On the Emergence of Accelerating Cosmic Expansion in f(R) Theories of Gravity

TL;DR

This paper investigates $f(R)$ gravity theories in cosmology, finding that only those mimicking $ ext{Λ}$CDM are viable, which do not solve existing cosmological problems or produce new large-scale behaviors.

Contribution

It demonstrates that viable $f(R)$ models must closely resemble standard cosmology, highlighting limitations in their ability to address dark energy issues.

Findings

Viable $f(R)$ theories match standard Friedmann solutions with $ ext{Λ}$.

Such theories do not resolve the cosmological constant problem.

They cannot introduce new large-scale behaviors without losing Newtonian limits.

Abstract

We consider cosmological modelling in $f(R)$ theories of gravity, using both top-down and bottom-up constructions. The top-down models are based on Robertson-Walker geometries, and the bottom-up constructions are built by patching together sub-horizon-sized regions of perturbed Minkowski space. Our results suggest that these theories do not provide a theoretically attractive alternative to the standard general relativistic cosmology. We find that the only $f(R)$ theories that can admit an observationally viable weak-field limit have large-scale expansions that are observationally indistinguishable from the Friedmann solutions of General Relativity with $\Lambda$. Such theories do not alleviate any of the difficulties associated with $\Lambda$, and cannot produce any new behaviour in the cosmological expansion without simultaneously destroying the Newtonian approximation to gravity on small scales.