Varying Gravitational Constant as Well as Cosmology from the Early Inflation to Late Acceleration and Future Universe

TL;DR

This paper proposes a cosmological model with a varying gravitational constant driven by a scalar field, explaining early inflation, late acceleration, and dark energy phenomena without additional matter fields.

Contribution

It introduces a scalar-tensor cosmological model with phase transitions that naturally produce dark matter and dark energy from gravitational effects alone.

Findings

Dark matter and dark energy originate from gravitational sector effects.

Fluctuations in scalar field lead to phantom dark energy.

Model avoids big-rip singularity in phantom era.

Abstract

Here, cosmology is obtained from the variable gravitational constant $ G \propto \phi^{-2}$ with $ \phi(x) $ being a scalar and its fluctuations around the ground state. The gravitational action contains Einstein-Hilbert like term with variable $ G $, kinetic energy and self-interaction potential for $ \phi(x) $. Two phase transitions take place in this model. The first one takes place at the GUT (grand unified theory) scale $ \sim 2.45 \times 10^{14}{\rm GeV} $, when the early universe exits the inflationay phase and the second one at the electro-weak scale. Spontaneous symmetry breaking takes place around this scale As a consequence, variable $ G $ acquires constant value $G_N$ (the Newtonian gravitational constant).The standard model of cosmology is obtained in the post-second phase transition era. Interestingly, the dark matter and quintessence dark energy are created from the gravitational sector as a combined effect of the linear term of scalar curvature and $ \phi(x) $ without using non-linear terms of curvature or any other matter fields. It is interesting to find that fluctuations in $ \phi(x) $ cause the phantom dark energy after the second phase transition, which grows later in the expanding universe. It is also found that the phantom era is free from big-rip singularity.