<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi><mml:mi>CDM</mml:mi></mml:mrow></mml:math> and early dark energy in latent space: A data-driven parametrization of the CMB temp

Finding the best parametrization for cosmological models in the absence of first-principle theories is an open question. We propose a data-driven parametrization of cosmological models given by the disentangled “latent” representation of a variational autoencoder (VAE) trained to compress cosmic microwave background (CMB) temperature power spectra. We consider a broad range of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi mathvariant="normal">Λ</a:mi></a:mrow></a:math>-cold-dark-matter (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>λ</d:mi><d:mi>CDM</d:mi></d:math>) and beyond-<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="normal">Λ</f:mi><f:mi>CDM</f:mi></f:math> cosmologies with an additional early dark energy (EDE) component. We show that these spectra can be compressed into five (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi mathvariant="normal">Λ</i:mi><i:mi>CDM</i:mi></i:math>) or eight (EDE) independent latent parameters, as expected when using temperature power spectra alone, and which reconstruct spectra at an accuracy well within the errors. These latent parameters have a physical interpretation in terms of well-known features of the CMB temperature spectrum: these include the position, height and even-odd modulation of the acoustic peaks, as well as the gravitational lensing effect. The VAE also discovers one latent parameter which entirely isolates the EDE effects from those related to <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi mathvariant="normal">Λ</l:mi><l:mi>CDM</l:mi></l:math> parameters, thus revealing a previously unknown degree of freedom in the CMB temperature power spectrum. We further showcase how to place constraints on the latent parameters using data as typically done for cosmological parameters, obtaining latent values consistent with previous <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="normal">Λ</o:mi><o:mi>CDM</o:mi></o:math> and EDE cosmological constraints. Our work demonstrates the potential of a data-driven reformulation of current beyond-<r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi mathvariant="normal">Λ</r:mi><r:mi>CDM</r:mi></r:math> phenomenological models into the independent degrees of freedom to which the data observables are sensitive.