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Observational constraints on interacting quintessence models

German Olivares, Fernando Atrio-Barandela, Diego Pavon

TL;DR

This work addresses how to constrain interacting quintessence models in which the quintessence field decays into cold dark matter, aiming to solve the coincidence problem and alter both background and perturbation evolution. The authors implement a six-parameter flat cosmology with a small coupling $c^2$, derive analytic background solutions with a late-time attractor for the matter–dark-energy ratio, and evolve perturbations to compare with WMAP CMB data using a grid-based likelihood approach. They find a best-fit model with $Ω_x\approx0.43$, $Ω_b\approx0.08$, $n_s\approx0.98$, $H_0\approx56$ km s$^{-1}$ Mpc$^{-1}$, and $c^2\approx0.005$, with $w_x\lesssim-0.86$, and show that non-interacting models are disfavored at ~99% CL; combining with supernova data shifts $Ω_x$ toward ~0.68 and increases $c^2$ slightly. Bayesian criteria modestly favor the interacting model over the no-interaction case, and the study demonstrates that a small dark sector coupling can better fit CMB observations while offering a testable explanation for cosmic coincidence, albeit requiring independent measurements of baryon and matter densities to robustly confirm or refute the scenario.

Abstract

We determine the range of parameter space of Interacting Quintessence Models that best fits the recent WMAP measurements of Cosmic Microwave Background temperature anisotropies. We only consider cosmological models with zero spatial curvature. We show that if the quintessence scalar field decays into cold dark matter at a rate that brings the ratio of matter to dark energy constant at late times,the cosmological parameters required to fit the CMB data are: Ω_x = 0.43 \pm 0.12, baryon fraction Ω_b = 0.08 \pm 0.01, slope of the matter power spectrum at large scals n_s = 0.98 \pm 0.02 and Hubble constant H_0 = 56 \pm 4 km/s/Mpc. The data prefers a dark energy component with a dimensionless decay parameter c^2 =0.005 and non-interacting models are consistent with the data only at the 99% confidence level. Using the Bayesian Information Criteria we show that this exra parameter fits the data better than models with no interaction. The quintessence equation of state parameter is less constrained; i.e., the data set an upper limit w_x \leq -0.86 at the same level of significance. When the WMAP anisotropy data are combined with supernovae data, the density parameter of dark energy increases to Ω_x \simeq 0.68 while c^2 augments to 6.3 \times 10^{-3}. Models with quintessence decaying into dark matter provide a clean explanation for the coincidence problem and are a viable cosmological model, compatible with observations of the CMB, with testable predictions. Accurate measurements of baryon fraction and/or of matter density independent of the CMB data, would support/disprove these models.

Observational constraints on interacting quintessence models

TL;DR

This work addresses how to constrain interacting quintessence models in which the quintessence field decays into cold dark matter, aiming to solve the coincidence problem and alter both background and perturbation evolution. The authors implement a six-parameter flat cosmology with a small coupling , derive analytic background solutions with a late-time attractor for the matter–dark-energy ratio, and evolve perturbations to compare with WMAP CMB data using a grid-based likelihood approach. They find a best-fit model with , , , km s Mpc, and , with , and show that non-interacting models are disfavored at ~99% CL; combining with supernova data shifts toward ~0.68 and increases slightly. Bayesian criteria modestly favor the interacting model over the no-interaction case, and the study demonstrates that a small dark sector coupling can better fit CMB observations while offering a testable explanation for cosmic coincidence, albeit requiring independent measurements of baryon and matter densities to robustly confirm or refute the scenario.

Abstract

We determine the range of parameter space of Interacting Quintessence Models that best fits the recent WMAP measurements of Cosmic Microwave Background temperature anisotropies. We only consider cosmological models with zero spatial curvature. We show that if the quintessence scalar field decays into cold dark matter at a rate that brings the ratio of matter to dark energy constant at late times,the cosmological parameters required to fit the CMB data are: Ω_x = 0.43 \pm 0.12, baryon fraction Ω_b = 0.08 \pm 0.01, slope of the matter power spectrum at large scals n_s = 0.98 \pm 0.02 and Hubble constant H_0 = 56 \pm 4 km/s/Mpc. The data prefers a dark energy component with a dimensionless decay parameter c^2 =0.005 and non-interacting models are consistent with the data only at the 99% confidence level. Using the Bayesian Information Criteria we show that this exra parameter fits the data better than models with no interaction. The quintessence equation of state parameter is less constrained; i.e., the data set an upper limit w_x \leq -0.86 at the same level of significance. When the WMAP anisotropy data are combined with supernovae data, the density parameter of dark energy increases to Ω_x \simeq 0.68 while c^2 augments to 6.3 \times 10^{-3}. Models with quintessence decaying into dark matter provide a clean explanation for the coincidence problem and are a viable cosmological model, compatible with observations of the CMB, with testable predictions. Accurate measurements of baryon fraction and/or of matter density independent of the CMB data, would support/disprove these models.

Paper Structure

This paper contains 4 sections, 8 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The interacting quintessence model
  3. Observational constraints on the matter-quintessence coupling
  4. Discussion

Figures (5)

  • Figure 1: Redshift evolution of different energy densities. Solid, dashed, dotted and dot-dashed lines correspond to $\Omega_{c}$, $\Omega_x$, $\Omega_{r}$ and $\Omega_{b}$, respectively. In panel (a) $c^2=0.1$, and in panel (b) $c^2=5\times 10^{-3}$. The following parameters were assumed: $\Omega_{c,0}= 0.25$, $\Omega_{x,0}= 0.7$, $\Omega_{b,0}= 0.05$, $\Omega_{r,0}= 10^{-5}$, and $w_{x} = -0.99$.
  • Figure 2: Evolution of the ratio $r = \rho_{c}/\rho_{x}$ from an unstable maximum toward a stable minimum (at late times) for different values of $c^{2}$. We took $r_{0}= 0.42$ as the current value.
  • Figure 3: Joint confidence intervals at 68%, 95% and 99.9% confidence level of IQM fitted to the "gold" sample of SNIa data of Riess et al.hubble
  • Figure 4: Joint confidence intervals at the 68%, 95% and 99.9% level for pairs of parameters after marginalizing over the rest. For convenience the $c^2$ axis is represented using a logarithmic scale and it has been cut to $c^2\le 10^{-4}$, though models with $c^2 = 0$ have been included in the analysis. In panels (a), (b) and (c) models were fit to CMB data alone. In panel (d) we included supernovae data of Riess et al.hubble.
  • Figure 5: Radiation Power Spectrum. The solid line is our best fit model ($c^2=5\times 10^{-3}$, $\Omega_{x}=0.43$, $\Omega_{b}=0.08$, $H_0=54\,km/s/Mpc$, $n_s=0.98$,$w=-0.99$). Dashed line corresponds to the $\Lambda CDM$ concordance model and dot-dashed line is $QCDM$ with parameters $\Omega_x=0.5$, $\Omega_b = 0.07$, $H_{0}=60\,km/s/Mpc$, $w=-0.75$ and $n_s=1.02$.