Unequal-time correlators for cosmology

• Published in: Physical review. D 2017-03, Vol.95 (6), Article 063522
• Main Authors: Kitching, T. D., Heavens, A. F.
• Format: Article
• Language: English
• Subjects: Amplitudes; Big Bang theory; Clustering; Computer simulation; Correlation analysis; Cosmology; Large scale structure of the universe; Perturbation theory; Red shift; Thermal energy
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.95.063522

Measurements of the power spectrum from large-scale structure surveys have, to date, assumed an equal-time approximation, where the full cross-correlation power spectrum of the matter density field evaluated at different times (or distances) has been approximated either by the power spectrum at a fixed time or in an improved fashion, by a geometric mean P(k;r1,r2)=[P(k;r1)P(k;r2)]1/2. In this paper we investigate the expected impact of the geometric mean ansatz and present an application in assessing the impact on weak-gravitational-lensing cosmological parameter inference, using a perturbative unequal time correlator. As one might expect, we find that the impact of this assumption is greatest at large separations in redshift Δz≳0.3 where the change in the amplitude of the matter power spectrum can be as much as 10 percent for k≳5  h Mpc−1. However, of more concern is that the corrections for small separations, where the clustering is not close to zero, may not be negligibly small. In particular, we find that for a Euclid- or LSST-like weak lensing experiment, the assumption of equal-time correlators may result in biased predictions of the cosmic shear power spectrum, and that the impact is strongly dependent on the amplitude of the intrinsic alignment signal. To compute unequal-time correlations to sufficient accuracy will require advances in either perturbation theory to high k modes or extensive use of simulations.