When scalar field is kinetically coupled to the Einstein tensor

TL;DR

This paper investigates a scalar field kinetically coupled to the Einstein tensor, revealing its potential as dark matter, dark energy, or inflaton, with unique properties like vanishing sound speed and crossing the phantom divide.

Contribution

It introduces a novel scalar field model with kinetic coupling to Einstein tensor, analyzing its cosmological roles and physical constraints across different scenarios.

Findings

Scalar behaves as pressureless matter with zero sound speed.

Scalar can act as both dark matter and dark energy, with crossing the phantom divide.

Coupling to multiple Einstein tensors yields an equation of state near -1, suitable for inflation.

Abstract

We explore the cosmic evolution of a scalar field with the kinetic term coupled to the Einstein tensor. We find that, in the absence of other matter sources or in the presence of only pressureless matter, the scalar behaves as pressureless matter and the sound speed of the scalar is vanishing. These properties enable the scalar field to be a candidate of cold dark matter. By also considering the scalar potential, we find the scalar field may play the role of both dark matter and dark energy. In this case, the equation of state of the scalar can cross the phantom divide, but this can lead to the sound speed becoming superluminal as it crosses the divide, and so is physically forbidden. Finally, if the kinetic term is coupled to more than one Einstein tensor, we find the equation of state is always approximately equal to -1 whether the potential is flat or not, and so the scalar may also be a candidate for the inflaton.