Curvature Quintessence

TL;DR

Curvature quintessence investigates whether cosmic acceleration can be explained within higher-order gravity by interpreting curvature corrections as an effective dark-energy fluid. The paper derives the FRW dynamics for general $f(R)$ theories, defines a curvature fluid with density $\\rho_{curv}$ and pressure $p_{curv}$, and shows acceleration corresponds to $\\rho_{tot}+3 p_{tot}<0$, depending on the form of $f(R)$. It identifies exact accelerating solutions for power-law models $f(R)=f_0 R^n$, notably $n=-1$ and $n=3/2$ with $k=0$, and discusses the conformal relation to Einstein-frame scalar fields (Liouville potential for $n=3/2$). The work emphasizes constraining $f(R)$ with observations to realize a geometrical quintessence without ad hoc choices, and highlights links to quantum gravity effective actions.

Abstract

The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order theories of gravity. We can define effective pressure and energy density directly connected to the Ricci scalar of curvature of a generic fourth order theory and then ask for the conditions to get an accelerated expansion. Exact accelerated expanding solutions can be achieved for several fourth order theories so that we get an alternative scheme to the standard quintessence scalar field, minimally coupled to gravity, usually adopted. We discuss also conformal transformations in order to see the links of quintessence between the Jordan and Einstein frames.