Alternative mechanism of avoiding the big rip or little rip for a scalar phantom field

TL;DR

This paper proposes a new mechanism in inverse-R gravity to prevent catastrophic universe fates like big and little rip caused by scalar phantom fields, showing that potential choice is not critical for avoiding these singularities.

Contribution

It introduces a novel approach in inverse-R gravity to avoid rip singularities regardless of the phantom field potential, supported by exact solutions and numerical analysis.

Findings

Singularity avoidance is possible with various potentials in inverse-R gravity.

Exact solutions demonstrate power-law evolution avoiding rip.

Numerical results confirm potential independence in singularity prevention.

Abstract

Depending on the choice of its potential, the scalar phantom field $\phi$ (the equation of state parameter $w<-1$) leads to various catastrophic fates of the universe including big rip, little rip and other future singularity. For example, big rip results from the evolution of the phantom field with an exponential potential and little rip stems from a quadratic potential in general relativity (GR). By choosing the same potential as in GR, we suggest a new mechanism to avoid these unexpected fates (big and little rip) in the inverse-\textit{R} gravity. As a pedagogical illustration, we give an exact solution where phantom field leads to a power-law evolution of the scale factor in an exponential type potential. We also find the sufficient condition for a universe in which the equation of state parameter crosses $w=-1$ divide. The phantom field with different potentials, including quadratic, cubic, quantic, exponential and logarithmic potentials are studied via numerical calculation in the inverse-\textit{R} gravity with $R^{2}$ correction. The singularity is avoidable under all these potentials. Hence, we conclude that the avoidance of big or little rip is hardly dependent on special potential.