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

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 $V=-s\varphi$ and linear non-minimal coupling $F=1-\lambda \varphi$. 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.

6 pages, 5 figures. Extended version. Accepted in Phys. Rev. D as regular article (to appear)

References in corpus (6)

• Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
• Cosmological implications of baryon acoustic oscillation (BAO) measurements
• Thawing quintessence with a nearly flat potential
• Cosmological dynamics of Scalar--Tensor Gravity
• The Limits of Extended Quintessence
• Negative potentials and collapsing universes

Cited by in corpus (8)

• Evolution of the $f{\sigma }_8$ tension with the Planck15/$\Lambda$CDM determination and implications for modified gravity theories
• Generalised teleparallel quintom dark energy non-minimally coupled with the scalar torsion and a boundary term
• The fate of bound systems through Sudden Future Singularities
• String-inspired Teleparallel Cosmology
• Sudden Future Singularities in Quintessence and Scalar-Tensor Quintessence Models
• Constraints on scalar coupling to electromagnetism
• Sudden Future Singularities and their observational signatures in Modified Gravity
• Degravitation and the relaxed Einstein equations