Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday

TL;DR

The paper studies $f(R)$ gravity models that combine negative and positive curvature powers as a geometric origin for cosmic acceleration. It shows that in the small-curvature regime of $f(R)=R-\gamma R^{-n}+\\eta R^2$ one can obtain an effective phantom state with $w_{eff}<-1$, and that a finite-time singularity may occur; including the $R^2$ term can halt curvature growth and yield a de Sitter attractor, avoiding doomsday. When coupled to matter with equation-of-state $w$, the model can realize phantom or quintessence-like behavior more readily, expanding the cosmological dynamics beyond pure vacuum gravity. The results argue that consistent modified gravity remains a viable alternative to dark energy, potentially testable by solar-system and cosmological observations.

Abstract

We discuss the modified gravity which includes negative and positive powers of the curvature and which provides the gravitational dark energy. It is shown that in GR plus the term containing negative power of the curvature the cosmic speed-up may be achieved, while the effective phantom phase (with $w$ less than -1) follows when such term contains the fractional positive power of the curvature. The minimal coupling with matter makes the situation more interesting: even 1/R theory coupled with the usual ideal fliud may describe the (effective phantom) dark energy. The account of $R^2$ term (consistent modified gravity) may help to escape of cosmic doomsday.