@article{discovery10028044,
           month = {March},
          volume = {95},
       publisher = {AMER PHYSICAL SOC},
            note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.},
          number = {6},
         journal = {Physical Review D},
            year = {2017},
           title = {Unequal-time correlators for cosmology},
        keywords = {Science \& Technology, Physical Sciences, Astronomy \& Astrophysics, Physics, Particles \& Fields, Physics, Cosmic Structure Formation, Redshift-Space, Power Spectrum, Galaxies},
          author = {Kitching, TD and Heavens, AF},
        abstract = {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
;
r
1
,
r
2
)
=
[
P
(
k
;
r
1
)
P
(
k
;
r
2
)
]
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 {\ensuremath{\Delta}}z {$\gtrsim$} 0.3 where the change in the amplitude of the matter power spectrum can be as
much as 10 percent for k {$\gtrsim$} 5 h {$\times$} 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.},
             url = {https://doi.org/10.1103/PhysRevD.95.063522},
            issn = {2470-0029}
}