Scaling solutions in general non-minimal coupling theories

TL;DR

This work analyzes generalized non-minimal coupling (NMC) theories of gravity with a scalar field to identify scaling attractors that drive late-time acceleration. In the strong-coupling limit and for potentials obeying $V(\phi)=A f(\phi)^M$, the dynamics reduce to a scalar field in General Relativity with an exponential potential and a matter coupling, revealing four attractors in the phase space. However, stringent constraints from the time variation of the gravitational constant and nucleosynthesis severely restrict the parameter space, effectively ruling out these models as explanations for present cosmic acceleration within the analyzed regime. The study highlights that only specific, potentially non-strong-coupling or non-$V\propto f^M$ scenarios could remain viable, guiding future model-building in NMC cosmologies.

Abstract

A class of generalized non-minimal coupling theories is investigated, in search of scaling attractors able to provide an accelerated expansion at the present time. Solutions are found in the strong coupling regime and when the coupling function and the potential verify a simple relation. In such cases, which include power law and exponential functions, the dynamics is independent of the exact form of the coupling and the potential. The constraint from the time variability of $G$, however, limits the fraction of energy in the scalar field to less than 4% of the total energy density, and excludes accelerated solutions at the present.