Galaxy clustering analysis with SimBIG and the wavelet scattering transform

Abstract

The non-Gaussian spatial distribution of galaxies traces the large-scale structure of the Universe and therefore constitutes a prime observable to constrain cosmological parameters. We conduct Bayesian inference of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Λ</a:mi><a:mi>CDM</a:mi></a:math> parameters <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi mathvariant="normal">Ω</d:mi><d:mi>m</d:mi></d:msub></d:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi mathvariant="normal">Ω</g:mi><g:mi>b</g:mi></g:msub></g:math>, <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>h</j:mi></j:math>, <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mi>n</l:mi><l:mi>s</l:mi></l:msub></l:math>, and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>σ</n:mi><n:mn>8</n:mn></n:msub></n:math> from the Baryon Oscillation Spectroscopic Survey CMASS galaxy sample by combining the wavelet scattering transform (WST) with a simulation-based inference approach enabled by the SimBIG forward model. We design a set of reduced WST statistics that leverage symmetries of redshift-space data. Posterior distributions are estimated with a conditional normalizing flow trained on 20,000 simulated SimBIG galaxy catalogs with survey realism. We assess the accuracy of the posterior estimates using simulation-based calibration and quantify generalization and robustness to the change of forward model using a suite of 2000 test simulations. When probing scales down to <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>k</p:mi><p:mi>max</p:mi></p:msub><p:mo>=</p:mo><p:mn>0.5</p:mn><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>h</p:mi><p:mo stretchy="false">/</p:mo><p:mi>Mpc</p:mi></p:math>, we are able to derive accurate posterior estimates that are robust to the change of forward model for all parameters, except <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>σ</s:mi><s:mn>8</s:mn></s:msub></s:math>. We mitigate the robustness issues with <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>σ</u:mi><u:mn>8</u:mn></u:msub></u:math> by removing the WST coefficients that probe scales smaller than <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>k</w:mi><w:mo>∼</w:mo><w:mn>0.3</w:mn><w:mtext> </w:mtext><w:mtext> </w:mtext><w:mi>h</w:mi><w:mo stretchy="false">/</w:mo><w:mi>Mpc</w:mi></w:math>. Applied to the Baryon Oscillation Spectroscopic Survey CMASS sample, our WST analysis yields seemingly improved constraints obtained from a standard perturbation-theory-based power spectrum analysis with <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msub><z:mi>k</z:mi><z:mi>max</z:mi></z:msub><z:mo>=</z:mo><z:mn>0.25</z:mn><z:mtext> </z:mtext><z:mtext> </z:mtext><z:mi>h</z:mi><z:mo stretchy="false">/</z:mo><z:mi>Mpc</z:mi></z:math> for all parameters except <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>h</cb:mi></cb:math>. However, we still raise concerns on these results. The observational predictions significantly vary across different normalizing flow architectures, which we interpret as a form of model misspecification. This highlights a key challenge for forward modeling approaches when using summary statistics that are sensitive to detailed model-specific or observational imprints on galaxy clustering. Published by the American Physical Society 2024

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