http://arxiv.org/abs/2204.00119
We consider a scalar-tensor theory of gravity wherein the scalar field $\phi$ includes the gravitational coupling $G$ and the speed of light $c$, both of which are allowed to be functions of the spacetime coordinates. The cosmological coupling $\Lambda$ turns out to be an emergent phenomenon from a possible behavior of $\phi$. The dynamics of $\phi$ is analysed in the phase space where we describe gravity from a precisely specified form of the action. For reasonable assumptions on the potential $V\left(\phi\right)$ and the matter-energy content, we show that an attractor point can be quickly reached within a period where the Hubble parameter becomes essentially constant. When the system gets to the stable point, the dynamics of $\phi$ ceases and the constraint $\dot{G}/G=\sigma\left(\dot{c}/c\right)$ with $\sigma=3$ must be satisfied for the rest of the cosmic evolution. Our findings thus provide a foundation for the phenomenological model used recently to interpret cosmological and astrophysical data. It is shown that cosmic evolution after the equilibrium accommodates radiation- and matter-dominated eras that naturally evolve to an accelerated expansion typical of dark energy. The generalized Brans-Dicke approach developed in this paper results in equations that can be readily tested with observational data.
R. Cuzinatto, R. Gupta and P. Pompeia
Mon, 4 Apr 22
16/50
Comments: 15 pages, 4 figures