Exploring suppressed long-distance correlations as the cause of suppressed large-angle correlations

Abstract

The absence of large-angle correlations in the map of cosmic microwave background temperature fluctuations is among the well-established anomalies identified in full-sky and cut-sky maps over the past three decades. Suppressed large-angle correlations are rare statistical flukes in standard inflationary cosmological models. One natural explanation could be that the underlying primordial density perturbations lack correlations on large distance scales. To test this idea, we replace Fourier modes by a wavelet basis with compact spatial support. While the angular correlation function of perturbations can readily be suppressed, the observed monopole and dipole-subtracted correlation function is not generally suppressed. This suggests that suppression of large-angle temperature correlations requires a mechanism that has both real-space and harmonic-space effects.

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

“…An attempt to ascribe the absence of large angle correlations (low S 1/2 ) to an absence of long distance correlations -by replacing Fourier modes with wavelets [1529], could suppress |C(θ > 60 • )|, but not |C ≥2 (θ > 60 • )|, and so not S 1/2 .…”

What is flat ΛCDM, and may we choose it?

“…There is no compelling reason to expect a sudden cutoff in the spectrum at scales just larger than observed structures. For example, some of us [52] demonstrated that such a cutoff, somewhat unexpectedly, does not naturally explain the absence of large angle correlations in the CMB temperature fluctuations. Cosmic topology would provide a cutoff, but only on JCAP02(2023)049 scales larger than the fundamental domain, which, as described above, is already known not to be much smaller than the sphere of last scattering -the limits of our direct electromagnetic observations.…”

Simultaneous Dependence of Matter Clustering on Scale and Environment

“…With a basis function (i.e., a "wavelet") that is well localized, both in the real domain and the frequency domain, the wavelet transform acts like a "mathematical microscope," which allows us to zoom in on fine structures of the universe at various scales and locations (e.g., Kaiser & Hudgins 1994;Addison 2017). There are two major types of wavelet transforms-the discrete wavelet transform (DWT) and the continuous wavelet transform (CWT)-both of which are widely employed in cosmology (see, e.g., Martínez et al 1993;Pando & Fang 1996;Fang & Feng 2000;Starck et al 2004;Liu & Fang 2008;Zhang et al 2011;Arnalte-Mur et al 2012;da Cunha et al 2018;Shi et al 2018;Copi et al 2019;. Besides, there are also some other wavelet transform variants, e.g., the wavelet scattering transform (Mallat 2012), which performs two operations repeatedly-(1) wavelet convolution and (2) modulus-and has been proved to be superior to the Fourier power spectrum for cosmological parameter inference (e.g., Allys et al 2020;Cheng et al 2020;Valogiannis & Dvorkin 2022).…”