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Dynamics of Interacting Quintessence Models: Observational Constraints

German Olivares, Fernando Atrio-Barandela, Diego Pavon

TL;DR

The paper analyzes the Chimento et al. interacting quintessence model (IQM) where dark matter decays into dark energy via a coupling $Q=3H c^2(\rho_x+\rho_c)$. It develops the dynamical system with dimensionless variables to identify fixed points and a late-time attractor with a constant DM/DE ratio $r=\rho_c/\rho_x$, and tests whether the model can reproduce the radiation, matter, and accelerated eras. By confronting the model with CMB, matter power spectrum, and SNIa data through MCMC and Bayesian model selection, it finds that current observations impose tight upper limits on the coupling ($c^2$ at most a few times $10^{-3}$ from CMB), with SDSS providing a weaker but complementary bound, while SN data are largely uninformative for $c^2$. The results suggest that, although the IQM can alleviate the coincidence problem, the data do not strongly favor the presence of the coupling, challenging the model’s viability as a robust solution without fine-tuning.

Abstract

Interacting quintessence models have been proposed to explain or, at least, alleviate the coincidence problem of late cosmic acceleration. In this paper we are concerned with two aspects of these kind of models: (i) the dynamical evolution of the model of Chimento et al. [L.P. Chimento, A.S. Jakubi, D. Pavon, and W. Zimdahl, Phys. Rev. D 67, 083513 (2003).], i.e., whether its cosmological evolution gives rise to a right sequence of radiation, dark matter and dark energy dominated eras, and (ii) whether the dark matter dark energy ratio asymptotically evolves towards a non-zero constant. After showing that the model correctly reproduces these eras, we correlate three data sets that constrain the interaction at three redshift epochs: $z\le 10^{4}$, $z=10^{3}$, and $z=1$. We discuss the model selection and argue that even if the model under consideration fulfills both requirements, it is heavily constrained by observation. The prospects that the coincidence problem can be explained by the coupling of dark matter to dark energy are not clearly favored by the data.

Dynamics of Interacting Quintessence Models: Observational Constraints

TL;DR

The paper analyzes the Chimento et al. interacting quintessence model (IQM) where dark matter decays into dark energy via a coupling . It develops the dynamical system with dimensionless variables to identify fixed points and a late-time attractor with a constant DM/DE ratio , and tests whether the model can reproduce the radiation, matter, and accelerated eras. By confronting the model with CMB, matter power spectrum, and SNIa data through MCMC and Bayesian model selection, it finds that current observations impose tight upper limits on the coupling ( at most a few times from CMB), with SDSS providing a weaker but complementary bound, while SN data are largely uninformative for . The results suggest that, although the IQM can alleviate the coincidence problem, the data do not strongly favor the presence of the coupling, challenging the model’s viability as a robust solution without fine-tuning.

Abstract

Interacting quintessence models have been proposed to explain or, at least, alleviate the coincidence problem of late cosmic acceleration. In this paper we are concerned with two aspects of these kind of models: (i) the dynamical evolution of the model of Chimento et al. [L.P. Chimento, A.S. Jakubi, D. Pavon, and W. Zimdahl, Phys. Rev. D 67, 083513 (2003).], i.e., whether its cosmological evolution gives rise to a right sequence of radiation, dark matter and dark energy dominated eras, and (ii) whether the dark matter dark energy ratio asymptotically evolves towards a non-zero constant. After showing that the model correctly reproduces these eras, we correlate three data sets that constrain the interaction at three redshift epochs: , , and . We discuss the model selection and argue that even if the model under consideration fulfills both requirements, it is heavily constrained by observation. The prospects that the coincidence problem can be explained by the coupling of dark matter to dark energy are not clearly favored by the data.

Paper Structure

This paper contains 10 sections, 9 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Dynamics of the Interacting Quintessence Model
  3. IQM and the coincidence problem
  4. Baryon dominated era
  5. Comparison with observational data
  6. Constraints on IQMs from WMAP 3yr data
  7. Constraints on IQMs from SDSS and 2dFRGS data
  8. Constraints from SNIa data
  9. Bayesian model selection
  10. Conclusions

Figures (7)

  • Figure 1: Evolution of the different energy densities with redshift. Left panel: $c^2=10^{-3}$, right panel: $c^2=0.1$. Thick and thin solid, and thick, and thin dot-dashed lines correspond to dark matter, dark energy, baryons and photons, respectively.
  • Figure 2: Matter, radiation power spectrum, and luminosity distance for a cosmological model with $\Omega_{x}=0.74$ and $w_x=-0.9$ and three different interaction parameters $c^2= 0, 10^{-2}, 0.1$, corresponding to solid, dotted, and long dashed lines, respectively. The cosmological parameters are those of the fiducial WMAP 3yr data.
  • Figure 3: 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 at $c^2\le 10^{-5}$.
  • Figure 4: Joint confidence intervals at the same confidence levels as in Fig. \ref{['fig:c2wmap3']} for pairs of parameters after marginalizing over the rest.
  • Figure 5: Contours as in Fig. \ref{['fig:c2wmap3']} obtained using the SDSS matter power spectrum data.
  • ...and 2 more figures