Disappearing cosmological constant in f(R) gravity

TL;DR

The paper addresses whether a disappearing cosmological constant can arise in $f(R)$ gravity while remaining consistent with cosmology and local tests. It proposes a regular $f(R)$ form with $f(0)=0$ and $f(R)\to R-2\Lambda$ at large $R$, yielding an effective curvature-induced DE that vanishes in flat space but acts as a cosmological constant at high curvature. It analyzes the FRW dynamics, deriving stability and viability conditions that can reproduce a $\Lambda$CDM-like background, and identifies observable consequences such as an enhanced growth of perturbations with $G_{\text{eff}}=G/f'(R)$ below the scalaron scale, leading to a potential $\Delta n_s = (\sqrt{33}-5)/[2(3n+2)]$ between galaxy surveys and CMB data, which currently constrains $n\ge 2$. A major theoretical challenge is avoiding overproduction of scalarons in the early universe, which may require suppressing the initial amplitude $C$ (and possibly adding an $R^2$ term at high curvature); the model thus provides a falsifiable curvature-driven alternative to $\Lambda$CDM with clear observational tests.

Abstract

For higher-derivative f(R) gravity where R is the Ricci scalar, a class of models is proposed which produce viable cosmology different from the LambdaCDM one at recent times and satisfy cosmological, Solar system and laboratory tests. These models have both flat and de Sitter space-times as particular solutions in the absence of matter. Thus, a cosmological constant is zero in flat space-time, but appears effectively in a curved one for sufficiently large R. A 'smoking gun' for these models would be small discrepancy in values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations. On the other hand, a new problem for dark energy models based on f(R) gravity is pointed which is connected with possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe.