Measuring the reionization optical depth without large-scale CMB polarization
William Giarè, Eleonora Di Valentino, A. Melchiorri
Abstract
We study the possibility of measuring the optical depth at reionization <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>τ</a:mi></a:math> without relying on large-scale cosmic microwave background (CMB) polarization. Our analysis is driven by the need to obtain competitive measurements that can validate the state-of-the-art constraints on this parameter, widely based on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>E</c:mi></c:math>-mode polarization measurements at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo>ℓ</e:mo><e:mo>≤</e:mo><e:mn>30</e:mn></e:math>. This need is partially motivated by the typical concerns regarding anomalies observed in the Planck large-scale CMB data as well as by the remarkable fact that, excluding these latter, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>τ</g:mi></g:math> consistently exhibits correlations with anomalous parameters, such as <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>A</i:mi><i:mrow><i:mi>lens</i:mi></i:mrow></i:msub></i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi mathvariant="normal">Ω</k:mi><k:mi>k</k:mi></k:msub></k:math>, suggesting that slightly higher values of the optical depth at reionization could significantly alleviate or even eliminate anomalies. Within the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi mathvariant="normal">Λ</n:mi></n:math> cold dark matter model, our most constraining result is <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>τ</q:mi><q:mo>=</q:mo><q:mn>0.080</q:mn><q:mo>±</q:mo><q:mn>0.012</q:mn></q:math>, obtained by combining Planck temperature and polarization data at <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mo>ℓ</s:mo><s:mo>></s:mo><s:mn>30</s:mn></s:math>, the Atacama Cosmology Telescope (ACT) and Planck measurements of the lensing potential, baryon acoustic oscillations (BAOs), and type-Ia supernova data from the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:mi>Pantheon</u:mi><u:mo>+</u:mo><u:mtext>catalog</u:mtext></u:mrow></u:math>. Notably, using only ACT temperature, polarization, and lensing data in combination with BAOs and supernovae, we obtain <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>τ</w:mi><w:mo>=</w:mo><w:mn>0.076</w:mn><w:mo>±</w:mo><w:mn>0.015</w:mn></w:math>, which is entirely independent of Planck. The relative precision of these results is approaching the constraints based on large-scale CMB polarization (<y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>τ</y:mi><y:mo>=</y:mo><y:mn>0.054</y:mn><y:mo>±</y:mo><y:mn>0.008</y:mn></y:math>). Despite the overall agreement, we report a slight <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mn>1.8</ab:mn><ab:mi>σ</ab:mi></ab:math> shift toward larger values of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>τ</cb:mi></cb:math>. We also test how these results change by extending the cosmological model. While in many extensions they remain robust, in general, obtaining precise measurements of <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>τ</eb:mi></eb:math> may become significantly more challenging. Published by the American Physical Society 2024