Cosmological consequences of exponential gravity in Palatini formalism

We investigate cosmological consequences of a class of exponential f(R)$f(R)$ gravity in the Palatini formalism. By using the current largest type Ia Supernova sample along with determinations of the cosmic expansion at intermediary and high-z   we impose tight constraints on the model parameters. Differently from other f(R)$f(R)$ models, we find solutions of transient acceleration, in which the large-scale modification of gravity will drive the Universe to a new decelerated era in the future. We also show that a viable cosmological history with the usual matter-dominated era followed by an accelerating phase is predicted for some intervals of model parameters.     

Affine gravity,Palatini formalism and charges

Affine gravity and the Palatini formalism contribute both to produce a simple and unique formula for calculating charges at spatial and null infinity for Lovelock type Lagrangians whose variational derivatives do not depend on second-order derivatives of the field components. The method is based on the covariant generalization due to Julia and Silva of the Regge–Teitelboim procedure that was used to define properly the mass in the classical formulation of Einstein’s theory of gravity. Numerous applications reproduce standard results obtained by other secure but mostly specialized method like in ADM energy for asymptotically flat spacetimes and in Abbot and Deser for asymptotically de Sitter and anti-de Sitter spacetimes, both at spatial infinity. As a novel application we calculate the Bondi energy loss in five dimensional gravity, based on the asymptotic solution given by Tanabe et al. and obtain, as expected, the same result. We also give the for Einstein–Gauss–Bonnet gravity and find the superpotential for Lovelock theories of gravity when the number of dimensions tends to infinity with maximally symmetrical boundaries. The paper is written in standard component formalism.     

Evolution of the cosmological constant in effective gravity

In contrast to the phenomenon of nullification of the cosmological constant in equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological constant to evolve in a nonequilibrium vacuum. An attempt is made to extend the Einstein equation in the direction suggested by the condensed matter analogy of the quantum vacuum. Different scenarios are found depending on the behavior of and the relation between the relaxation parameters involved, some of these scenarios having been discussed in the literature. One of them reproduces the scenario in which the effective cosmological constant emerges as a constant of integration. The second one describes the situation when, after the cosmological phase transition, the cosmological constant drops from zero to a negative value; this scenario describes the relaxation from this big negative value back to zero and then to a small positive value. In the third example, the relaxation time is not a constant but depends on matter; this scenario demonstrates that vacuum energy (or its fraction) can play the role of cold dark matter.     

Screening of cosmological constant in non-local gravity

We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of non-local gravity with the Lagrangian of the form, R+f(^□−1R)−2Λ$R+f({\square }^{-1}R)-2\Lambda$ where f(X)$f(X)$ is a quadratic function of X, there is a flat spacetime solution despite the presence of the cosmological constant Λ. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of ‘time’. Nevertheless our result suggests the possibility of solving the cosmological constant problem in the context of non-local gravity.     

Unimodular quantum gravity and the cosmological constant

It is shown that the one-loop effective action of unimodular gravity is the same as that of ordinary gravity, restricted to unimodular metrics. The only difference is in the treatment of the global scale degree of freedom and of the cosmological term. A constant vacuum energy does not gravitate, addressing one aspect of the cosmological constant problem.     

Quantizing gravity with a cosmological constant

We argue that the quantization of gravity with a cosmological constant, Λ, is both necessary and feasible (in the sense that the evaluation of the functional integral is no more difficult than when Λ= 0). We illustrate this point by evaluating the one-loop counterterms and anomalous scaling behavior for pure gravity with a Λ term and for matter fieldsin an external gravitational field. Previous attempts at these calculations are found to be in error. The new results have implications for Hawking's “spacetime foam”.     

Palatini formulation of modified gravity with squared scalar curvature

In this comment we indicate that in the Palatini formulation of R² gravity, there will be no gravity-driven inflation and under some particular assumptions there will be a mild power-law inflation a t².     

Stability of gravity with a cosmological constant

The stability properties of Einstein theory with a cosmological constant Λ are investigated. For Λ > 0, stability is established for small fluctuations, about the de Sitter background, occurring inside the event horizon and semiclassical stability is analyzed. For Λ < 0, stability is demonstrated for all asymptotically anti-de Sitter metrics. The analysis is based on the general construction of conserved flux-integral expressions associated with the symmetries of a chosen background. The effects of an event horizon, which lead to Hawking radiation, are expressedfor general field hamiltonians. Stability for Λ < 0 is proved, using supergravity techniques, in terms of the graded anti-de Sitter algebra with spinorial charges also expressed as flux integrals.     

Instabilities in thermal gravity with a cosmological constant

It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature.     

Three-dimensional cosmological gravity: Dynamics of constant curvature

In three space-time dimensions, Einstein's equations with cosmological constant Λ imply that the curvature is constant outside sources. When particles are present, they alter the global properties of the exterior geometry. In the De Sitter case, space is a two-sphere and static many-body solutions are quite different from their Λ = 0 counterparts; in particular particles lie at antipodal points, with the great-circle wedge between them excised. These configurations are analyzed in terms of the general static solution to the exterior field equations.     

Energy and momentum from the Palatini formalism

I derive from the Palatini formalism, in which metric and affinity are varied independently, an energy-momentum complex qualitatively different in form from the usual energy-momentum representations of general relativity. A similar procedure can be carried out for electrodynamics, illuminating by analogy the structure of the gravitational Lagrangian. The new energy density vanishes for all static vacuum solutions of the Einstein equations, and the radiated energy from an isolated system in an asymptotically flat space in general diverges. These facts suggest that the formalism could be used to express Mach's principle.     

Domain walls without cosmological constant in higher order gravity

We consider a class of higher order corrections in the form of Euler densities of arbitrary rank n to the standard gravity action in D dimensions. We present a generating functional and an explicit form of the conserved energy-momentum tensors. We show that this class of corrections allows for domain-wall solutions despite the presence of higher powers of the curvature. The existence of such solutions no longer depends on the presence of cosmological constants. For example, the Randall-Sundrum-type scenario can be realized without bulk and/or brane cosmological constant.     

Energy-momentum complex of gravitational field in the Palatini formalism

It is shown that Murphy's energy-momentum complex of the gravitational field, derived from the Hilbert Lagrangian by use of the Palatini formalism, is identical to the complex derived from the same Lagrangian in a standard way by Mitskievic. The explicitly tensorial formulation of conservation laws in general relativity is eflectively used and some properties of the complex in question are discussed in connection with Murphy's article.     

Dynamical Chern–Simons modified gravity,Gödel Universe and variable cosmological constant

We study the condition for the consistency of the Gödel metric with the dynamical Chern–Simons modified gravity. It turns out to be that this compatibility can be achieved only if the cosmological constant is variable in the space.     

Positive cosmological constant,non-local gravity and horizon entropy

We discuss a class of (local and non-local) theories of gravity that share same properties: (i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; (ii) the on-shell action of such a theory vanishes and (iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant Λ>0$\Lambda >0$ and with zero Λ. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive Λ, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entropy proportional to the area. We conclude that, somewhat surprisingly, the presence of any, even extremely tiny, positive cosmological constant should be important for the proper resolution of the entropy problem and, possibly, the information puzzle.     

Loop quantum modified gravity and its cosmological application

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.     

A Gauss type law for gravity with a cosmological constant

It is shown that Komar's conserved quantities can be generalized to space-times with a cosmological constant in which matter, electric charge, and massless scalar field are sources. In the special case of the Kerr-Newman-de Sitter solution, treated as a solution external to matter sources, these quantities are equal to the global mass and angular momentum of its source. They are determined regardless of any local distribution of the mass and angular momentum of sources in addition to the electric charge given by the classical Gauss' law.     

Localising gravity in composite monopole brane worlds without bulk cosmological constant

We study a 7-dimensional brane world scenario with a Ricci-flat 3-brane residing in the core of a composite monopole defect, i.e., a defect composed of a 't Hooft–Polyakov and a global monopole. Admitting a direct interaction between the two bosonic sectors of the theory, we analyse the structure of the space–time in the limits of small, respectively large direct interaction coupling constant. For large direct interaction, the global monopole disappears from the system and leaves behind a negative cosmological constant in the bulk such that gravity-localising solutions are possible without a priori introduction of a bulk cosmological constant.