Forecasting Cosmological Constraints from Redshift Surveys

TL;DR

This paper develops a Fisher-matrix forecasting framework to quantify how redshift-space distortions in spectroscopic galaxy surveys constrain the growth of structure and gravity. Starting from a simple linear, Gaussian model and extending to non-linear velocity dispersion and multi-tracer scenarios, it shows how survey volume, galaxy density, and bias affect constraints on $f(z)\sigma_8(z)$ and can potentially yield percent-level measurements. It demonstrates substantial gains from including multiple galaxy populations (multi-tracer or multi-population approach) and discusses practical forecast scenarios for upcoming surveys like BOSS, WFMOS, and EUCLID/JDEM, including the importance of priors on velocity correlations and non-linear effects. The work provides a versatile, modular forecasting toolkit to inform survey design and theorical modeling of redshift-space distortions, while outlining key limitations such as velocity bias and the need for robust priors on the velocity cross-spectrum.

Abstract

Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for observing the build-up of cosmological structure, which depends both on the expansion rate of the Universe and our theory of gravity. In this paper we present a formalism for forecasting the constraints on the growth of structure which would arise in an idealized survey. This Fisher matrix based formalism can be used to study the power and aid in the design of future surveys.

Figures (5)

• Figure 1: The correlation coefficient, $r(k)$, between the density and velocity divergence of the dark matter in an N-body simulation of a $\Lambda$CDM cosmology, with the same cosmological parameters as our fiducial model.
• Figure 2: (Top) $P_{\Theta\Theta}(k_i,z_j)$ in redshift bins of width $\Delta z=0.2$ at $z_j=0.5$ (solid) and 1.5 (dashed) from a half-sky survey with $b=1.5$ and $\bar{n} = 5\times 10^{-3}\,h^3\,{\rm Mpc}^{-3}$. (Bottom) The fractional error on $P_{\Theta\Theta}(k_i,z_j)$ in the same bins weighting modes with $\sigma_{\rm th}=0.1$ (see text).
• Figure 3: The fractional error on $f(z)\sigma_8(z)$ arising from a $10\,(h^{-1}{\rm Gpc})^3$ survey at $z=0$ populated with two types of galaxies. The first population is held fixed with $b_1=1$ and $\bar{n}_1=10^{-2}\,h^3\,{\rm Mpc}^{-2}$, i.e. $\bar{n}P\gg 1$. The second population has $b_2=1.4$ (solid), $b_2=2$ (dashed) or $b_2=4$ (dotted) and the constraint is plotted vs. $\bar{n}_2$. All else being equal, the fractional constraints would be tighter at higher $z$ where $f$ is larger.
• Figure 4: The fractional error on $f(z)\sigma_8(z)$ in bins of width $\Delta z=0.1$, arising from fiducial surveys with parameters given in Table \ref{['tab:surveys']}. We consider all galaxies in a single bin (solid lines), and split into 4 bins as a function of bias (dashed lines). The existing constraints, as collected in Song08b and with the addition of Ang08, are shown as solid squares (see text).
• Figure 5: The fractional error on $P_{\Theta\Theta}$ using the experimental parameters in Table \ref{['tab:surveys']}. We show only a single, representative bin in redshift for each experiment, to avoid clutter.