Phys. Rev. D 103, 043501 (2021) - Primordial information content of Rayleigh anisotropies

Primordial information content of Rayleigh anisotropies

William R. Coulton, Benjamin Beringue, and P. Daniel Meerburg

Phys. Rev. D 103, 043501 – Published 1 February 2021

Abstract

Anisotropies in the cosmic microwave background (CMB) are primarily generated by Thomson scattering of photons by free electrons. Around the time of recombination, the Thomson scattering probability quickly diminishes as the free electrons combine with protons to form neutral hydrogen. This production of neutral hydrogen enables a new type of scattering to occur: Rayleigh scattering of photons by hydrogen atoms. Unlike Thomson scattering, Rayleigh scattering is frequency dependent resulting in the generation of anisotropies with a different spectral dependence. Unfortunately the Rayleigh scattering efficiency rapidly decreases with the expansion of the neutral universe, with the result that only a small percentage of photons are scattered off of neutral hydrogen after recombination. Although the effect is very small, future CMB missions with higher sensitivity and improved frequency coverage are poised to measure the effect of Rayleigh scattering. The uncorrelated component of the Rayleigh anisotropies contains unique information on the primordial perturbations that could potentially be leveraged to expand our knowledge of the early universe. In this paper we explore whether measurements of Rayleigh scattering anisotropies can be used to constrain primordial non-Gaussianity and examine the hints of anomalies found by WMAP and Planck satellites. We show that the additional Rayleigh information has the potential to improve primordial non-Gaussianity constraints over pure Thompson constraints by 30%, or more. Primordial bispectra that are not of the local type benefit the most from these additional scatterings, which we attribute to the different scale dependence of the Rayleigh anisotropies. Unfortunately this different scaling means that Rayleigh measurements cannot be used to constrain anomalies or features on large scales. On the other hand, anomalies that may persist to smaller scales, such as the potential power asymmetry seen in WMAP and Planck, could be improved by the addition of Rayleigh scattering measurements.

Received 5 November 2020
Accepted 11 January 2021

DOI:https://doi.org/10.1103/PhysRevD.103.043501

Physics Subject Headings (PhySH)

Cosmic microwave background Cosmological parameters Inflation

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

William R. Coulton ^1,2, Benjamin Beringue ³, and P. Daniel Meerburg⁴

¹Institute of Astronomy and Kavli Institute for Cosmology, Madingley Road, Cambridge CB3 0HA, United Kingdom
²Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
³DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
⁴Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

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Vol. 103, Iss. 4 — 15 February 2021

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Figure 1
The ratio of the measured CMB Thomson and Rayleigh autospectra for a broken power-law primordial power spectrum, given in Eq. (2), to the $Λ CDM$ spectrum. We find that the Rayleigh temperature spectrum is unaffected by the large-scale feature.
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Figure 2
The contributions to Thomson and Rayleigh temperature power spectrum from the different source terms including both the auto and cross terms. The cross terms include a factor of 2 as this is their contribution to the total power spectrum. Dashed lines denote negative values. Note that we do not show the contributions arising from cross correlations with the quadrupole as these are highly subdominant.
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Figure 3
In the top panels we examine the cosmic variance limited constraining power of Thomson only (green lines), Rayleigh only (red lines), and combined (blue lines) measurements for three types of primordial non-Gaussianity as a function of the maximum scale used in the analysis. The dashed lines are the results when lensing effects are included in the power spectra. In the bottom panels we show the ratio of the joint Thomson and Rayleigh constraints compared to the Thomson only constraint. We find that adding Rayleigh measurements to Thomson measurements would improve the constraints on all types of non-Gaussianity by up to a factor of 2.
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Figure 4
In the top panels we explore how the constraining power of combined Thomson and Rayleigh (solid lines) and Thomson only measurements (dashed lines) varies as a function of instrument noise level and experimental beam for three types of primordial non-Gaussianity. The noise is treated as white and instrument properties are specified at 545 GHz, the observation frequency. In the bottom panels we show the ratio of the joint Thomson and Rayleigh constraints compared to the Thomson only constraint for the equivalent experimental setup. Both sets of measurements include modes up to $ℓ_{\max} = 5500$ . We see that experiments, which can isolate the Rayleigh signal with $≲ 5 μ K$ effective noise, obtain tighter constraints on primordial non-Gaussianity. We find that significant improvements can be obtained even for experiments with moderately large beams $\sim 4 arcmin$ full-width half-maximum.
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Figure 5
A comparison of expected primordial non-Gaussianity constraints from CMB measurements (both with and without including Rayleigh measurements) and from a range of up-coming large-scale structure surveys (LSS). We report the predictions for LSS surveys from Castorina et al. [30], Karagiannis et al. [31, 32]; the radio-continuum survey, the spectroscopic survey and the photometric survey are based on SKA-like, DESI-like and LSST-like surveys respectively. We see that the future CMB constraints, when Rayleigh measurements are included, provide competitive constraints to these upcoming LSS surveys.
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Physical Review D

covering particles, fields, gravitation, and cosmology

Primordial information content of Rayleigh anisotropies

William R. Coulton, Benjamin Beringue, and P. Daniel Meerburg

Phys. Rev. D 103, 043501 – Published 1 February 2021

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Physical Review D

covering particles, fields, gravitation, and cosmology

Primordial information content of Rayleigh anisotropies

William R. Coulton, Benjamin Beringue, and P. Daniel Meerburg

Phys. Rev. D 103, 043501 – Published 1 February 2021

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