Palatini approach to 1/R gravity and its implications to the late Universe

TL;DR

This paper applies the Palatini approach to 1/R gravity to explain late-time cosmic acceleration, revealing modifications to Einstein's equations and predicting a transition from power-law to exponential expansion.

Contribution

It introduces a modified energy-momentum tensor within the Palatini framework for 1/R gravity, leading to new insights into late Universe dynamics and cosmic acceleration.

Findings

Curvature effects cause non-conservation of matter energy-momentum tensor.

Modified Einstein equations include a varying effective cosmological constant.

Cosmic scale factor transitions from power-law to exponential growth.

Abstract

By applying the Palatini approach to the 1/R-gravity model it is possible to explain the present accelerated expansion of the Universe. Investigation of the late Universe limiting case shows that: (i) due to the curvature effects the energy-momentum tensor of the matter field is not covariantly conserved; (ii) however, it is possible to reinterpret the curvature corrections as sources of the gravitational field, by defining a modified energy-momentum tensor; (iii) with the adoption of this modified energy-momentum tensor the Einstein's field equations are recovered with two main modifications: the first one is the weakening of the gravitational effects of matter whereas the second is the emergence of an effective varying "cosmological constant"; (iv) there is a transition in the evolution of the cosmic scale factor from a power-law scaling $a\propto t^{11/18}$ to an asymptotically exponential scaling $a\propto \exp(t)$; (v) the energy density of the matter field scales as $\rho_m\propto (1/a)^{36/11}$; (vi) the present age of the Universe and the decelerated-accelerated transition redshift are smaller than the corresponding ones in the $\Lambda$CDM model.