Guido Cognola

Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hierarchy problem

Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of gravity where an arbitrary function of the GB invariant, f(G), is added to the general relativity action. We show that a theory of this kind is endowed with a quite rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence, or phantom cosmic acceleration, with a possibility for the transition from deceleration to acceleration. It is demonstrated in the paper that this theory is perfectly viable, since it is compliant with the solar system constraints. Specific properties of f(G) gravity in a de Sitter (dS) universe, such as dS and SdS solutions, their entropy, and its explicit one-loop quantization are studied. The issue of a possible solution of the hierarchy problem in modified gravities is also addressed.

Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories

We study the thermodynamics of four-dimensional Kerr-Newman-AdS black holes both in the canonical and the grand-canonical ensemble. The stability conditions are investigated, and the complete phase diagrams are obtained, which include the Hawking-Page phase transition in the grand-canonical ensemble. In the canonical case, one has a first-order transition between small and large black holes, which disappears for a sufficiently large electric charge or angular momentum. This disappearance corresponds to a critical point in the phase diagram. Via the AdS/CFT conjecture, the obtained phase structure is also relevant for the corresponding conformal field theory living in a rotating Einstein universe, in the presence of a global background U (1) current. An interesting limit arises when the black holes preserve some supersymmetry. These BPS black holes correspond to highly degenerate zero-temperature states in the dual CFT, which lives in an Einstein universe rotating with the speed of light.

Class of viable modified f(R) gravities describing inflation and the onset of accelerated expansion

A general approach to viable modified f(R) gravity is developed in both the Jordan and the Einstein frames. A class of exponential, realistic modified gravities is introduced and investigated with care. Special focus is made on step-class models, most promising from the phenomenological viewpoint and which provide a natural way to classify all viable modified gravities. One- and two-step models are explicitly considered, but the analysis is extensible to N-step models. Both inflation in the early universe and the onset of recent accelerated expansion arise in these models in a natural, unified way. Moreover, it is demonstrated that models in this category easily pass all local tests, including stability of spherical body solution, nonviolation of Newtons law, and generation of a very heavy positive mass for the additional scalar degree of freedom.

One-loop f(R) gravity in de Sitter universe

Motivated by the dark energy issue, the one-loop quantization approach for a family of relativistic cosmological theories is discussed in some detail. Specifically, general f(R) gravity at the one-loop level in a de Sitter universe is investigated, extending a similar program developed for the case of pure Einstein gravity. Using generalized zeta regularization, the one-loop effective action is explicitly obtained off shell, which allows us to study in detail the possibility of (de)stabilization of the de Sitter background by quantum effects. The one-loop effective action may also be useful for the study of the constant curvature black hole nucleation rate and it provides a plausible way of resolving the cosmological constant problem.

String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy

We consider scalar-Gauss-Bonnet and modified Gauss-Bonnet gravities and reconstruct these theories from the universe expansion history. In particular, we are able to construct versions of those theories (with and without ordinary matter), in which the matter-dominated era makes a transition to the cosmic acceleration epoch. In several of the cases under consideration, matter dominance and the deceleration-acceleration transition occur in the presence of matter only. The late-time acceleration epoch is described asymptotically by de Sitter space but may also correspond to an exact {lambda}CDM cosmology, having in both cases an effective equation of state parameter w close to -1. The one-loop effective action of modified Gauss-Bonnet gravity on the de Sitter background is evaluated and it is used to derive stability criteria for the ensuing de Sitter universe.

Quantum fields and extended objects in space-times with constant curvature spatial section

Abstract The heat-kernel expansion and ζ-regularization techniques for quantum field theory and extended objects on curved space-times are reviewed. In particular, ultrastatic space-times with spatial section consisting in manifold with constant curvature are discussed in detail. Several mathematical results, relevant to physical applications are presented, including exact solutions of the heat-kernel equation, a simple exposition of hyperbolic geometry and an elementary derivation of the Selberg trace formula. With regard to the physical applications, the vacuum energy for scalar fields, the one-loop renormalization of a self-interacting scalar field theory on a hyperbolic space-time, with a discussion on the topological symmetry breaking, the finite-temperature effects and the Bose-Einstein condensation, are considered. Some attempts to generalize the results to extended objects are also presented, including some remarks on path-integral quantization, asymptotic properties of extended objects and a novel representation for the one-loop (super) string free energy.

Nearly Starobinsky inflation from modified gravity

We study inflation induced by (power-low) scalar curvature corrections to General Relativity. The class of inflationary scalar potentials

Initial and final de Sitter universes from modified f(R) gravity

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Electromagnetic fields in Schwarzschild and Reissner-Nordstrom geometry. Quantum corrections to the black hole entropy

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On the Stability of a Class of Modified Gravitational Models

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