Coupled and Extended Quintessence: theoretical differences and structure formation

TL;DR

This work investigates two prominent nonminimal-dark-energy scenarios—Coupled Quintessence (CQ) and Extended Quintessence (EQ)—and clarifies their theoretical relation via Weyl scaling, mapping CQ in the Einstein frame to EQ in the Jordan frame. It analyzes linear perturbations and the Newtonian limit to reveal that CQ generally enhances clustering through an effectively strengthened gravity, while EQ can slow structure growth depending on the coupling sign and magnitude, partly due to nonzero anisotropic stress. The authors derive explicit corrections for N-body simulations, detailing how the expansion history, gravity strength, and growth rate must be modified in each framework. These results provide a concrete path to constrain nonminimal dark-energy models with large-scale structure observations and cosmological simulations across linear and nonlinear regimes.

Abstract

The case of a coupling between dark energy and matter (Coupled Quintessence) or gravity (Extended Quintessence) has recently attracted a deep interest and has been widely investigated both in the Einstein and in the Jordan frames (EF, JF), within scalar tensor theories. Focusing on the simplest models proposed so far, in this paper we study the relation existing between the two scenarios, isolating the Weyl scaling which allows to express them in the EF and JF. Moreover, we perform a comparative study of the behavior of linear perturbations in both scenarios, which turn out to behave in a markedly different way. In particular, while the clustering is enhanced in the considered CQ models with respect to the corresponding Quintessence ones where the coupling is absent and to the ordinary cosmologies with a Cosmological Constant and Cold Dark Matter (LCDM), structures in EQ models may grow slower. This is likely to have direct consequences on the inner properties of non-linear structures, like cluster concentration, as well as on the weak lensing shear on large scales. Finally, we specialize our study for interfacing linear dynamics and N-body simulations in these cosmologies, giving a recipe for the corrections to be included in N-body codes in order to take into account the modifications to the expansion rate, growth of structures, and strength of gravity.

Figures (4)

• Figure 1: Energy densities of CDM and dark energy. The left panel shows the case of coupled dark energy for $C = 0.05$ as well as for $C = 0$ vs $1+z$, where $z$ is the redshift. The right panel shows the case of extended quintessence for both positive and negative coupling corresponding to $\omega_{JBD0} \sim 30$. During MDE the energy density of the scalar field (the non conserved one) is more enhanced in the case of coupled dark energy than in extended quintessence, in which the dynamics of the R-boost has its major influence during RDE. The plotted densities are in units of $Mpc^{-2}$.
• Figure 2: Hubble parameter vs redshift for CQ and EQ with a non minimal coupling (for positive and negative couplings). The case of $\Lambda$CDM is also shown for reference. The value of $\xi$ corresponds to $\omega_{JBD0} \sim 30$. $H$ is in units of $Mpc^{-1}$.
• Figure 3: Growth factor as a function of redshift for coupled dark energy and extended quintessence with a non minimal coupling (for positive and negative couplings). The case of LCDM is also shown for reference. The value of $\xi$ corresponds to $\omega_{JBD0} \sim 30$.
• Figure 4: Gravitational correction as a function of redshift for CQ and EQ models. The value of $\xi$ corresponds to $\omega_{JBD_0} \sim 30$.