Cosmological Consequences of Varying Couplings in Gravity Action

TL;DR

The paper develops a Lagrangian framework in which both the Newtonian and cosmological couplings, $G$ and $\Lambda$, vary in time via a single scalar field $\xi$, with matter dynamics untouched. In FLRW cosmology, the authors derive modified Friedmann-like equations with an effective Hubble rate $H_{\xi} = H + (\dot{\xi})/(2\xi)$ and show that density evolution $\rho a^{3(1+w)}$ remains standard, while $G$ and $\Lambda$ evolve as power laws, $\xi \propto t^{\alpha}$ and $\lambda \propto t^{\beta}$ with $\alpha - \beta = 2$. They obtain observationally relevant constraints on the variation rates: $1.67\times 10^{-11} \mathrm{yr}^{-1} < \frac{\dot{G}}{G} < 3.34\times 10^{-11} \mathrm{yr}^{-1}$ and $-6.7\times 10^{-11} \mathrm{yr}^{-1} > \frac{\dot{\Lambda}}{\Lambda} > -13.4\times 10^{-11} \mathrm{yr}^{-1}$, and show that a slowly growing $G$ with a negative equation of state today can reproduce distance–redshift data while ruling out Dirac's large-number hypothesis. A key conceptual result is that the effective $\Lambda$ is linked to the matter content, enabling a dynamical solution to the cosmic coincidence problem by keeping the ratio of matter to $\Lambda$ densities of the same order across broad cosmic epochs, except during the radiation era.

Abstract

We develop a Lagrangian formulation for gravity with matter where the gravitational couplings are universally treated as being field-dependent. The solutions for FLRW geometries and the associated time evolution of the Newton and cosmological couplings are found. The distance-redshift relations are shown to prefer a slowly growing Newton's coupling along with a negative equation of state ($w\geq -\frac{1}{3}$) for the matter fluid at the present epoch of accelerated expansion, while ruling out Dirac's large number hypothesis. We obtain an improved bound on $\dot{G}(t)$ as: $1.67\times 10^{-11} yr^{-1}<\frac{\dot{G}}{G}<3.34\times 10^{-11} yr^{-1}$ in the context of supernova cosmology, as well as a new constraint on $\dotΛ(t)$ as: $-0.67\times 10^{-11} yr^{-1}<\frac{\dotΛ}Λ<-1.34\times 10^{-11} yr^{-1}$. Based on this formulation, we also present a dynamical solution to the `cosmic coincidence' problem.

Figures (2)

• Figure 1: Comoving distance for dust matter domination ($w=0$) for different positive and negative exponents $\alpha$ ($=1,\frac{1}{2},0,-\frac{1}{2},-\frac{3}{2}$). The null curve ($\alpha=0$) corresponds to a pure matter-domination ($\Omega_\Lambda=0$) in a $\Lambda CDM$ Universe. The thick black line refers to the $\Lambda CDM$ curve assuming $\Omega_m=0.32,\Omega_\Lambda=0.68$.
• Figure 2: Comoving distance for the EOS $w=-\frac{1}{3}$, plotted for different positive and negative exponents $\alpha$ ($=1,\frac{1}{2},-\frac{1}{2},-1$). $\alpha=1$ corresponds to Dirac's conjecture (LNH) $G\sim t^{-1}$, which is clearly disfavoured.