Lensing-induced morphology changes in CMB temperature maps in modified gravity theories

TL;DR

This paper explores how lensing-induced changes in CMB temperature map morphology can be used to test modified gravity theories, employing topological descriptors and kurt-spectra with high detection potential in future CMB missions.

Contribution

It introduces the use of kurt-spectra and topological estimators to probe modified gravity theories through CMB lensing effects, demonstrating their high sensitivity and potential to distinguish models.

Findings

High signal-to-noise detection estimates for lensing-induced morphology changes.

Many modified gravity theories can be rejected with high significance using this technique.

Topological estimators can distinguish lensing from other secondary effects like the kSZ.

Abstract

Lensing of the Cosmic Microwave Background (CMB) changes the morphology of pattern of temperature fluctuations, so topological descriptors such as Minkowski Functionals can probe the gravity model responsible for the lensing. We show how the recently introduced two-to-two and three-to-one kurt-spectra (and their associated correlation functions), which depend on the power spectrum of the lensing potential, can be used to probe modified gravity theories such as $f({R})$ theories of gravity and quintessence models. We also investigate models based on effective field theory, which include the constant-$\Omega$ model, and low-energy Ho\vrava theories. Estimates of the cumulative signal-to-noise for detection of lensing-induced morphology changes, reaches ${\cal O}(10^3)$ for the future planned CMB polarization mission COrE$^{+}$. Assuming foreground removal is possible to $\ell_{max}=3000$, we show that many modified gravity theories can be rejected with a high level of significance, making this technique comparable in power to galaxy weak lensing or redshift surveys. These topological estimators are also useful in distinguishing {\em lensing} from other scattering secondaries at the level of the four-point function or trispectrum. Examples include the kinetic Sunyaev-Zel'dovich (kSZ) effect which shares, with lensing, a lack of spectral distortion. We also discuss the complication of foreground contamination from unsubtracted point sources.