We provide a formula for extracting the value of the rms of the linear matter fluctuations on a scale R directly from redshift survey data. It allows us to constrain the real-space amplitude of σR without requiring any modelling of the nature and power spectrum of the matter distribution. Furthermore, the formalism is completely insensitive to the character of the bias function, namely its eventual scale or non-linear dependence. By contrasting measurements of σR with predictions from linear perturbation theory, one can test for eventual departures from the standard description of gravity on large cosmological scales.
The proposed estimator exploits the information contained in the one-point moments and two-point correlators of the matter and galaxy density fields, and it can be applied on cosmic scales where linear and semi-linear perturbative approximations of the evolution of matter overdensities offer a satisfactory description of the full underlying theory. We implement the test with N-body simulations to quantify potential systematics and successfully show that we are able to recover the present-day value of σ8‘hidden’ in them. We also design a consistency check to gauge the soundness of the results inferred when the formalism is applied to real (as opposed to simulated) data. We expect that this approach will provide a sensitive probe of the clustering of matter when applied to future large redshift surveys such as BigBOSS and Euclid.