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<https://discovery.ucl.ac.uk/id/eprint/10028044> <http://purl.org/ontology/bibo/abstract> "Measurements of the power spectrum from large-scale structure surveys have, to date, assumed an\r\nequal-time approximation, where the full cross-correlation power spectrum of the matter density field\r\nevaluated at different times (or distances) has been approximated either by the power spectrum at a fixed\r\ntime or in an improved fashion, by a geometric mean P\r\n(\r\nk\r\n;\r\nr\r\n1\r\n,\r\nr\r\n2\r\n)\r\n=\r\n[\r\nP\r\n(\r\nk\r\n;\r\nr\r\n1\r\n)\r\nP\r\n(\r\nk\r\n;\r\nr\r\n2\r\n)\r\n]\r\n1\r\n/\r\n2. In this paper we\r\ninvestigate the expected impact of the geometric mean ansatz and present an application in assessing the\r\nimpact on weak-gravitational-lensing cosmological parameter inference, using a perturbative unequal\r\ntime correlator. As one might expect, we find that the impact of this assumption is greatest at large\r\nseparations in redshift Δz ≳ 0.3 where the change in the amplitude of the matter power spectrum can be as\r\nmuch as 10 percent for k ≳ 5 h × Mpc−1. However, of more concern is that the corrections for small\r\nseparations, where the clustering is not close to zero, may not be negligibly small. In particular, we find\r\nthat for a Euclid- or LSST-like weak lensing experiment, the assumption of equal-time correlators may\r\nresult in biased predictions of the cosmic shear power spectrum, and that the impact is strongly dependent\r\non the amplitude of the intrinsic alignment signal. To compute unequal-time correlations to sufficient\r\naccuracy will require advances in either perturbation theory to high k modes or extensive use of\r\nsimulations."^^<http://www.w3.org/2001/XMLSchema#string> .
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