Representation learning approach to probe for dynamical dark energy in matter power spectra

We present DE-VAE, a variational autoencoder (VAE) architecture to search for a compressed representation of dynamical dark energy (DE) models in observational studies of the cosmic large-scale structure.DE-VAE is trained on matter power spectra boosts generated at wavenumbers k ∈ (0.01 -2.5) h/Mpc and at four redshift values z ∈ (0.1, 0.48, 0.78, 1.5) for the most typical dynamical DE parametrization with two extra parameters describing an evolving DE equation of state.The boosts are compressed to a lower-dimensional representation, which is concatenated with standard cold dark matter (CDM) parameters and then mapped back to reconstructed boosts; both the compression and the reconstruction components are parametrized as neural networks.Remarkably, we find that a single latent parameter is sufficient to predict 95% (99%) of DE power spectra generated over a broad range of cosmological parameters within 1σ (2σ) of a Gaussian error which includes cosmic variance, shot noise and systematic effects for a Stage IV-like survey.This single parameter shows a high mutual information with the two DE parameters, and these three variables can be linked together with an explicit equation through symbolic regression.Considering a model with two latent variables only marginally improves the accuracy of the predictions, and adding a third latent variable has no significant impact on the model's performance.We discuss how the DE-VAE architecture can be extended from a proof of concept to a general framework to be employed in the search for a common lower-dimensional parametrization of a wide range of beyond-ΛCDM models and for different cosmological datasets.Such a framework could then both inform the development of cosmological surveys by targeting optimal probes, and provide theoretical insight into the common phenomenological aspects of beyond-ΛCDM models.