Late-time cosmology in (phantom) scalar-tensor theory: dark energy and the cosmic speed-up

TL;DR

This paper investigates late-time cosmology in phantom scalar-tensor theories with an exponential potential, demonstrating that one can realize cosmic acceleration with a near-$-1$ EOS parameter $w$ and that phantom behavior can be frame-dependent between Jordan and Einstein representations. It develops exact FRW solutions via an extension of Russo’s method, showing conditions for eternal or transient acceleration and highlighting the possibility of de Sitter or power-law endpoints depending on parameters. The authors then argue that quantum corrections, including one-loop and conformal anomaly effects, can avert a finite-time Big Rip by driving the future toward a quantum de Sitter phase. Additionally, they introduce a novel higher-derivative gravity–matter coupling, $R^\alpha L_d$, which can produce gravity-assisted dark energy dominance and an effective phantom/quintessence description with transient acceleration. Together, these results provide a framework connecting frame choice, quantum effects, and higher-derivative couplings to viable late-time cosmologies with w near -1 and without an inevitable singularity.

Abstract

We consider late-time cosmology in a (phantom) scalar-tensor theory with an exponential potential, as a dark energy model with equation of state parameter close to -1 (a bit above or below this value). Scalar (and also other kinds of) matter can be easily taken into account. An exact spatially-flat FRW cosmology is constructed for such theory, which admits (eternal or transient) acceleration phases for the current universe, in correspondence with observational results. Some remarks on the possible origin of the phantom, starting from a more fundamental theory, are also made. It is shown that quantum gravity effects may prevent (or, at least, delay or soften) the cosmic doomsday catastrophe associated with the phantom, i.e. the otherwise unavoidable finite-time future singularity (Big Rip). A novel dark energy model (higher-derivative scalar-tensor theory) is introduced and it is shown to admit an effective phantom/quintessence description with a transient acceleration phase. In this case, gravity favors that an initially insignificant portion of dark energy becomes dominant over the standard matter/radiation components in the evolution process.