Coupled quintessence with a $Λ$CDM background: removing the $σ_8$ tension

TL;DR

The paper tackles the $σ_8$ tension between CMB-inferred clustering and late-Universe measurements by proposing a coupled quintessence model with a constant conformal coupling to dark matter that exactly reproduces a $\Lambda$CDM background. By fixing the background expansion to $H^2=H^2_{\Lambda\mathrm{CDM}}$, the authors show that perturbations differ due to an interplay between an additional scalar force and a reduced dark-matter density near today, leading to an overall slower growth of structure. The main result is that the best-fit parameters $|β|=0.079^{+0.059}_{-0.067}$ and $σ_8^0=0.818^{+0.115}_{-0.088}$ yield good agreement with $fσ_8$ data and KiDS-450 lensing, effectively alleviating the tension; future missions SKA and Euclid are forecast to constrain $β$ and $σ_8^0$ at the level of $1.5\times10^{-3}$ and $1.8\times10^{-3}$, respectively. Overall, the model demonstrates that background observables can remain ΛCDM-like while perturbations exhibit signatures capable of reconciling early- and late-Universe clustering, providing a testable target for upcoming surveys.

Abstract

A well-known problem of the $Λ$CDM model is the tension between the relatively high level of clustering, as quantified by the parameter $σ_8$, found in cosmic microwave background experiments and the smaller one obtained from large-scale observations in the late Universe. In this paper we show that coupled quintessence, i.e. a single dark energy scalar field conformally coupled to dark matter through a constant coupling, can solve this problem if the background is taken to be identical to the $Λ$CDM one. We show that two competing effects arise. On one hand, the additional scalar force is attractive, and is therefore expected to increase the clustering. On the other, in order to obtain the same background as $Λ$CDM, coupled quintessence must have a smaller amount of dark matter near the present epoch. We show that the second effect is dominating today and leads to an overall slower growth. Comparing to redshift distortion data, we find that coupled quintessence with $Λ$CDM background solves the tension between early and late clustering. We find for the coupling $β$ and for $σ_8$ the best fit values $|β| = 0.079^{+ 0.059}_{- 0.067}$ and $σ_8 = 0.818^{+0.115}_{-0.088}$. These values also fit the lensing data from the KiDS-450 survey. We also estimate that the future missions SKA and Euclid will constrain $β$ with an error of $\pm\, 1.5\times10^{-3}$ and for $σ_8$ of $\pm \,1.8\times10^{-3}$ at $1σ$ level.

Figures (6)

• Figure 1: Abundances for the coupled quintessence model, for radiation (dash-dotted line), matter (solid lines) and dark energy (dash lines) for three different values of the coupling, $\beta = 0$ ($\Lambda$CDM), $\beta = 0.05$ and $\beta=0.08$ (darker to lighter curves).
• Figure 2: Function $f\sigma_8$ for $\Lambda$CDM (solid line) and for the coupled quintessence model with $\beta=0.05$ (dashed line) and $\beta=0.08$ (dotted line) fixing a value of $\sigma_8(0)=0.818$Ade:2015xua. The observational data points were taken from delaTorre:2013rpaOkada:2015vfaGuzzo:2008acChuang:2013wga2012MNRAS.425..405BTegmark:2006azGil-Marin:2015sqa2012MNRAS.424.2339TSatpathy:2016tct2012MNRAS.420.2102S2011MNRAS.415.2876BPercival:2004fsHowlett:2014opa2012MNRAS.423.3430BSong:2008qt and can be found summarized in Table II of Albarran:2016mdu.
• Figure 3: Total matter (baryons + CDM) fluctuation $\delta$, given by Eq. \ref{['totalmatterfluct']}, for $\Lambda$CDM (solid line) and for the coupled quintessence model with $\beta=0.05$ (dashed line) and $\beta=0.08$ (dotted line). It was used the value $\sigma_8(0)=0.818$.
• Figure 4: Observational constraints for $\beta$ and $\sigma_8$. Contour plot for the 1$\sigma$ and 2$\sigma$ regions with a dot on the best fit values, and the respective marginalized curves.
• Figure 5: Mock data for the estimated error bars for the future SKA (black) and Euclid (gray) missions Raccanelli:2015qqa. The presented lines are the ones of Fig. \ref{['fgdata']}.