Scalar-Tensor Quintessence with a linear potential: Avoiding the Big Crunch cosmic doomsday

TL;DR

This paper demonstrates that non-minimal coupling in scalar-tensor quintessence models with a linear potential can prevent the universe's collapse, leading to a stable de Sitter phase instead of a Big Crunch.

Contribution

It shows that non-minimal coupling modifies the effective potential, allowing avoidance of the cosmic doomsday in linear quintessence models, a result previously not established.

Findings

Non-minimal coupling prevents future collapse in linear quintessence models.

Critical coupling parameter increases linearly with the potential slope.

The universe evolves towards a de Sitter phase with positive potential energy.

Abstract

All quintessence potentials that are either monotonic with negative interval or have a minimum at negative values of the potential, generically predict a future collapse of the scale factor to a "doomsday" singularity. We show that this doomsday is generically avoided in models with a proper non-minimal coupling of the quintessence scalar field to the curvature scalar $R$. For simplicity we consider linear quintessence potential $V=-s\phi$ and linear non-minimal coupling $F=1-\lambda \phi$. However our result is generic and is due to the fact that the non-minimal coupling modifies the effective potential that determines the dynamics of the scalar field. Thus for each positive value of the parameter $s$ we find a critical value $\lambda_{crit}(s)$ such that for $\lambda>\lambda_{crit}(s)$ the negative potential energy does not dominate the universe and the cosmic doomsday Big Crunch singularity is avoided because the scalar field eventually rolls up its potential. We find that $\lambda_{crit}(s)$ increases approximately linearly with $s$. For $\lambda>\lambda_{crit}(s)$ the potential energy of the scalar field becomes positive and it eventually dominates while the dark energy equation of state parameter tends to $w=-1$ leading to a deSitter Universe.