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Clustering in dynamical dark energy: observational constraints from DESI, CMB, and supernovae

Yuhang Yang, Qingqing Wang, Xin Ren, Emmanuel N. Saridakis, Yi-Fu Cai

TL;DR

The paper investigates whether dynamical dark energy clusters by constraining the dark-energy sound speed using two complementary perturbation frameworks, PPF and EFT, against DESI DR2 BAO, Planck 2018 CMB, and Union3 SNe data. It analyzes $w$CDM and $w_0w_a$CDM backgrounds, finding that $c_s^2$ is unconstrained for $w$CDM under PPF, while $w_0w_a$CDM+PPF prefers a small $c_s^2$ with a MAP around $ ext{log}_{10} c_s^2 \, o\,-0.9780$; EFT suggests a mean $c_s^2$ of roughly $0.3$–$0.4$ with sizable uncertainties. The inferred equation of state shows quintom-B behavior with deviations from ΛCDM at ~3.2–3.6σ, depending on the perturbation framework. Model selection via AIC favors the $w_0w_a$CDM without clustering, whereas BIC still prefers ΛCDM. Overall, current data mildly favor dynamical dark energy but do not provide evidence for significant DE clustering, highlighting the need for future high-precision observations to test perturbative properties more definitively.

Abstract

We investigate the clustering properties of dynamical dark energy using the latest cosmological observations. We describe the dark energy perturbation within two complementary frameworks, namely the Parameterized Post-Friedmann (PPF) approach and the Effective Field Theory (EFT) of dark energy. Using DESI DR2 baryon acoustic oscillations together with Planck 2018 CMB data and the Union3 supernova sample, we constrain the effective sound speed of dark energy in both the $w$CDM and $w_0w_a$CDM backgrounds. Within the PPF description, the sound speed remains unconstrained for $w$CDM, while for the $w_0w_a$CDM case we obtain $\log_{10} c_s^2 = -3.00^{+2.9}_{-0.99}$. Additionally, in the EFT framework, both models favor a small sound speed, with a mean value $c_s^2 \simeq 0.3$--$0.4$ but with significant uncertainties. For dynamical dark energy, the reconstructed equation of state clearly exhibits a quintom-B behavior, and its deviation from $Λ$CDM reaches $3.42σ$, rising to $3.63σ$ when PPF perturbations are included and reducing to $3.19σ$ in the EFT case. Finally, model comparison using information criteria shows that the $w_0w_a$CDM model with a smooth, non-clustering dark energy component ($c_s^2 = 1$) is preferred by AIC, whereas BIC favors $Λ$CDM. In summary, current data indicate a mild preference for dynamical dark energy but no evidence for significant clustering, which implies the need for future high-precision observations to probe the perturbative behavior more definitively.

Clustering in dynamical dark energy: observational constraints from DESI, CMB, and supernovae

TL;DR

The paper investigates whether dynamical dark energy clusters by constraining the dark-energy sound speed using two complementary perturbation frameworks, PPF and EFT, against DESI DR2 BAO, Planck 2018 CMB, and Union3 SNe data. It analyzes CDM and CDM backgrounds, finding that is unconstrained for CDM under PPF, while CDM+PPF prefers a small with a MAP around ; EFT suggests a mean of roughly – with sizable uncertainties. The inferred equation of state shows quintom-B behavior with deviations from ΛCDM at ~3.2–3.6σ, depending on the perturbation framework. Model selection via AIC favors the CDM without clustering, whereas BIC still prefers ΛCDM. Overall, current data mildly favor dynamical dark energy but do not provide evidence for significant DE clustering, highlighting the need for future high-precision observations to test perturbative properties more definitively.

Abstract

We investigate the clustering properties of dynamical dark energy using the latest cosmological observations. We describe the dark energy perturbation within two complementary frameworks, namely the Parameterized Post-Friedmann (PPF) approach and the Effective Field Theory (EFT) of dark energy. Using DESI DR2 baryon acoustic oscillations together with Planck 2018 CMB data and the Union3 supernova sample, we constrain the effective sound speed of dark energy in both the CDM and CDM backgrounds. Within the PPF description, the sound speed remains unconstrained for CDM, while for the CDM case we obtain . Additionally, in the EFT framework, both models favor a small sound speed, with a mean value -- but with significant uncertainties. For dynamical dark energy, the reconstructed equation of state clearly exhibits a quintom-B behavior, and its deviation from CDM reaches , rising to when PPF perturbations are included and reducing to in the EFT case. Finally, model comparison using information criteria shows that the CDM model with a smooth, non-clustering dark energy component () is preferred by AIC, whereas BIC favors CDM. In summary, current data indicate a mild preference for dynamical dark energy but no evidence for significant clustering, which implies the need for future high-precision observations to probe the perturbative behavior more definitively.

Paper Structure

This paper contains 12 sections, 9 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. PPF description for the dark energy perturbations
  3. Effective field theory of dark energy
  4. Data and Results
  5. Data
  6. Results and discussion
  7. Constraints from PPF dark energy perturbations
  8. EFT constraints on dark energy perturbations
  9. Reconstruction of the sound speed in EFT
  10. Constraints on the equation of state
  11. Summary of constraints and model comparison
  12. Conclusions

Figures (6)

  • Figure 1: Normalized marginalized 1D posteriors for $\log_{10}{c_s^2}$, for $w$CDM+PPF and $w_0w_a$CDM+PPF using BAO+CMB+SNe datasets. The dashed line represents the the Maximum A Posteriori (MAP) value $\log_{10}{c_s^2}=-0.9780$ for $w_0w_a$CDM model, marginalized using procoli.
  • Figure 2: Constraints on $w$CDM model under Parameterized Post-Friedmann (PPF) and Effective Field Theory (EFT) perturbation descriptions, using BAO+CMB+SNe datasets. The contours represent the 68% and 95% credible intervals. The results are summarized in Table \ref{['table:mcmc_result']}.
  • Figure 3: Constraints on $w_0w_a$CDM model under Parameterized Post-Friedmann (PPF) and Effective Field Theory (EFT) perturbation descriptions, using BAO+CMB+SNe datasets. The contours represent the 68% and 95% credible intervals. The results are summarized in Table \ref{['table:mcmc_result']}. Additionally, the dashed lines represent the Maximum A Posteriori (MAP) values for $w_0w_a$CDM+PPF, namely $\Omega_\mathrm{m}=0.3258$, $H_0=66.09$$\mathrm{km}$$\mathrm{s}^{-1}$$\mathrm{Mpc}^{-1}$, $w_0=-0.6871$, $w_a=-0.9867$, $\log_{10}{c_s^2}=-0.9780$, marginalized using procoli.
  • Figure 4: 2D posterior distributions for the EFT coefficients $c_\mathrm{M}$ and $c_\mathrm{B}$, for $w$CDM+EFT and $w_0w_a$CDM+EFT using BAO+CMB+SNe datasets.
  • Figure 5: Comparison of the reconstructed sound speed square of dark energy $c_s^2$ between $w$CDM+EFT and $w_0w_a$CDM+EFT, using BAO+CMB+SNe datasets. The $w$CDM+EFT reconstruction is shown in blue, accompanied by shaded 68% and 95% confidence intervals. While the $w_0w_a$CDM+EFT is shown in green, the green dashed curve and green dot-dashed curve represent 68% and 95% confidence intervals, respectively. Additionally, both solid curves represent the mean values. Finally, the reconstruction is truncated at $z=5$ since $\Omega_\mathrm{de}$ becomes negligible at higher redshift.
  • ...and 1 more figures