[Paper Review] Confronting the sound speed of dark energy with future cluster surveys

Tobias Basse, Ole Eggers Bjælde+2 more|arXiv (Cornell University)|May 2, 2012

Cosmology and Gravitation Theories29 references12 citations

TL;DR

This paper investigates how future galaxy cluster surveys, particularly the Euclid mission, can constrain dark energy parameters—specifically the equation of state $w$ and non-adiabatic sound speed $c_s^2$—by analyzing scale-dependent clustering in the halo mass function. Using the spherical collapse model and Fisher matrix forecasts, it shows that Euclid combined with Planck data can measure $w$ to sub-percent precision and $c_s^2$ within an order of magnitude, with dark energy contributing up to 0.1% to cluster masses due to virialization effects.

ABSTRACT

Future cluster surveys will observe galaxy clusters numbering in the hundred thousands. We consider this work how these surveys can be used to constrain dark energy parameters: in particular, the equation of state parameter w and the non-adiabatic sound speed c_s^2. We demonstrate that, in combination with Cosmic Microwave Background (CMB) observations from Planck, cluster surveys such as that in the ESA Euclid project will be able to determine a time-independent w with subpercent precision. Likewise, if the dark energy sound horizon falls within the length scales probed by the cluster survey, then c_s^2 can be pinned down to within an order of magnitude. In the course of this work, we also investigate the process of dark energy virialisation in the presence of an arbitrary sound speed. We find that dark energy clustering and virialisation can lead to dark energy contributing to the total cluster mass at approximately the 0.1% level at maximum.

Motivation & Objective

• To assess the sensitivity of future cluster surveys, such as Euclid, to dark energy parameters $w$ and $c_s^2$.
• To model the virialization process of dark energy in the spherical collapse framework for arbitrary $c_s^2$.
• To quantify the contribution of clustering dark energy to total cluster mass and its impact on the halo mass function.
• To forecast parameter constraints using the Fisher matrix method under realistic survey specifications.
• To evaluate the synergy between Euclid cluster surveys and Planck CMB observations in breaking parameter degeneracies.

Proposed method

• The Press-Schechter formalism is used to compute the halo mass function, with input from linear matter power spectra generated via the CLASS Boltzmann code for various $w$ and $c_s^2$ values.
• A modified spherical collapse model is developed to track virialization in the presence of clustering dark energy with arbitrary $c_s^2$, accounting for the dark energy's dynamical response to gravitational collapse.
• The linear threshold density for collapse is estimated using a method previously established for $c_s^2 \neq 0,1$, enabling mass-dependent collapse criteria.
• Fisher matrix forecasts are performed using survey specifications from the Euclid mission, assuming detection of ~500,000 clusters via weak lensing.
• Degeneracy breaking is analyzed by combining Euclid cluster data with Planck CMB observations, particularly for $c_s^2$ which is poorly constrained by CMB alone.
• The fiducial cosmological model is calibrated using Planck 2013 parameters, and parameter sensitivities are computed with and without marginalization over other cosmological parameters.

Experimental results

Research questions

• RQ1 Can future cluster surveys like Euclid detect the imprint of dark energy clustering on the halo mass function through scale-dependent growth?
• RQ2 What is the maximum fractional contribution of virialized dark energy to the total mass of a galaxy cluster?
• RQ3 How precisely can the equation of state parameter $w$ be constrained by combining Euclid cluster data with Planck CMB observations?
• RQ4 To what extent does the dark energy sound speed $c_s^2$ affect the cluster abundance, and can it be constrained to within an order of magnitude?
• RQ5 How do parameter degeneracies between $w$, $c_s^2$, and other cosmological parameters affect the sensitivity of cluster surveys?

Key findings

• The maximum contribution of clustering dark energy to the total virialized cluster mass is approximately 0.1%, occurring at the time of virialization.
• For dark energy sound speeds in the range $c_s^2 = 10^{-6}$ to $10^{-4}$, the number of massive clusters ($\sim 10^{16} M_\odot$) can change by up to 15% compared to the non-clustering case.
• With Planck CMB data, Euclid can constrain the time-independent equation of state $w$ to sub-percent precision ($\sim 0.1\%$) in the fiducial model.
• The combination of Euclid and Planck improves the sensitivity to $\log c_s^2$ by a factor of two compared to Euclid alone, enabling $c_s^2$ to be constrained within an order of magnitude.
• Marginalization over other parameters reduces sensitivity, but the combined Planck+Euclid analysis still improves constraints on $n_s$ by a factor of two and on $\Omega_b h^2$ by about 30%.
• The scale-dependent clustering induced by $c_s^2 \neq 1$ leads to a distinctive mass-function dependence that is detectable in future cluster surveys.