Cosmological constraints on induced gravity dark energy models

TL;DR

This paper investigates induced gravity dark energy models with a monomial potential $V(σ)=λ_n σ^n$ ($n>0$) and a Ricci-coupling $γ$, analyzing background evolution and linear perturbations to predict CMB and matter spectra. By extending the CLASS code to generic $n$ and confronting the predictions with Planck 2015 data and BAO (and, in some cases, local $H_0$ measurements), the authors derive tight cosmological bounds on $γ$ and on the variation of Newton's constant $G_N$, with $n=4$ (quartic) serving as a benchmark. They find that while the standard cosmological parameters are largely insensitive to $n$, the derived constraints on $\dot G_N/G_N$ and $\ddot G_N/G_N$ depend on the potential, and including BAO data significantly strengthens the $γ$ bounds. The work shows current cosmological data impose stringent limits on deviations from General Relativity in IG-like models and highlights the potential of future surveys to further discriminate the form of the dark-energy potential.

Abstract

We study induced gravity dark energy models coupled with a simple monomial potential $\propto σ^n$ and a positive exponent $n$. These simple potentials lead to viable dark energy models with a weak dependence on the exponent, which characterizes the accelerated expansion of the cosmological model in the asymptotic attractor, when ordinary matter becomes negligible. We use recent cosmological data to constrain the coupling $γ$ to the Ricci curvature, under the assumptions that the scalar field starts at rest deep in the radiation era and that the gravitational constant in the Einstein equations is compatible with the one measured in a Cavendish-like experiment. By using $Planck$ 2015 data only, we obtain the 95 % CL bound $γ< 0.0017$ for $n=4$, which is further tightened to $γ< 0.00075$ by adding Baryonic Acoustic Oscillations (BAO) data. This latter bound improves by $\sim 30$ % the limit obtained with the $Planck$ 2013 data and the same compilation of BAO data. We discuss the dependence of the $γ$ and $\dot G_N/G_N (z=0)$ on $n$.

Figures (10)

• Figure 1: Evolution of $\sigma/\sigma_0$ (upper left panel), $w_{\rm DE}$ (upper right panel) and $G_\textup{N} (a)/G \equiv \sigma_0^2/\sigma^2$ (lower right panel) as function of the scale factor $a$ for $\gamma = 10^{-3}$ and different values of $n$. In the lower left panel we show the critical densities $\Omega_i$: radiation in red, matter in green and effective dark energy in blue. See text for more details.
• Figure 2: Comparison of the theoretical quasi-static approximations for $\mu (k,a)$ and $\delta(k,a)$ parameters (black lines) with our exact numerical results for $k = 0.005\ \mathrm{Mpc}^{-1}$ and $\gamma=10^{-2}$ when $n$ is varied.
• Figure 3: To the left, from the upper to the lower panel respectively, CMB TT, EE and TE power spectra for $\gamma = 10^{-3} \,, 10^{-4}$ and $n=4$. In the upper and middle right panels, we show the relative differences for TT and EE spectra with respect to a reference $\Lambda$CDM model. In the lower right panel we show the differences for $C_\ell^{TE}$ normalized to $\sqrt{C_\ell^{TT} C_\ell^{EE}}$.
• Figure 4: Relative differences for the CMB temperature anisotropies power spectrum with respect to a reference $\Lambda$CDM for $\gamma = 10^{-2}$ and different values of $n$ are shown for $\ell < 300$ (left panel) and for $\ell > 200$ (right panel).
• Figure 5: Relative differences for the CMB polarization E-mode anisotropies power spectrum with respect to a reference $\Lambda$CDM for $\gamma = 10^{-2}$ and different values of $n$ are shown for $\ell < 300$ (left panel) and for $\ell > 200$ (right panel).