CMB and BAO constraints for an induced gravity dark energy model with a quartic potential

TL;DR

This paper investigates structure formation in an induced gravity dark energy model with a quartic potential by evolving background and linear perturbations with a self-consistent Einstein-Boltzmann code and without resorting to parametrizations. It links the scalar field $\sigma$ to an effective gravitational constant and derives quasi-static limits for the perturbations, comparing them to full numerical solutions. Using Planck 2013 data and BAO measurements, it constrains the coupling to Ricci curvature $\gamma$, obtaining $\gamma<0.0012$ (95% CL) and a corresponding post-Newtonian parameter bound, along with limits on $\Delta G_N/G_N$ and $\dot G_N/G_N$, while noting a degeneracy with $H_0$. The results show the IG quartic model is not preferred over $\Lambda$CDM at current cosmological precision but demonstrates tight cosmological constraints on time-varying gravity and sets the stage for future refinements with improved data.

Abstract

We study the predictions for structure formation in an induced gravity dark energy model with a quartic potential. By developing a dedicated Einstein-Boltzmann code, we study self-consistently the dynamics of homogeneous cosmology and of linear perturbations without using any parametrization. By evolving linear perturbations with initial conditions in the radiation era, we accurately recover the quasi-static analytic approximation in the matter dominated era. We use Planck 2013 data and a compilation of baryonic acoustic oscillation (BAO) data to constrain the coupling $γ$ to the Ricci curvature and the other cosmological parameters. By connecting the gravitational constant in the Einstein equation to the one measured in a Cavendish-like experiment, we find $γ< 0.0012$ at 95% CL with Planck 2013 and BAO data. This is the tightest cosmological constraint on $γ$ and on the corresponding derived post-Newtonian parameters. Because of a degeneracy between $γ$ and the Hubble constant $H_0$, we show how larger values for $γ$ are allowed, but not preferred at a significant statistical level, when local measurements of $H_0$ are combined in the analysis with Planck 2013 data.

Figures (7)

• Figure 1: Evolution of $\sigma/\sigma_0$ (left panel), $\Omega_i$ (middle panel) and $w_{\rm DE}$ (right panel) as function of $\ln (a)$ for different choices of $\gamma$.
• Figure 2: Comparison of theoretical approximations for $\mu$ and $\delta$ which parametrize deviations from Einstein gravity (black lines) with our numerical results for two wavenumbers ($k\ \mathrm{Mpc} = 0.05 \,, 0.005$) and two values of the coupling to the Ricci curvature ($\gamma=10^{-2} \,, 10^{-3}$).
• Figure 3: CMB temperature anisotropies power spectrum for different values of $\gamma$ (left panel) and relative differences with respect to a reference $\Lambda$CDM (right panel).
• Figure 4: Lensing power spectrum for different values of $\gamma$ (left panel) and relative differences with respect to a reference $\Lambda$CDM (right panel).
• Figure 5: Temperature-lensing cross-correlation power spectrum for different values of $\gamma$ (left panel) and differences with respect to a reference $\Lambda$CDM (right panel).