A 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 $k\in(0.01-2.5) \ h/\rm{Mpc}$ and at four redshift values $z\in(0.1,0.48,0.78,1.5)$ 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 $1\sigma$ ($2\sigma$) 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-$\Lambda$CDM 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-$\Lambda$CDM models.