Search

We describe a general constitutive framework for a teleparallel extension of the general theory of relativity. This approach goes beyond the teleparallel equivalent of general relativity (TEGR) by broadening the analogy with the electrodynamics of media. In particular, the main purpose of this paper is to investigate in detail a local constitutive extension of TEGR that is the local limit of non-local gravity. Within this framework, we study the modified Friedmann–Lemaître–Robertson–Walker cosmological models. Of these, the most cogent turns out to be the modified Cartesian flat model which is shown to be inconsistent with the existence of a positive cosmological constant. Moreover, dynamic dark energy and other components of the modified Cartesian flat model evolve differently with the expansion of the universe as compared to the standard flat cosmological model. The observational consequences of the modified Cartesian flat model are briefly explored and it is shown that the model is capable of resolving the H 0 tension. [ABSTRACT FROM AUTHOR]

Nonlocal gravity (NLG), a classical extension of Einstein's theory of gravitation, has been studied mainly in linearized form. In particular, nonlinearities have thus far prevented the treatment of cosmological models in NLG. In this essay, we discuss the local limit of NLG and apply this limit to the expanding homogenous and isotropic universe. The theory only allows spatially flat cosmological models; furthermore, de Sitter spacetime is forbidden. The components of the model will have different dynamics with respect to cosmic time as compared to the standard Λ CDM model; specifically, instead of the cosmological constant, the modified flat model of cosmology involves a dynamic dark energy component in order to account for the accelerated phase of the expansion of the universe. [ABSTRACT FROM AUTHOR]

Within the framework of the local limit of nonlocal gravity (NLG), we investigate a class of Bianchi type I spatially homogeneous but anisotropic cosmological models. The modified field equations are presented in this case, and some special solutions are discussed in detail. This modified gravity theory contains a susceptibility function S(x) such that general relativity (GR) is recovered for S = 0. In the modified anisotropic cosmological models, we explore the contribution of S(t) and its temporal derivative to the local anisotropic cosmic acceleration. The implications of our results for observational cosmology are briefly discussed. [ABSTRACT FROM AUTHOR]

We propose a new probe to test the nature of gravity at various redshifts through large-scale cosmological observations. We use our void catalog, extracted from the Sloan Digital Sky Survey (SDSS, DR10), to trace the distribution of matter along the lines of sight to SNe Ia that are selected from the Union II catalog. We study the relation between SNe Ia luminosities and convergence and also the peculiar velocities of the sources. We show that the effects, on SNe Ia luminosities, of convergence and of peculiar velocities predicted by the theory of general relativity and theories of modified gravities are different and hence provide a new probe of gravity at various redshifts. We show that the present sparse large-scale data does not allow us to determine any statistically-significant deviation from the theory of general relativity but future more comprehensive surveys should provide us with means for such an exploration. [ABSTRACT FROM AUTHOR]