Narrow Results

We study a model with global scale invariance within the framework of unimodular gravity. The global scale invariant gravitational action which follows the unimodular general coordinate transformations is considered without invoking any scalar field. This is generalization of conformal theory described [P. D. Mannheim and D. Kazanas, Astrophys. J.342, 635 (1989)]. The possible solutions for the gravitational potential under static linear field approximation are discussed. The new modified solution has additional corrections to the Schwarzschild solution which describe the galactic rotational curve. A comparative study of unimodular theory with conformal theory is also presented. Furthermore, the cosmological solution is studied and it is shown that the unimodular constraint preserve the de Sitter solution explaining the dark energy of the universe.

We investigate the Newton law in the unimodular F(R) gravity. In the standard F(R) gravity, due to the extra scalar mode, there often appear the large corrections to the Newton law and such models are excluded by the experiments and/or the observations. In the unimodular F(R) gravity, however, the extra scalar mode become not to be dynamical due to the unimodular constraint and there is not any correction to the Newton law. Even in the unimodular Einstein gravity, the Newton law is reproduced but the mechanism is a little bit different from that in the unimodular F(R) gravity. We also investigate the unimodular F(R) gravity in the covariant formulation. In the covariant formulation, we include the three-form field. We show that the three-form field could not have any unwanted property, like ghost nor correction to the Newton law. In the covariant formulation, however, the above extra scalar mode becomes dynamical and could give a correction to the Newton law. We also show that there are no difference in the Friedmann–Robertson–Walker (FRW) dynamics in the non-covariant and covariant formulation.

It is well known that classical Unimodular Gravity (UG) is equivalent to General Relativity, but the equivalence at the quantum level is not clear. Here we exhibit, in the UG framework, the Quantum Cosmology (QC) for a Friedmann–Lemaitre–Robertson–Walker (FLRW) universe, considering an inflationary scenario and also introducing a deformation on the commutation relations for the minisuperspace variables (NCC).

Recently, Borzou et al. (BSSY) generalized the Shiromizu–Maeda–Sasaki (SMS) formulation to $f(R)$-bulks. BSSY brane projected equation carries an additional stress tensor, besides SMS correction for Einstein’s theory on the brane. If we change this perspective, by requiring BSSY tensor in the geometrical side, acting as $f(R)$-brane generator, it is possible to relate $f(R)$-brane/bulk theories, by using curvature dynamical constraint (CDC), a concept that we developed. Since brane and bulk are $f(R)$, 5D/4D scalar curvatures also play a dynamical role and, thus, a dynamical version to Gauss equation trace, or CDC, must be offered. We will work yet in a specific case to obtain $f(R)$-unimodular gravity, formally identical with that obtained by Nojiri et al. (NOO). Therefore, two applications which consider cosmological scenarios in $f(R)$-unimodular gravity with dark radiation correction will be offered.

There is a formulation of unimodular gravity (UG) in which the unimodular metric is obtained out of an unrestricted one as ${\gamma }_{\mu \nu }=|g{|}^{-\frac{1}{n}}{g}_{\mu \nu }$. This unrestricted metric is only defined up to a Weyl rescaling. Physical charges like ADM energy or horizon entropy, however, are not Weyl invariant in general. In this paper a Weyl invariant definition of some physical charges is given.

We study the modified Reissner–Nordstrom (RN) metric in the unimodular gravity. So far the spherical symmetric Einstein field equation in unimodular gravity has been studied in the absence of any source. We consider static electric and magnetic charge as source. We solve for Maxwell equations in unimodular gravitational background. We show that in unimodular gravity, the electromagnetic field strength tensor is modified. We also show that the solution in unimodular gravity differs from the usual RN metric in Einstein gravity with some corrections. We further study the thermodynamical properties of the RN black hole solution in this theory.

We study some aspects of cosmological inflation in the framework of unimodular $f(R)$ gravity. To be more clearer, we consider a generic $f(R)$ of the type $f(R)=R+\alpha R^n$. By considering the Einstein frame counterpart of the unimodular $f(R)$ gravity, we set the scalaron to be responsible for cosmological inflation in this setup. We confront our model parameters space with observational data and impose some constraints on the value of $n$ in this manner. We show that for the number of $e$-folds $N=60$, the model is consistent with observation if $1.89<n<1.918$.

In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or $\mathrm{\Lambda }$CDM as separate scenarios. We reconstruct the $f(T)$ gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and Standard Model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular $f(T)$ gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.

The thermodynamics of local causal horizons has been shown to imply gravitational dynamics. In this essay, we discuss the principles underlying this observation, and its significance in our understanding of (quantum) gravity. We also show why the local thermodynamic methods cannot by themselves recover general relativity. Instead, they lead to the so-called Weyl transverse gravity. Because of this, local thermodynamic approaches avoid huge vacuum energy contributions to the cosmological constant. They even suggest a possible source for its small observed value. We also outline a way in which thermodynamics allows us to study low energy quantum gravitational effects. We arrive at quantum corrections to the gravitational equations which are suppressed by the Planck length squared.

This paper is devoted to the construction of a unified formalism for Palatini and unimodular gravity. The idea is to employ a relationship between unified formalism for a Griffiths variational problem and its classical Lepage-equivalent variational problem. The main geometrical tools involved in these constructions are canonical forms living on the first jet of the frame bundle for the spacetime manifold. These forms play an essential role in providing a global version of the Palatini Lagrangian and expressing the metricity condition in an invariant form. With them, we were able to find the associated equations of motion in invariant terms and, by using previous results from the literature, to prove their involutivity. As a bonus, we showed how this construction can be used to provide a unified formalism for the so-called unimodular gravity by employing a reduction of the structure group of the frame bundle to the special linear group.

In this review, we discuss the emergence of unimodular gravity (or, more precisely, Weyl transverse gravity) from the thermodynamics of spacetime. By analyzing three different ways to obtain gravitational equations of motion by thermodynamic arguments, we show that the results point to unimodular rather than fully diffeomorphism invariant theories and that this is true even for modified gravity. The unimodular character of dynamics is especially evident from the status of cosmological constant and energy-momentum conservation.

In this study, unimodular $f({𝒢},T)$ gravity is proposed as an alternative theory of gravity. Field equations of unimodular $f({𝒢},T)$ gravity are suggested. The field equation and their solutions are obtained for exponential expansion and power-law expansion models. Energy conditions of unimodular $f({𝒢},T)$ gravity are defined by using Raychaudhuri equations. Energy conditions for exponential expansion and power-law expansion models are investigated. Hubble parameter and deceleration parameter are calculated by considering power-law expansion model and obtained solutions. It has been shown that both deceleration parameter and Hubble parameter are compatible with the current observational data.