Reconstructing the history of structure formation using redshift distortions

TL;DR

This work argues that redshift-space distortions offer a bias-free window into the growth of structure, enabling robust tests of cosmic acceleration. By focusing on the observable $f\sigma_8^{\rm mass}$, the authors show it can distinguish dark energy models from modified gravity without requiring prior knowledge of galaxy bias, and can probe dark energy clustering and DM–DE coupling. They compare standard dark energy, DGP-like modified gravity, clumping dark energy, and interacting dark energy scenarios, highlighting how peculiar velocity measurements will improve with future surveys (BOSS, WFMOS, EUCLID) to constrain growth across $0<z<2$. Beyond simple constraints, the paper outlines methods to reconstruct the Newtonian potential, test the continuity equation, and bound anisotropic stress, providing a multifaceted framework to discriminate among acceleration mechanisms and to test fundamental physics with structure formation.

Abstract

Measuring the statistics of galaxy peculiar velocities using redshift-space distortions is an excellent way of probing the history of structure formation. Because galaxies are expected to act as test particles within the flow of matter, this method avoids uncertainties due to an unknown galaxy density bias. We show that the parameter combination measured by redshift-space distortions, $fσ_8^{\rm mass}$ provides a good test of dark energy models, even without the knowledge of bias or $σ_8^{\rm mass}$ required to extract $f$ from this measurement (here $f$ is the logarithmic derivative of the linear growth rate, and $σ_8^{\rm mass}$ is the root-mean-square mass fluctuation in spheres with radius $8h^{-1}$Mpc). We argue that redshift-space distortion measurements will help to determine the physics behind the cosmic acceleration, testing whether it is related to dark energy or modified gravity, and will provide an opportunity to test possible dark energy clumping or coupling between dark energy and dark matter. If we can measure galaxy bias in addition, simultaneous measurement of both the overdensity and velocity fields can be used to test the validity of equivalence principle, through the continuity equation.

Figures (4)

• Figure 1: The top panel shows the percentage difference in $f$ between the sDE and DGP model (long dashed line). The sDE and DGP models are described in detail in Section \ref{['sec:mods']}. The background expansion has been matched between these two models. The bottom panel shows the percentage difference of $f\sigma_8^{\rm mass}$ between sDE and DGP. Here, the long-dashed curve includes CMB data, normalising the models at the epoch of last scattering (using $\Delta^2_{\zeta_{ini}}$), while the dashed curve shows the model normalised using a low redshift measurement of $\sigma_8^{\rm mass}(z=0)=0.82$, matching the 5-year WMAP best-fit $\Lambda$CDM value Komatsu08. The blue and black error bars are estimated from BOSS and EUCLID respectively (see Section \ref{['sec:future_constraints']} for details).
• Figure 2: The top panel shows the time evolution of $f$: solid curve is for sDE model, and a long-dash curve is for DGP. The sDE and DGP models are described in detail in Section \ref{['sec:mods']}. The bottom panel shows the evolution of $f\sigma_8^{\rm mass}$: the solid curve shows the sDE model, the long-dash curve DGP normalized using $\Delta^2_{\zeta_{ini}}$, and the short-dashed line, DGP $\sigma_8^{\rm mass}(z=0)=0.82$. The blue and black error bars are estimated from BOSS and EUCLID respectively (see Section \ref{['sec:future_constraints']} for details).
• Figure 3: The solid curve represents sDE, long-dash curve represents DGP, and dotted curve represents IDE. These models predict approximately the same background expansion, which is normalised at high redshift to match the fluctuations observed in the CMB. The left panel shows the current constraints discussed in the text. The three other panels show simulated data for BOSS, WFMOS and EUCLID-type experiments (see text for details).
• Figure 4: Constraints on physical measurements that can be derived from a EUCLID type survey. The solid lines, long-dash lines, dashed lines and dotted lines are sDE models, DGP, cDE model and IDE model respectively. The top panel shows the reconstruction of $\Psi$ from $\sigma_{8}^{\theta}$, the middle panel shows the test of the continuity equation song08b, and the bottom panel shows the constraint on anisotropic stress. The errors shown in this figure assume that we can recover $\sigma_{8}^{\theta}$ from both $P_{\theta\theta}$ and $P_{g\theta}$.