How to detect lensing rotation

Mathew Robertson; Antony Lewis

Home/Archive/arXiv

arXiv · 2303.13313

How to detect lensing rotation

Mathew Robertson·Antony Lewis

View original source ↗Read source document ↗Export metadata ↓

Abstract

Gravitational lensing rotation of images is predicted to be negligible at linear order in density perturbations, but can be produced by the post-Born lens-lens coupling at second order. This rotation is somewhat enhanced for Cosmic Microwave Background (CMB) lensing due to the large source path length, but remains small and very challenging to detect directly by CMB lensing reconstruction alone. We show the rotation may be detectable at high significance as a cross-correlation signal between the curl reconstructed with Simons Observatory (SO) or CMB-S4 data, and a template constructed from quadratic combinations of large-scale structure (LSS) tracers. Equivalently, the lensing rotation-tracer-tracer bispectrum can also be detected, where LSS tracers considered include the CMB lensing convergence, galaxy density, and the Cosmic Infrared Background (CIB), or optimal combinations thereof. We forecast that an optimal combination of these tracers can probe post-Born rotation at the level of $5.7σ$-$6.1σ$ with SO and $13.6σ$-$14.7σ$ for CMB-S4, depending on whether standard quadratic estimators or maximum a posteriori iterative methods are deployed. We also show possible improvement up to $21.3σ$ using a CMB-S4 deep patch observation with polarization-only iterative lensing reconstruction. However, these cross-correlation signals have non-zero bias because the rotation template is quadratic in the tracers, and exists even if the lensing is rotation free. We estimate this bias analytically, and test it using simple null-hypothesis simulations to confirm that the bias remains subdominant to the rotation signal of interest. Detection and then measurement of the lensing rotation cross-spectrum is therefore a realistic target for future observations.

Explore related subjects

astro-ph.CO

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Mathew Robertson, Antony Lewis. 2025-01-27. How to detect lensing rotation. https://arxiv.org/abs/2303.13313

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

From quantum fluctuations to galaxy power spectrum multipoles

These notes trace large-scale structure from primordial curvature perturbations generated by inflationary quantum fluctuations to galaxy power-spectrum multipoles. Three core lectures develop the linear matter power spectrum, spherical and anisotropic collapse, galaxy bias, redshift-space distortions, the Kaiser model, and multipole estimators with Gaussian covariance. The extension develops nonlinear bias and the one-loop effective field theory model used in full-shape analyses. Derivations are explicit; appendices collect longer calculations and solutions. The core lectures assume undergraduate-level cosmology; the extension assumes familiarity with perturbation theory.

astro-ph.CO↗

arXiv2026

A universal connection between lens density profiles and low-frequency wave optics in gravitational-wave lensing

We investigate the low-frequency behavior of the amplification factor in gravitational lensing and explore how it encodes information about the density profile of the lensing object. We derive the low-frequency expansion of the amplification factor under the Born approximation for a broad class of projected density profiles. For spherically symmetric profiles that decay faster than any power law at large distances, we derive a systematic expansion of the amplification factor in powers of frequency, with the logarithmic dependence appearing only in the leading term, and show that each expansion coefficient is determined by a finite set of moments of the density profile. We then extend the analysis to profiles with power-law tails and demonstrate that such profiles induce additional non-analytic frequency dependences, including fractional powers and logarithmic terms, which directly reflect the asymptotic behavior of the density distribution. Furthermore, we investigate the effects of non-sphericity and show that contributions from the quadrupole moment appear only as higher-order corrections relative to the spherically symmetric component in the low-frequency regime. Finally, we investigate the validity of the Born approximation in the low-frequency expansion. We derive a criterion for the maximum order of the low-frequency expansion up to which the Born approximation remains dominant over the post-Born corrections.

astro-ph.CO↗

arXiv2026

Initial clustering of primordial black holes: A general formulation for arbitrary local non-Gaussianity

Initial spatial clustering of primordial black holes (PBHs) induced by local-type non-Gaussianity (LNG) can substantially modify cosmological constraints on PBH abundance. Several inflationary scenarios that enhance curvature perturbations at small scales relevant to PBH formation predict LNG that is not necessarily perturbative. Therefore, it is crucial to establish a theoretical framework capable of investigating the initial clustering induced by arbitrary LNG. Here, we present a general analytical formulation for the PBH two-point correlation function applicable to arbitrary LNGs in the alternative approach. Under the assumptions that PBHs form only at the large peaks of perturbations, and that large-scale modes weakly modulate the local variance of small-scale perturbations, we derive an analytic expression for the PBH bias parameter, directly connecting initial clustering to the primordial trispectrum in the collapsed limit. We demonstrate the versatility of our formula by computing the bias parameters in the ultra-slow-roll inflation, curvaton, and modulated reheating scenarios. We also formally generalize the framework to broad power spectra to account for correlations across different PBH mass scales. Because our formulation does not rely on weak or perturbative non-Gaussianity assumptions, our result provides a universal theoretical basis for evaluating initial clustering impact on PBH observables.

astro-ph.CO↗