Measuring Dark Energy Clustering with CMB-Galaxy Correlations

TL;DR

The paper investigates how dark energy clustering can be constrained via the ISW effect measured through CMB–galaxy cross-correlations. It develops a framework incorporating an effective sound speed $c_e$ to parameterize the smoothness of dark energy and analyzes horizon-scale clustering, including quintessence with canonical kinetic term ($c_e=1$). Forecasts for a deep all-sky survey reaching $z\sim2$ suggest a total $S/N$ near $10$, enabling ~10% measurements of the ISW cross-spectrum and ~3% bounds on changes in the gravitational potential on Gpc scales, with sensitivity amplified by projection effects. These results imply that such cross-correlations could test the quintessence hypothesis ($|1+w| \gtrsim 0.05$) and help distinguish dark energy clustering from modified gravity, albeit requiring stringent control of systematics at the largest scales.

Abstract

The integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB) as measured through its correlation with galaxies provides a unique opportunity to study the dynamics of the dark energy through its large scale clustering properties. Ultimately, a deep all-sky galaxy survey out to z~2 can make a 10sigma or ~10% measurement of the correlation and limit ~3% changes in the gravitational potential or total density fluctuation due to dark energy clustering on the Gpc scale. A canonical single scalar field or quintessence model predicts that these clustering effects will appear on the horizon scale with a strength that reflects the evolution of the dark energy density. In terms of a constant equation of state, this would allow tests of the quintessence prediction for models where |1+w| > 0.05.

Figures (9)

• Figure 1: Fractional difference in the gravitational potential today between smooth and clustered dark energy models as a function of $w$ (upper panel) where $\Omega_{\rm DE}$ and $h$ are adjusted to keep the distance to recombination and the expansion rate at high-$z$ fixed. Also shown are the predictions for quintessence dark energy (canonical kinetic term with sound speed $c_e=1$) near the horizon scale $k=10^{-4}$ Mpc$^{-1}$ and near the broad peak of the ISW effect at low multipoles $k=10^{-3}$ Mpc$^{-1}$.
• Figure 2: Fractional change in the gravitational potential in the transition regime between smooth ($\Phi_{s}$) and clustered dark energy for several choices of the sound speed and a $w=-0.8$ model. The quintessence prediction corresponds to $c_e=1$.
• Figure 3: CMB temperature power spectrum for the $w=-0.8$ model compared with the WMAP 1 year data with noise errors and the $68\%$ and $95\%$ cosmic variance confidence bands plotted for $c_e=1$. The $c_e=0.1$ model is difficult to distinguish from the $c_e=1$ model even with perfect data despite the fact that the ISW effect changes by up to a factor of 2.
• Figure 4: Bias and redshift distribution of the galaxies. The total number density $n^{g_{\rm tot}}$ (here multiplied by $2/n_A^{g_{\rm tot}}$, with $n_A= 70$ gal arcmin$^{-2}$ for clarity) defines the linear bias $b^{n_{\rm tot}}(0;z)$ under the halo model HuJai03. This total number density is divided into photometric redshift bins of $5 \sigma(z)$ with photometric redshift errors of $\sigma(z)=0.03 (1+z)$.
• Figure 5: Galaxy-CMB cross correlation through the ISW effect for the $w=-0.8$ model. Upper panel: $c_e=1$ cross power spectra for 10 different galaxy redshift populations of Fig. \ref{['fig:redshift']}. Lower panel: ratio of the $c_e=0.1$ and $c_e=1$ power spectra. Note that the intrinsic 10% change in the gravitational potential has been amplified by up to a factor of 3 through the sensitivity of the ISW effect to changes in the gravitational potential.