General relativistic effects in weak lensing angular power spectra

Abstract

Advances in upcoming weak lensing surveys pose new challenges for an accurate modeling of the lensing observables. The wide sky coverage of Euclid makes angular scales down to lmin=10 accessible. At such large angular scales, general relativistic effects manifest themselves, and the lensing magnification cannot be correctly described by the standard lensing convergence only. The impact of lineof-sight velocities on the magnification angular power spectrum, referred to as the Doppler magnification, is already well recognized in literature. In particular, it was suggested that the Doppler magnification could be extracted by measurements of both cosmic shear and magnification. In this work, we point out two previously neglected aspects with respect to this method. First, the impact of the Doppler magnification is reduced through nonvanishing cross terms with the standard lensing convergence. This is particularly relevant when the sources are averaged over a bin of width Δz0.1, such as in Euclid's tomographic weak lensing survey. Second, general relativistic potential terms slightly enhance the signal. We present numerical calculations of all relativistic effects in the weak lensing angular power spectra on large scales.

Living in a Non-Flat Universe: Theoretical Formalism

“…Since gravitational lensing is a relativistic phenomenon, the relativistic effects are naturally part of the dominant contributions, and many groups have studied the additional relativistic contributions to the weak lensing observables [62][63][64][65][66][67][68][69][70][71][72][73][74][75]. Similar to the case in galaxy clustering, relatively less attention has been paid to weak gravitational lensing in a non-flat universe (see, however, [25]).…”

Living in a non-flat universe: theoretical formalism

“…Since gravitational lensing is a relativistic phenomenon, the relativistic effects are naturally part of the dominant contributions, and many groups have studied the additional relativistic contributions to the weak lensing observables [70][71][72][73][74][75][76][77][78][79][80][81][82][83]. Similar to the case in galaxy clustering, relatively less attention has been paid to weak gravitational lensing in a non-flat universe (see, however, [33]).…”

Second-order gauge-invariant formalism for the cosmological observables: complete verification of their gauge-invariance

“…Given the relativistic nature of weak gravitational lensing and cosmic microwave background (CMB) anisotropies, their theoretical descriptions were largely complete from the inception for weak lensing [27,[46][47][48][49] and for CMB [25,50] (see, e.g., [51][52][53][54] for a review). However, extra relativistic contributions were found even at the linear order in perturbations for weak gravitational lensing [55][56][57][58][59][60][61][62][63][64] and for CMB [65][66][67].…”