Second order geodesic corrections to cosmic shear

113

204

Lensing of the CMB is affected by post-Born lensing, producing corrections to the convergence power spectrum and introducing field rotation. We show numerically that the lensing convergence power spectrum is affected at the 0.2% level on accessible scales, and that this correction and the field rotation are negligible for observations with arcminute beam and noise levels 1 µK arcmin. The field rotation generates ∼ 2.5% of the total lensing B-mode polarization amplitude (0.2% in power on small scales), but has a blue spectrum on large scales, making it highly subdominant to the convergence B modes on scales where they are a source of confusion for the signal from primordial gravitational waves. Since the post-Born signal is non-linear, it also generates a bispectrum with the convergence. We show that the post-Born contributions to the bispectrum substantially change the shape predicted from large-scale structure non-linearities alone, and hence must be included to estimate the expected total signal and impact of bispectrum biases on CMB lensing reconstruction quadratic estimators and other observables. The field-rotation power spectrum only becomes potentially detectable for noise levels 1 µK arcmin, but its bispectrum with the convergence may be observable at ∼ 3σ with Stage IV observations. Rotation-induced and convergence-induced B modes are slightly correlated by the bispectrum, and the bispectrum also produces additional contributions to the lensed BB power spectrum.

Section: B Leading-order Resultsmentioning

confidence: 99%

Impact of post-Born lensing on the CMB

Pratten

Lewis

2016

113

204

“…Broadly speaking, on small scales terms with the most angular derivatives are expected to dominate. At second order this are the well known Born approximation, lens-lens coupling, and reduced shear contributions [12,13,15,16,18,19,31]. Third order terms derived from the aforementioned have at least the same number of angular derivatives and are therefore expected to be the dominant third order contributions.…”

Section: Correctionsmentioning

confidence: 99%

“…In this work we investigate the effect of higher order lensing terms on the tSZ-lensing cross correlation. There has been considerable effort to characterize higher order contributions to correlations of lensing observables [12][13][14][15][16][17][18][19][20][21][22][23]. Some of these higher order effects, like the rotation power spectrum, have been successfully observed in high-resolution ray-tracing simulations [24,25].…”

Section: Introductionmentioning

confidence: 99%

Weak lensing corrections to tSZ-lensing cross correlation

Tröster

Waerbeke

2014

Abstract. The cross correlation between the thermal Sunyaev-Zeldovich (tSZ) effect and gravitational lensing in wide field has recently been measured. It can be used to probe the distribution of the diffuse gas in large scale structure, as well as inform us about the missing baryons. As for any lensing-based quantity, higher order lensing effects can potentially affect the signal. Here, we extend previous higher order lensing calculations to the case of tSZ-lensing cross correlations. We derive terms analogous to corrections due to the Born approximation, lens-lens coupling, and reduced shear up to order O(Φ 4 ) in the Newtonian potential. Redshift distortions and vector modes are shown to be negligible at this order. We find that the dominant correction due to the reduced shear exceeds percent-level only at multipoles of 3000.

“…There are differences in the details of the deflection angle too: There is an additional second order scalar term contributing to the deflection angle in [32]. This is the U N U N,I term that appeared in (3.9) but was argued to be negligible both here and in [15]. In [32], this term has been kept in case the PPN parameters are large enough to make the term observable.…”

Section: Comparison To Previous Resultsmentioning

confidence: 99%

“…Weak-lensing calculations have been carried out both in the Newtonian regime [7] and with GR perturbation theory (see e.g. [14,15]). However, there are few studies that both apply on smaller, non-linear scales in cosmology and are fully relativistic, thus justifying the standard ray tracing approach to extracting lensing observables from N-body simulations.…”

Section: Introductionmentioning

confidence: 99%

Relativistic weak lensing from a fully non-linear cosmological density field

Thomas

Bruni

Wands

2015

Abstract. In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E-and B-mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a welldefined manner. Specifying General Relativity, we write down a complete set of equations for a GR+ΛCDM universe for computing all of the possible lensing terms from Newtonian Nbody simulations. We illustrate this with the vector potential and show that, in a GR+ΛCDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a ΛCDM cosmology.