SciPost Submission Page
On the sensitivity of weak gravitational lensing to the cosmic expansion function
by Christian F. Schmidt, Matthias Bartelmann
|As Contributors:||Matthias Bartelmann|
|Date submitted:||2021-09-17 08:26|
|Submitted by:||Bartelmann, Matthias|
|Submitted to:||SciPost Astronomy|
We analyse the functional derivative of the cosmic-shear power spectrum $C_\ell^\gamma$ with respect to the cosmic expansion function. Our interest in doing so is two-fold: (i) In view of attempts to detect minor changes of the cosmic expansion function which may be due to a possibly time-dependent dark-energy density, we wish to know how sensitive the weak-lensing power spectrum is to changes in the expansion function. (ii) In view of recent empirical determinations of the cosmic expansion function from distance measurements, independent of specific cosmological models, we wish to find out how uncertainties in the expansion function translate to uncertainties in the cosmic-shear power spectrum. We find the following answers: Relative changes of the expansion function are amplified by the cosmic-shear power spectrum by a factor $\approx 4-6$ on intermediate and small angular scales, weakly depending on the scale factor where the change is applied, and the current uncertainty of one example for an empirically determined expansion function translates to a relative uncertainty of the cosmic-shear power spectrum of $\approx15\,\%$.
Author comments upon resubmission
we thank the referee for the favourable report on our paper. In response to it, we have added one panel to Fig. 3, now Fig. 3b, which shows that the numerically evaluated functional derivative of the growth factor with respect to the expansion function agrees very well with the analytic result shown in the paper. In the paragraph below Eq. (31), we comment on this additional panel.
In addition, we had to correct Eq. (25) by adding a term we had previously missed and which leaves our final results essentially unchanged.
We hope that our paper is now acceptable for publication in SciPost Astronomy.
Matthias Bartelmann and Christian F. Schmidt
List of changes
In response to the referee's report, we have:
– Added a panel to Fig. 3 (now Fig. 3b) showing the numerically evaluated functional derivative of the growth factor with respect to the expansion function for an Einstein-de Sitter universe, for comparison with the respective analytic expression;
– Added text after Eq. (31) to hint at this Fig. 3b.
In addition, we have corrected Eq. (25) by an additional term, which has essentially no effect on our final results.