gauss-Bonnet invariant is the only known interaction term between a scalar and the metric that: respects shift symmetry; does not lead to higher order equations; inevitably introduces black hole hair in asymptotically flat, 4-dimensional spacetimes. Here we focus on the simplest theory that includes such a term and we explore the dynamical formation of scalar hair. In particular, we work in the decoupling limit that neglects the backreaction of the scalar onto the metric and evolve the scalar configuration numerically in the background of a Schwarzschild black hole or a collapsing dust star described by the Oppenheimer-Snyder solution. For all types of initial data that we consider, the scalar relaxes at late times to the known, static, analytic configuration that is associated with a hairy, spherically symmetric black hole. This suggests that the corresponding black hole solutions are indeed endpoints of collapse.

### Black hole hair formation in shift-symmetric generalised scalar-tensor gravity [Cross-Listing]

A linear coupling between a scalar field and the Gauss-Bonnet invariant is the only known interaction term between a scalar and the metric that: respects shift symmetry; does not lead to higher order equations; inevitably introduces black hole hair in asymptotically flat, 4-dimensional spacetimes. Here we focus on the simplest theory that includes such a term and we explore the dynamical formation of scalar hair. In particular, we work in the decoupling limit that neglects the backreaction of the scalar onto the metric and evolve the scalar configuration numerically in the background of a Schwarzschild black hole or a collapsing dust star described by the Oppenheimer-Snyder solution. For all types of initial data that we consider, the scalar relaxes at late times to the known, static, analytic configuration that is associated with a hairy, spherically symmetric black hole. This suggests that the corresponding black hole solutions are indeed endpoints of collapse.

### Black hole hair formation in shift-symmetric generalised scalar-tensor gravity

A linear coupling between a scalar field and the Gauss-Bonnet invariant is the only known interaction term between a scalar and the metric that: respects shift symmetry; does not lead to higher order equations; inevitably introduces black hole hair in asymptotically flat, 4-dimensional spacetimes. Here we focus on the simplest theory that includes such a term and we explore the dynamical formation of scalar hair. In particular, we work in the decoupling limit that neglects the backreaction of the scalar onto the metric and evolve the scalar configuration numerically in the background of a Schwarzschild black hole or a collapsing dust star described by the Oppenheimer-Snyder solution. For all types of initial data that we consider, the scalar relaxes at late times to the known, static, analytic configuration that is associated with a hairy, spherically symmetric black hole. This suggests that the corresponding black hole solutions are indeed endpoints of collapse.

### Dynamical dark energy: scalar fields and running vacuum [Replacement]

Recent analyses in the literature suggest that the concordance $\Lambda$CDM model with rigid cosmological term, $\Lambda=$const., may not be the best description of the cosmic acceleration. The class of "running vacuum models", in which $\Lambda=\Lambda(H)$ evolves with the Hubble rate, has been shown to fit the string of $SNIa+BAO+H(z)+LSS+CMB$ data significantly better than the $\Lambda$CDM. Here we provide further evidence on the time-evolving nature of the dark energy (DE) by fitting the same cosmological data in terms of scalar fields. As a representative model we use the original Peebles & Ratra potential, $V\propto\Phi^{-\alpha}$. We find clear signs of dynamical DE at $\sim 4\sigma$ c.l., thus reconfirming through a nontrivial scalar field approach the strong hints formerly found with other models and parametrizations.

### Dynamical dark energy: scalar fields and running vacuum [Replacement]

Recent analyses in the literature suggest that the concordance $\Lambda$CDM model with rigid cosmological term, $\Lambda=$const., may not be the best description of the cosmic acceleration. The class of "running vacuum models", in which $\Lambda=\Lambda(H)$ evolves with the Hubble rate, has been shown to fit the string of $SNIa+BAO+H(z)+LSS+CMB$ data significantly better than the $\Lambda$CDM. Here we provide further evidence on the time-evolving nature of the dark energy (DE) by fitting the same cosmological data in terms of scalar fields. As a representative model we use the original Peebles & Ratra potential, $V\propto\Phi^{-\alpha}$. We find clear signs of dynamical DE at $\sim 4\sigma$ c.l., thus reconfirming through a nontrivial scalar field approach the strong hints formerly found with other models and parametrizations.

### Dynamical dark energy: scalar fields and running vacuum [Replacement]

Recent analyses in the literature suggest that the concordance $\Lambda$CDM model with rigid cosmological term, $\Lambda=$const., may not be the best description of the cosmic acceleration. The class of "running vacuum models", in which $\Lambda=\Lambda(H)$ evolves with the Hubble rate, has been shown to fit the string of $SNIa+BAO+H(z)+LSS+CMB$ data significantly better than the $\Lambda$CDM. Here we provide further evidence on the time-evolving nature of the dark energy (DE) by fitting the same cosmological data in terms of scalar fields. As a representative model we use the original Peebles & Ratra potential, $V\propto\Phi^{-\alpha}$. We find clear signs of dynamical DE at $\sim 4\sigma$ c.l., thus reconfirming through a nontrivial scalar field approach the strong hints formerly found with other models and parametrizations.

### Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics [Replacement]

The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invariance under the spatial Killing symmetries, unitarity of the dynamics selects a unique Fock representation for the canonical commutation relations, up to unitary equivalence. In this work, we generalize these results to anisotropic spacetimes with shear, which are therefore not conformally symmetric, by considering the case of a free scalar field in a Bianchi I cosmology.

### Inflation and reheating in scale-invariant scalar-tensor gravity [Replacement]

We consider the scale-invariant inflationary model studied in [1]. The Lagrangian includes all the scale-invariant operators that can be built with combinations of $R, R^{2}$ and one scalar field. The equations of motion show that the symmetry is spontaneously broken after an arbitrarily long inflationary period and a fundamental mass scale is generated. Upon symmetry breaking, and in the Jordan frame, both Hubble function and the scalar field undergo damped oscillations that can eventually amplify Standard Model fields and reheat the Universe. In the present work, we study in detail inflation and the reheating mechanism of this model in the Einstein frame and we compare some of the results with the latest observational data.

### Inflation and reheating in scale-invariant scalar-tensor gravity [Cross-Listing]

We consider the scale-invariant inflationary model studied in [1]. The Lagrangian includes all the scale-invariant operators that can be built with combinations of $R, R^{2}$ and one scalar field. The equations of motion show that the symmetry is spontaneously broken after an arbitrarily long inflationary period and a fundamental mass scale is generated. Upon symmetry breaking, and in the Jordan frame, both Hubble function and the scalar field undergo damped oscillations that can eventually amplify Standard Model fields and reheat the Universe. In the present work, we study in detail inflation and the reheating mechanism of this model in the Einstein frame and we compare some of the results with the latest observational data.

### Inflation and reheating in scale-invariant scalar-tensor gravity [Replacement]

We consider the scale-invariant inflationary model studied in [1]. The Lagrangian includes all the scale-invariant operators that can be built with combinations of $R, R^{2}$ and one scalar field. The equations of motion show that the symmetry is spontaneously broken after an arbitrarily long inflationary period and a fundamental mass scale is generated. Upon symmetry breaking, and in the Jordan frame, both Hubble function and the scalar field undergo damped oscillations that can eventually amplify Standard Model fields and reheat the Universe. In the present work, we study in detail inflation and the reheating mechanism of this model in the Einstein frame and we compare some of the results with the latest observational data.

### Inflation and reheating in scale-invariant scalar-tensor gravity

We consider the scale-invariant inflationary model studied in [1]. The Lagrangian includes all the scale-invariant operators that can be built with combinations of $R, R^{2}$ and one scalar field. The equations of motion show that the symmetry is spontaneously broken after an arbitrarily long inflationary period and a fundamental mass scale is generated. Upon symmetry breaking, and in the Jordan frame, both Hubble function and the scalar field undergo damped oscillations that can eventually amplify Standard Model fields and reheat the Universe. In the present work, we study in detail inflation and the reheating mechanism of this model in the Einstein frame and we compare some of the results with the latest observational data.

### Inflation and reheating in scale-invariant scalar-tensor gravity [Cross-Listing]

We consider the scale-invariant inflationary model studied in [1]. The Lagrangian includes all the scale-invariant operators that can be built with combinations of $R, R^{2}$ and one scalar field. The equations of motion show that the symmetry is spontaneously broken after an arbitrarily long inflationary period and a fundamental mass scale is generated. Upon symmetry breaking, and in the Jordan frame, both Hubble function and the scalar field undergo damped oscillations that can eventually amplify Standard Model fields and reheat the Universe. In the present work, we study in detail inflation and the reheating mechanism of this model in the Einstein frame and we compare some of the results with the latest observational data.

### Greybody factor of scalar field from Reissner-Nordstrom-de Sitter black hole

In this work we derive a general expression for the greybody factor of non-minimally coupled scalar fields in Reissner-Nordstr{\"o}m-de Sitter spacetime in low frequency approximation. In particular case of zero momentum, greybody factor tends to zero in low frequency limit as frequency squared goes to zero for non-vanishing coupling. We also elaborate the significance of the results by giving formulae of differential energy rate and general absorption cross section. The greybody factor gives insight into the spectrum of Hawking radiations.

### Greybody factor of scalar field from Reissner-Nordstrom-de Sitter black hole [Cross-Listing]

In this work we derive a general expression for the greybody factor of non-minimally coupled scalar fields in Reissner-Nordstr{\"o}m-de Sitter spacetime in low frequency approximation. In particular case of zero momentum, greybody factor tends to zero in low frequency limit as frequency squared goes to zero for non-vanishing coupling. We also elaborate the significance of the results by giving formulae of differential energy rate and general absorption cross section. The greybody factor gives insight into the spectrum of Hawking radiations.

### Particle Creation in Bouncing Cosmologies [Cross-Listing]

We investigate scalar particle creation in a set of bouncing models where the bounce occurs due to quantum cosmological effects described by the Wheeler-DeWitt equation. The scalar field can be either conformally or minimally coupled to gravity, and it can be massive or massless, without self interaction. The analysis is made for models containing a single radiation fluid, and for the more realistic case of models containing the usual observed radiation and dust fluids, which can fit most of the observed features of our Universe, including an almost scale invariant power spectrum of scalar cosmological perturbations. In the conformal coupling case, the particle production is negligible. In the minimal coupling case, for massive particles, the results point to the same physical conclusion within observational constraints: particle production is most important at the bounce energy scale, and it is not sensitive neither to its mass nor whether there is dust in the background model. The only caveat is the case where the particle mass is larger than the bounce energy scale. On the other hand, the energy density of produced massive particles depend on their masses and the energy scale of the bounce. For very large masses and deep bounces, this energy density may overcome that of the background. In the case of massless particles, the energy density of produced particles can become comparable to the background energy density only for bounces occurring at energy scales comparable to the Planck scale or above, which lies beyond the scope of this paper: we expect that the simple Wheeler-DeWitt approach we are using should be valid only at scales some few orders of magnitude below the Planck energy. Nevertheless, in the case in which dust is present, there is an infrared divergence, which becomes important only for scales much larger than today's Hubble radius.

### Particle Creation in Bouncing Cosmologies [Cross-Listing]

We investigate scalar particle creation in a set of bouncing models where the bounce occurs due to quantum cosmological effects described by the Wheeler-DeWitt equation. The scalar field can be either conformally or minimally coupled to gravity, and it can be massive or massless, without self interaction. The analysis is made for models containing a single radiation fluid, and for the more realistic case of models containing the usual observed radiation and dust fluids, which can fit most of the observed features of our Universe, including an almost scale invariant power spectrum of scalar cosmological perturbations. In the conformal coupling case, the particle production is negligible. In the minimal coupling case, for massive particles, the results point to the same physical conclusion within observational constraints: particle production is most important at the bounce energy scale, and it is not sensitive neither to its mass nor whether there is dust in the background model. The only caveat is the case where the particle mass is larger than the bounce energy scale. On the other hand, the energy density of produced massive particles depend on their masses and the energy scale of the bounce. For very large masses and deep bounces, this energy density may overcome that of the background. In the case of massless particles, the energy density of produced particles can become comparable to the background energy density only for bounces occurring at energy scales comparable to the Planck scale or above, which lies beyond the scope of this paper: we expect that the simple Wheeler-DeWitt approach we are using should be valid only at scales some few orders of magnitude below the Planck energy. Nevertheless, in the case in which dust is present, there is an infrared divergence, which becomes important only for scales much larger than today's Hubble radius.

### The Qualitative and Numerical Analysis of the Cosmological Model Based on Phantom Scalar Field with Self

In this paper we investigate the asymptotic behavior of the cosmological model based on phantom scalar field on the ground of qualitative analysis of the system of the cosmological model's differential equations and show that as opposed to models with classical scalar field, such models have stable asymptotic solutions with constant value of the potential both in infinite past and infinite future. We also develop numerical models of the cosmological evolution models with phantom scalar field in this paper. {\bf keywords}: cosmological model, phantom scalar field, quality analysis, asymptotic behavior, numerical simulation, numerical gravitation.\\ {\bf PACS}: 04.20.Cv, 98.80.Cq, 96.50.S 52.27.Ny

### Reconstruction of the Scalar Field Potential in Inflationary Models with a Gauss-Bonnet term

We study inflationary models with a Gauss-Bonnet term to reconstruct the scalar field potentials and the Gauss-Bonnet coupling functions from the observable quantities. Using the observationally favored relations for both $n_s$ and $r$, we derive the expressions for both the scalar field potentials and the coupling functions. The implication of the blue-tilted spectrum, $n_t>0$, of the primordial tensor fluctuations is discussed for the reconstructed configurations of the scalar field potential and the Gauss-Bonnet coupling.

### Reconstruction of the Scalar Field Potential in Inflationary Models with a Gauss-Bonnet term [Cross-Listing]

We study inflationary models with a Gauss-Bonnet term to reconstruct the scalar field potentials and the Gauss-Bonnet coupling functions from the observable quantities. Using the observationally favored relations for both $n_s$ and $r$, we derive the expressions for both the scalar field potentials and the coupling functions. The implication of the blue-tilted spectrum, $n_t>0$, of the primordial tensor fluctuations is discussed for the reconstructed configurations of the scalar field potential and the Gauss-Bonnet coupling.

### Reconstruction of the Scalar Field Potential in Inflationary Models with a Gauss-Bonnet term [Cross-Listing]

We study inflationary models with a Gauss-Bonnet term to reconstruct the scalar field potentials and the Gauss-Bonnet coupling functions from the observable quantities. Using the observationally favored relations for both $n_s$ and $r$, we derive the expressions for both the scalar field potentials and the coupling functions. The implication of the blue-tilted spectrum, $n_t>0$, of the primordial tensor fluctuations is discussed for the reconstructed configurations of the scalar field potential and the Gauss-Bonnet coupling.

### Numerical study of the gravitational shock wave inside a spherical charged black hole

We numerically investigate the interior of a four-dimensional, asymptotically flat, spherically symmetric charged black hole perturbed by a scalar field $\Phi$. Previous study by Marolf and Ori indicated that late infalling observers will encounter an effective shock wave as they approach the left portion of the inner horizon. This shock manifests itself as a sudden change in the values of various fields, within a tremendously short interval of proper time $\tau$ of the infalling observers. We confirm this prediction numerically for both test and self-gravitating scalar field perturbations. In both cases we demonstrate the effective shock in the scalar field by exploring $\Phi(\tau)$ along a family of infalling timelike geodesics. In the self-gravitating case we also demonstrate the shock in the area coordinate $r$ by exploring $r(\tau)$. We confirm the theoretical prediction concerning the shock sharpening rate, which is exponential in the time of infall into the black hole. In addition we numerically probe the early stages of shock formation. We also employ a family of null (rather than timelike) ingoing geodesics to probe the shock in $r$. We use a finite-difference numerical code with double-null coordinates combined with a recently developed adaptive gauge method in order to solve the (Einstein + scalar) field equations and to evolve the spacetime (and scalar field) $-$ from the region outside the black hole down to the vicinity of the Cauchy horizon and the spacelike $r=0$ singularity.

### Spectator fields and their imprints on the Cosmic Microwave Background

When a subdominant light scalar field ends slow roll during inflation, but well after the Hubble exit of the pivot scales, it may determine the cosmological perturbations. This thesis investigates how such a scalar field, the spectator, may leave its impact on the Cosmic Microwave Background (CMB) radiation and be consequently constrained. We first introduce the observables of the CMB, namely the power spectrum $P_\zeta$, spectral index $n_s$ and its running $dn_s/d\ln k$, the non-Gaussianities $f_{NL}$, $g_{NL}$ and $\tau_{NL}$, and the lack of isocurvature and polarization modes. Based on these studies, we derive the cosmological predictions for the spectator scenario, revealing its consistency with the CMB for inflection point potentials, hyperbolic tangent potentials, and those with a sudden phase transition. In the end, we utilize the spectator scenario to explain the CMB power asymmetry, with a brief tachyonic fast-roll phase.

### Particle production in a gravitational wave background

We study the possibility that massless particles, such as photons, are produced by a gravitational wave. That such a process should occur is implied by tree-level, Feynman diagrams such as two gravitons turning into two photons {\it i.e.} $g + g \rightarrow \gamma + \gamma$. Here we calculate the rate at which a gravitational wave creates a massless, scalar field. This is done by placing the scalar field in the background of a plane gravitational wave and calculating the 4-current of the scalar field. Even in the vacuum limit of the scalar field it has a non-zero vacuum expectation value (similar to what occurs in the Higgs mechanism) and a non-zero current. We associate this with the production of scalar field quanta by the gravitational field. This effect has potential consequences for the attenuation of gravitational waves since the massless particles are being produced at the expense of the gravitational field. This is related to the (time-dependent) Schwinger effect but with the electric field replaced by the the gravitational wave background and the electrons/positrons replaced by massless scalar "photons". Since the produced scalar quanta are massless there is no exponential suppression as occurs in the Schwinger effect due to the electron mass.

### Gravitomagnetic effects in quadratic gravity with a scalar field

The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.

### Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions [Replacement]

We consider a real, massive scalar field on ${\rm PAdS}_{d+1}$, the Poincar\'e domain of the $(d+1)$-dimensional AdS spacetime. We first determine all admissible boundary conditions that can be applied on the conformal boundary, noting that there exist instances where "bound states" solutions are present. Then, we address the problem of constructing the two-point function for the ground state satisfying those boundary conditions, finding ultimately an explicit closed form. In addition, we investigate the singularities of the resulting two-point functions, showing that they are consistent with the requirement of being of Hadamard form in every globally hyperbolic subregion of ${\rm PAdS}_{d+1}$ and proposing a new definition of Hadamard states which applies to ${\rm PAdS}_{d+1}$.

### Scalar field with the source in the form of the stress-energy tensor trace as a dark energy model

We consider a scalar-tensor theory of gravitation with the scalar source being the trace of the stress-energy tensor of the scalar field itself and matter. We obtain an example of a numerical solution of the cosmological equations which shows that under some special choice of the scalar parameters, there exists a slow-roll regime in which the modern values of the Hubble and deceleration parameters may be obtained.

### Screening three-form fields

Screening mechanisms for a three-form field around a dense source such as the Sun are investigated. Working with the dual vector, we can obtain a thin-shell where field interactions are short range. The field outside the source adopts the configuration of a dipole which is a manifestly distinct behaviour from the one obtained with a scalar field or even a previously proposed vector field model. We identify the region of parameter space where this model satisfies present solar system tests.

### Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity

We study soliton and black hole solutions of Einstein charged scalar field theory in cavity. We examine the effect of introducing a scalar field mass on static, spherically symmetric solutions of the field equations. We focus particularly on the spaces of soliton and black hole solutions, as well as studying their stability under linear, spherically symmetric perturbations of the metric, electromagnetic field, and scalar field.

### Super-Planckian Spatial Field Variations and Quantum Gravity [Cross-Listing]

We study scenarios where a scalar field has a spatially varying vacuum expectation value such that the total field variation is super-Planckian. We focus on the case where the scalar field controls the coupling of a U(1) gauge field, which allows us to apply the Weak Gravity Conjecture to such configurations. We show that this leads to evidence for a conjectured property of quantum gravity that as a scalar field variation in field space asymptotes to infinity there must exist an infinite tower of states whose mass decreases as an exponential function of the scalar field variation. We determine the rate at which the mass of the states reaches this exponential behaviour showing that it occurs quickly after the field variation passes the Planck scale.

### Dark Energy and Dark Matter in a Model of an Axion Coupled to a Non-Abelian Gauge Field [Cross-Listing]

We study cosmological field configurations (solutions) in a model in which the pseudo-scalar phase of a complex field couples to the Pontryagin density of a massive non-abelian gauge field, in analogy to how the Peccei-Quinn axion field couples to the $SU(3)$-color gauge field of QCD. Assuming that the self-interaction potential of the complex scalar field has the typical {\it Mexican hat} form, we find that the radial fluctuations of this field can act as {\it Dark Matter}, while its phase may give rise to tracking {\it Dark Energy}. In our model, Dark-Energy domination will, however, not continue for ever. A new component of dark matter, namely the one originating from the gauge field, will dominate in the future.

### Evolution of scalar fields surrounding black holes on compactified constant mean curvature hypersurfaces

Motivated by the goal for high accuracy modeling of gravitational radiation emitted by isolated systems, recently, there has been renewed interest in the numerical solution of the hyperboloidal initial value problem for Einstein's field equations in which the outer boundary of the numerical grid is placed at null infinity. In this article, we numerically implement the tetrad-based approach presented in [J.M. Bardeen, O. Sarbach, and L.T. Buchman, Phys. Rev. D 83, 104045 (2011)] for a spherically symmetric, minimally coupled, self-gravitating scalar field. When this field is massless, the evolution system reduces to a regular, first-order symmetric hyperbolic system of equations for the conformally rescaled scalar field which is coupled to a set of singular elliptic constraints for the metric coefficients. We show how to solve this system based on a numerical finite-difference approximation, obtaining stable numerical evolutions for initial black hole configurations which are surrounded by a spherical shell of scalar field, part of which disperses to infinity and part of which is accreted by the black hole. As a non-trivial test, we study the tail decay of the scalar field along different curves, including one along the marginally trapped tube, one describing the world line of a time-like observer at a finite radius outside the horizon, and one corresponding to a generator of null infinity. Our results are in agreement with the usual power-law decay predicted by the linearized theory and with previous numerical simulations of the nonlinear equations.

### Jacobi stability analysis of scalar field models with minimal coupling to gravity in a cosmological background [Cross-Listing]

We perform the study of the stability of the cosmological scalar field models, by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. In the KCC approach we describe the time evolution of the scalar field cosmologies in geometric terms, by performing a "second geometrization", by considering them as paths of a semispray. By introducing a non-linear connection and a Berwald type connection associated to the Friedmann and Klein-Gordon equations, five geometrical invariants can be constructed, with the second invariant giving the Jacobi stability of the cosmological model. We obtain all the relevant geometric quantities, and we formulate the condition of the Jacobi stability for scalar field cosmologies in the second order formalism. As an application of the developed methods we consider the Jacobi stability properties of the scalar fields with exponential and Higgs type potential. We find that the Universe dominated by a scalar field exponential potential is in Jacobi unstable state, while the cosmological evolution in the presence of Higgs fields has alternating stable and unstable phases. By using the standard first order formulation of the cosmological models as dynamical systems we have investigated the stability of the phantom quintessence and tachyonic scalar fields, by lifting the first order system to the tangent bundle. It turns out that in the presence of a power law potential both these models are Jacobi unstable during the entire cosmological evolution.

### Jacobi stability analysis of scalar field models with minimal coupling to gravity in a cosmological background

We perform the study of the stability of the cosmological scalar field models, by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. In the KCC approach we describe the time evolution of the scalar field cosmologies in geometric terms, by performing a "second geometrization", by considering them as paths of a semispray. By introducing a non-linear connection and a Berwald type connection associated to the Friedmann and Klein-Gordon equations, five geometrical invariants can be constructed, with the second invariant giving the Jacobi stability of the cosmological model. We obtain all the relevant geometric quantities, and we formulate the condition of the Jacobi stability for scalar field cosmologies in the second order formalism. As an application of the developed methods we consider the Jacobi stability properties of the scalar fields with exponential and Higgs type potential. We find that the Universe dominated by a scalar field exponential potential is in Jacobi unstable state, while the cosmological evolution in the presence of Higgs fields has alternating stable and unstable phases. By using the standard first order formulation of the cosmological models as dynamical systems we have investigated the stability of the phantom quintessence and tachyonic scalar fields, by lifting the first order system to the tangent bundle. It turns out that in the presence of a power law potential both these models are Jacobi unstable during the entire cosmological evolution.

### Jacobi stability analysis of scalar field models with minimal coupling to gravity in a cosmological background [Cross-Listing]

We perform the study of the stability of the cosmological scalar field models, by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. In the KCC approach we describe the time evolution of the scalar field cosmologies in geometric terms, by performing a "second geometrization", by considering them as paths of a semispray. By introducing a non-linear connection and a Berwald type connection associated to the Friedmann and Klein-Gordon equations, five geometrical invariants can be constructed, with the second invariant giving the Jacobi stability of the cosmological model. We obtain all the relevant geometric quantities, and we formulate the condition of the Jacobi stability for scalar field cosmologies in the second order formalism. As an application of the developed methods we consider the Jacobi stability properties of the scalar fields with exponential and Higgs type potential. We find that the Universe dominated by a scalar field exponential potential is in Jacobi unstable state, while the cosmological evolution in the presence of Higgs fields has alternating stable and unstable phases. By using the standard first order formulation of the cosmological models as dynamical systems we have investigated the stability of the phantom quintessence and tachyonic scalar fields, by lifting the first order system to the tangent bundle. It turns out that in the presence of a power law potential both these models are Jacobi unstable during the entire cosmological evolution.

### Evidence of Cosmic Strings by Observation of the Alignment of Quasar Polarization Axes [Replacement]

We find an approximate bounded wavelike solution to second order of the coupled Einstein-scalar gauge field on a warped five dimensional axially symmetric brane world spacetime, where the standard model matter field resides on the brane and gravity can propagate into the bulk. For a zero effective cosmological constant, one can explain the self-acceleration of our universe by the projection of the five dimensional Weyl tensor on the brane. The self-gravitating U(1) scalar gauge field builds up a huge mass per unit length in the bulk and can induce massive Kaluza-Klein-modes felt on the brane and cause fluctuations on this hyper surface. Due to the warp factor, disturbances don't fade away during the expansion of the universe. The late-time behavior could deviate significant from the standard evolution of the universe. Disturbances are no longer axially symmetric. It turns out, by using a multiple-scale method, that equations for the first and second order perturbations of the metric and scalar-gauge field show a spectrum of polar-angle dependent wavelike modes with extremal values dependent of the winding numbers of the background, first and second order perturbations of the scalar field respectively. This result can be used to explain the recently found spooky alignment of the rotation axes of quasars over large distances.

### Evidence of Cosmic Strings by Observation of the Alignment of Quasar Polarization Axes [Replacement]

We find an approximate bounded wavelike solution to second order of the coupled Einstein-scalar gauge field on a warped five dimensional axially symmetric brane world spacetime, where the standard model matter field resides on the brane and gravity can propagate into the bulk. For a zero effective cosmological constant, one can explain the self-acceleration of our universe by the projection of the five dimensional Weyl tensor on the brane. The self-gravitating U(1) scalar gauge field builds up a huge mass per unit length in the bulk and can induce massive Kaluza-Klein-modes felt on the brane and cause fluctuations on this hyper surface. Due to the warp factor, disturbances don't fade away during the expansion of the universe. The late-time behavior could deviate significant from the standard evolution of the universe. Disturbances are no longer axially symmetric. It turns out, by using a multiple-scale method, that equations for the first and second order perturbations of the metric and scalar-gauge field show a spectrum of polar-angle dependent wavelike modes with extremal values dependent of the winding numbers of the background, first and second order perturbations of the scalar field respectively. This result can be used to explain the recently found spooky alignment of the rotation axes of quasars over large distances.

### Inflation with teleparallelism: Can torsion generate primordial fluctuations without local Lorentz symmetry?

Arbitrary generalization to the teleparallel equivalent of general relativity loses local Lorentz invariance to reparametrize the orthonormal coordinate system and gives rise to asymmetry field equations. We investigate consequences of local Lorentz violation to primordial fluctuations in extended single field inflationary models based on the scalar-tensor formulation of the torsion scalar $T$ that effectively includes $f(T)$ gravity as a special case. We show that despite some asymmetry part of the field equations are removed in a spatially homogeneous and isotropic cosmic background, no subhorizon scalar-perturbation mode can survive by the time of horizon crossing. As a result, any scalar field mediated in torsion cannot generate enough primordial density inhomogeneity alone, even if it brings some de Sitter background solutions in generalized teleparallel gravity.

### Radiation Like Scalar Field and Gauge Fields in Cosmology for a theory with Dynamical Time [Cross-Listing]

Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spacial curvature of the universe. This is because only such $k=0$ radiation solutions poses a homothetic Killimg vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved space time, and there are no deviations from standard gauge filed equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang Mills equations, for more general space times.

### Radiation Like Scalar Field and Gauge Fields in Cosmology for a theory with Dynamical Time

Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spacial curvature of the universe. This is because only such $k=0$ radiation solutions poses a homothetic Killimg vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved space time, and there are no deviations from standard gauge filed equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang Mills equations, for more general space times.