Cosmic acceleration in asymptotically Ricci flat Universe

TL;DR

This paper investigates an exponential $f(R)$ gravity model that allows for transient cosmic acceleration and a vanishing effective cosmological constant in the far future, while also supporting relativistic stars without singularities.

Contribution

It introduces a specific exponential $f(R)$ model that achieves transient acceleration and asymptotically Ricci flat spacetime, contrasting with previous models with non-zero asymptotic cosmological constant.

Findings

The model produces transient accelerated expansion compatible with cosmological observations.

It allows for stable relativistic stars in asymptotically flat spacetimes without singularities.

The effective cosmological constant vanishes as $R o 0$, differing from other $f(R)$ models.

Abstract

We analyze the evolution of a Friedmann-Robertson-Walker spacetime within the framework of $f(R)$ metric gravity using an exponential model. We show that $f(R)$ gravity may lead to a vanishing effective cosmological constant in the far future (i.e. $R\rightarrow 0$) and yet produce a transient accelerated expansion at present time with a potentially viable cosmological history. This is in contrast with several $f(R)$ models which, while viable, produce in general a non-vanishing effective cosmological constant asymptotically in time ($R\rightarrow 4\Lambda_{\rm eff}$). We also show that relativistic {stars in asymptotically flat spacetimes can be supported within this framework without encountering any singularity, notably in the Ricci scalar $R$.