Extended Quintessence

TL;DR

This paper investigates Extended Quintessence, where a non-minimally coupled Quintessence field φ to the Ricci scalar R induces a time-varying Newton’s constant and modifies cosmological perturbations. The authors formulate the general scalar-tensor dynamics in the Jordan frame, implement two representative models—Induced Gravity (IG) with F(φ)=ξφ^{2} and Non-Minimal Coupling (NMC) with F(φ)=1+ξφ^{2}—and solve the background and linear perturbation equations, predicting CMB and matter power spectra. They identify QR-effects, including an enhanced Integrated Sachs-Wolfe effect, horizon-crossing delays, peak shifts in the CMB, and suppressed large-scale structure power, with effects consistent with solar-system bounds on ξ; both IG and NMC produce similar phenomenology. The results suggest that forthcoming CMB and LSS observations could detect these signatures, providing a test for scalar-tensor extensions to quintessence and guiding future work on alternative potentials and gravity sectors. Overall, the work highlights a concrete observational handle on non-minimally coupled scalar fields contributing to late-time cosmic acceleration.

Abstract

We study Quintessence cosmologies in the context of scalar-tensor theories of gravity, where a scalar field $φ$, assumed to provide most of the cosmic energy density today, is non-minimally coupled to the Ricci curvature scalar $R$. Such `Extended Quintessence' cosmologies have the appealing feature that the same field causing the time (and space) variation of the cosmological constant is the source of a varying Newton's constant à la Jordan-Brans-Dicke. We investigate here two classes of models, where the gravitational sector of the Lagrangian is $F(φ)R$ with $F(φ)=ξφ^{2}$ (Induced Gravity, IG) and $F(φ)=1+ξφ^{2}$ (Non-Minimal Coupling, NMC). As a first application of this idea we consider a specific model, where the Quintessence field, $φ$, obeying the simplest inverse power potential, has $Ω_φ=0.6$ today, in the context of the Cold Dark Matter scenario, with scale-invariant adiabatic initial perturbations. We find that, if $ξ\lesssim 5\times 10^{-4}$ for IG and $ξ\lesssim 5\times 10^{-3}(\sqrt{G}φ_{0})^{-1}$ for NMC ($φ_{0}$ is the present Quintessence value) our Quintessence field satisfies the existing solar system experimental constraints. Using linear perturbation theory we then obtain the polarization and temperature anisotropy spectra of the Cosmic Microwave Background (CMB) as well as the matter power-spectrum. The perturbation behavior possesses distinctive features, that we name `QR-effects', regarding acoustic peak location and height, late time integrated Sachs-Wolfe effect, as well as turnover and amplitude in the matter power spectrum. These features could be detected in the upcoming observations on CMB and large-scale structure.

Figures (10)

• Figure 1: Numerical analysis of the time variation of the gravitational constant versus the QR coupling constant in EQ models.
• Figure 2: Time behavior of the Hubble length in EQ models versus ordinary Quintessence.
• Figure 3: Time behavior of the cosmic equation of state in EQ models versus ordinary Quintessence.
• Figure 4: Time behavior of the $\Omega$ parameters relative to matter, radiation and Quintessence.
• Figure 5: Time behavior of the $\Omega_{\phi}$ parameters relative to the potential, kinetic and purely QR terms.