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arXiv2013

Self-completeness and spontaneous dimensional reduction

A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity -- spontaneous dimensional reduction and self-completeness. The former suggests the spacetime background at the Planck scale may be effectively two-dimensional, while the latter implies a condition of maximal compression of matter by the formation of an event horizon for Planckian scattering. We generalize such a result to an arbitrary number of dimensions, and show that gravity in higher than four dimensions remains self-complete, but in lower dimensions it is not. In such a way we established an "exclusive disjunction" or "exclusive or" (XOR) between the occurrence of self-completeness and dimensional reduction, with the goal of actually reducing the unknowns for the scenario of the physics at the Planck scale. Potential phenomenological implications of this result are considered by studying the case of a two-dimensional dilaton gravity model resulting from dimensional reduction of Einstein gravity.

hep-th↗

arXiv2013

Endomorphisms and automorphisms of locally covariant quantum field theories

In the framework of locally covariant quantum field theory, a theory is described as a functor from a category of spacetimes to a category of *-algebras. It is proposed that the global gauge group of such a theory can be identified as the group of automorphisms of the defining functor. Consequently, multiplets of fields may be identified at the functorial level. It is shown that locally covariant theories that obey standard assumptions in Minkowski space, including energy compactness, have no proper endomorphisms (i.e., all endomorphisms are automorphisms) and have a compact automorphism group. Further, it is shown how the endomorphisms and automorphisms of a locally covariant theory may, in principle, be classified in any single spacetime. As an example, the endomorphisms and automorphisms of a system of finitely many free scalar fields are completely classified.

math-ph↗

arXiv2013

Einstein Manifolds As Yang-Mills Instantons

It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.

hep-th↗

arXiv2013

Quasinormal modes of charged dilaton black holes and their entropy spectra

In this study, we employ the scalar perturbations of the charged dilaton black hole (CDBH) found by Chan, Horne and Mann (CHM), and described with an action which emerges in the low-energy limit of the string theory. A CDBH is neither asymptotically flat (AF) nor non-asymptotically flat (NAF) spacetime. Depending on the value of its dilaton parameter "a", it has both Schwarzschild and linear dilaton black hole (LDBH) limits. We compute the complex frequencies of the quasinormal modes (QNMs) of the CDBH by considering small perturbations around its horizon. By using the highly damped QNMs in the process prescribed by Maggiore, we obtain the quantum entropy and area spectra of these BHs. Although the QNM frequencies are tuned by "a", we show that the quantum spectra do not depend on "a", and they are equally spaced. On the other hand, the obtained value of undetermined dimensionless constant ε is the double of Bekenstein's result. The possible reason of this discrepancy is also discussed.

gr-qc↗

arXiv2013

Schwarzschild-de Sitter Metric and Inertial Beltrami Coordinates

Under consideration of coordinate conditions, we get the Schwarzschild-Beltrami-de Sitter (S-BdS) metric solution of the Einstein field equations with a cosmological constant $Λ$. A brief review to the de Sitter invariant special relativity (dS-SR), and de Sitter general relativity (dS-GR, or GR with a $Λ$) is presented. The Beltrami metric $B_{μν}$ provides inertial reference frame for the dS-spacetime. By examining the Schwarzschild-de Sitter (S-dS) metric $g_{μν}^{(M)}$ existed in literatures since 1918, we find that the existed S-dS metric $g_{μν}^{(M)}$ describes some mixing effects of gravity and inertial-force, instead of a pure gravity effect arisen from "solar mass" $M$ in dS-GR. In this paper, we solve the vacuum Einstein equation of dS-GR, with the requirement of gravity-free metric $g_{μν}^{(M)}|_{M\rightarrow 0}=B_{μν}$. In this way we find S-BdS solution of dS-GR, written in inertial Beltrami coordinates. This is a new form of S-dS metric. Its physical meaning and possible applications are discussed.

gr-qc↗

arXiv2013

Black-hole solution without curvature singularity

An exact solution of the vacuum Einstein field equations over a nonsimply-connected manifold is presented. This solution is spherically symmetric and has no curvature singularity. It can be considered to be a regularization of the Schwarzschild solution over a simply-connected manifold, which has a curvature singularity at the center. Spherically symmetric collapse of matter in R^4 may result in this nonsingular black-hole solution, if quantum-gravity effects allow for topology change near the center.

gr-qc↗

arXiv2018

Thermal corrections to the Casimir energy in a Lorentz-breaking scalar field theory

In this paper, we investigate the thermal effect on the Casimir energy associated with a massive scalar quantum field confined between two large parallel plates in a CPT-even, aether-like Lorentz-breaking scalar field theory. In order to do that we consider a nonzero chemical potential for the scalar field assumed to be in thermal equilibrium at some finite temperature. The calculations of the energies are developed by using the Abel-Plana summation formula, and the corresponding results are analyzed in several asymptotic regimes of the parameters of the system, like mass, separations between the plates and temperature.

hep-th↗

arXiv2013

Modified Supergravity and Early Universe: the Meeting Point of Cosmology and High-Energy Physics

We review the new theory of modified supergravity, dubbed F(\cal R) supergravity, and some of its recent applications to inflation and reheating in the early universe cosmology. The F(\cal R) supergravity is the N=1 locally supersymmetric extension of the f(R) gravity in four space-time dimensions. A manifestly supersymmetric formulation of the F(\cal R) supergravity exist in terms of N=1 superfields, by using the (old) minimal Poincar'e supergravity in curved superspace. We find the conditions for stability, the absence of ghosts and tachyons. Three models of the F(\cal R) supergravity are studied. The first example is devoted to a recovery of the standard (pure) N=1 supergravity with a negative cosmological constant from the F(\cal R) supergravity. As the second example, a generic {\cal R}^2-type supergravity is investigated, and the existence of the AdS bound on the scalar curvature is found. As the third (and most important) example, a simple viable realization of chaotic inflation in supergravity is found. Our approach is {\it minimalistic} since it does not introduce new exotic fields or new interactions, beyond those already present in (super)gravity. The universal reheating mechanism is automatic. We establish the consistency of our approach and also apply it to preheating and reheating after inflation. The Higgs inflation and its correspondence to the Starobinsky inflation is established in the context of supergravity. We briefly review other relevant issues such as non-Gaussianity, CP-violation, origin of baryonic asymmetry, lepto- and baryo-genesis. The F(\cal R) supergravity has promise for possible solutions to those outstanding problems too.

hep-th↗

arXiv2013

Advanced Methods in Black-Hole Perturbation Theory

Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved spacetime. Current state-of-the-art techniques are pedagogically explained and exciting open problems are presented.

gr-qc↗

arXiv2013

Comparison of metrics from retarded integrals and transverse traceless subgauge

The time-varying gravitational field produced by a Weber bar is used to explore mathematical features of the linearized Einstein equation. We present a self-contained formal framework for the treatment of the linear field, which is applicable to several situations where the standard quadrupolar formulas are not adequate. The expressions for retarded integrals reveal a singularity associated with boundary conditions. Results from the transverse traceless subgauge are compared with the radiation calculated from retarded integrals. Lienard-Wiechert potentials are used in a treatment of the Weber bar as a collection of point particles and further possible applications are outlined. The Riemann tensor clarifies the transition from near-field geodesic forces to tidal forces in the far field.

gr-qc↗

arXiv2013

Neutral Massive Spin 1/2 Particles Emission in a Rindler Spacetime

The Unruh effect for the rate of emission and absorption of neutral massive Majorana spinor particles -- the most plausible consituents of Dark Matter -- in a Rindler spacetime is thoroughly investigated. The corresponding Bogolyubov coefficients are explicitly calculated and the consistency with Fermi-Dirac statistics and the Pauli principle is actually verified.

hep-th↗

arXiv2013

Information conservation is fundamental: recovering the lost information in Hawking radiation

In both classical and quantum world, information cannot appear or disappear. This fundamental principle, however, is questioned for a black hole, by the acclaimed "information loss paradox". Based on the conservation laws of energy, charge, and angular momentum, we recently show the total information encoded in the correlations among Hawking radiations equals exactly to the same amount previously considered lost, assuming the non-thermal spectrum of Parikh and Wilczek. Thus the information loss paradox can be falsified through experiments by detecting correlations, for instance, through measuring the covariances of Hawking radiations from black holes, such as the manmade ones speculated to appear in LHC experiments. The affirmation of information conservation in Hawking radiation will shine new light on the unification of gravity with quantum mechanics.

gr-qc↗

arXiv2013

Dark energy with rigid voids versus relativistic voids alone

The standard model of cosmology is dominated - at the present epoch - by dark energy. Its voids are rigid and Newtonian within a relativistic background. The model prevents them from becoming hyperbolic. Observations of rapid velocity flows out of voids are normally interpreted within the standard model that is rigid in comoving coordinates, instead of allowing the voids' density parameter to drop below critical and their curvature to become negative. Isn't it time to advance beyond nineteenth century physics and relegate dark energy back to the "no significant evidence" box?

astro-ph.CO↗

arXiv2013

Hybrid modified gravity unifying local tests, galactic dynamics and late-time cosmic acceleration

The non-equivalence between the metric and Palatini formalisms of $f(R)$ gravity is an intriguing feature of these theories. However, in the recently proposed hybrid metric-Palatini gravity, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed à la Palatini, the "true" gravitational field is described by the interpolation of these two non-equivalent approaches. The theory predicts the existence of a light long-range scalar field, which passes the local constraints and affects the galactic and cosmological dynamics. Thus, the theory opens new possibilities for a unified approach, in the same theoretical framework, to the problems of dark energy and dark matter, without distinguishing a priori matter and geometric sources, but taking their dynamics into account under the same standard.

gr-qc↗

arXiv2013

Viscous Modified Cosmic Chaplygin Gas Cosmology

In this paper we construct modified cosmic Chaplygin gas which has viscosity. We use exponential function method to solve non-linear equation and obtain time-dependent dark energy density. Then discuss Hubble expansion parameter and scale factor and fix them by using observational data. We also investigate stability of this theory.

gr-qc↗

arXiv2013

Dark Energy From Fifth Dimensional Brans-Dicke Theory

Following the approach of the induced-matter theory, we investigate the cosmological implications of a five-dimensional Brans-Dicke theory, and propose to explain the acceleration of the universe. After inducing in a four-dimensional hypersurface, we classify the energy-momentum tensor into two parts in a way that, one part represents all kind of the matter (the baryonic and dark) and the other one contains every extra terms emerging from the scale factor of the fifth dimension and the scalar field, which we consider as the energy-momentum tensor of dark energy. We also separate the energy-momentum conservation equation into two conservation equations, one for matter and the other for dark energy. We perform this procedure for different cases, without interacting term and with two particular (suitable) interacting terms between the two parts. By assuming the parameter of the state equation for dark energy to be constant, the equations of the model admit the power-law solutions. Though, the non-interacting case does not give any accelerated universe, but the interacting cases give both decelerated and accelerated universes. For the interacting cases, we figure out analytically the acceptable ranges of some parameters of the model, and also investigate the data analysis to test the model parameter values consistency with the observational data of the distance modulus of 580 SNe Ia compiled in Union2.1. For one of these interacting cases, the best fitted values suggest that the Brans-Dicke coupling constant (ω) is -7.75, however, it also gives the state parameter of dark energy (wX) equal to -0.67. In addition, the model gives the Hubble and deceleration parameters at the present time to be H0 = 69.4 (km/s)/Mpc and q0 = -0.38 (within their confidence intervals), where the scale factor of the fifth dimension shrinks with the time.

gr-qc↗

arXiv2013

Cosmological dynamics of $f(R)$ gravity scalar degree of freedom in Einstein frame

$f(R)$ gravity models belong to an important class of modified gravity models where the late time cosmic accelerated expansion is considered as the manifestation of the large scale modification of the force of gravity. $f(R)$ gravity models can be expressed in terms of a scalar degree of freedom by redefinition of models variable. The conformal transformation of the action from Jordan frame to Einstein frame makes the scalar degree of freedom more explicit and can be studied conveniently. We have investigated the features of the scalar degree of freedoms and the consequent cosmological implications of the power-law ($ξR^n$) and the Starobinsky (disappearing cosmological constant) $f(R)$ gravity models numerically in the Einstein frame. Both the models show interesting behaviour of their scalar degree of freedom and could produce the accelerated expansion of the Universe in the Einstein frame with the negative equation of state of the scalar field. However the scalar field potential for the power-law model is the well behaved function of the field, whereas the potential becomes flat for higher value of field in the case of the Starobinsky model. Moreover, the equation of state of the scalar field for the power-law model is always negative and less than -1/3, which corresponds to the behaviour of the dark energy that produces the accelerated expansion of the Universe. This is not always the case for the Starobinsky model. At late times Starobinsky model behaves as cosmological constant $Λ$ as behaves by power-law model for the values of $n\rightarrow 2$ at all times.

gr-qc↗

arXiv2013

Reflections on the hyperbolic plane

The most general solution to the Einstein equations in $4=3+1$ dimensions in the asymptotical limit close to the cosmological singularity under the BKL (Belinski-Khalatnikov-Lifshitz) hypothesis, for which space gradients are neglected and time derivatives only are considered, can be visualized by the behavior of a billiard ball in a triangular domain on the Upper Poincaré Half Plane (UPHP). The behavior of the billiard system (named 'big billiard') can be schematized by dividing the succesions of trajectories according to Poincaré return map on the sides of the billiard table, according to the paradigms implemented by the BKL investigation and by the CB-LKSKS (Chernoff- Barrow- Lifshitz- Khalatnikov- Sinai- Khanin- Shchur) one. Different maps are obtained, according to different symmetry-quotienting mechanisms used to analyze the dynamics according to the symmetries of the billiard domain and to the features of the geodesics on the UPHP. In the inhomogenous case, new structures have been uncovered, such that, in this framework, the billiard table (named 'small billiard') consists of 1/6 of the previous one. The connections between the symmetry-quotienting mechanisms are further investigated on the UPHP. The relation between the complete billiard and the small billiard are also further explained according to the role of Weyl reflections. The quantum properties of the system are sketched as well, and the physical interpretation of the wavefunction is further developped. In particular, a physical interpretation for the symmetry-quotienting maps is proposed, according to the Fourier decomposition of the energy levels of the wavefunction of the universe, as far as the meaning of epochs and eras is concerned from a quantum point of view.

gr-qc↗