Unequal time correlators and the Zeldovich approximation

Abstract

The modeling of cosmological observables is based on the statistics of the matter density, velocity and gravitational fields in the Universe as a function of time. Typically, calculations are restricted to “equal time” correlations, where any given fields are evaluated at the same redshift. For some applications, it is necessary to make accurate predictions of “unequal time correlators,” where the fields considered are evaluated at different redshifts. In this work, we show that the Zel’dovich approximation provides an accurate ( < 10 % ) analytical prescription to model unequal time correlators, which we validate against numerical N -body simulations. The Zel’dovich approximation introduces a scale-dependent exponential suppression of unequal time correlators, which depends on cosmology and the redshifts of the fields considered. Comparing the Zel’dovich case to previous approximations, we show that it can yield accurate predictions for wave numbers that extend well into the nonlinear regime. However, we also show that correlations over such scales are typically suppressed by the geometry of the light cone, and thus should normally be negligible for cosmology with galaxy surveys. We discuss potential exceptions, such as intrinsic galaxy alignments, where unequal time correlators could play a role in the modeling of the observables.