A representation learning approach to probe for dynamical dark energy in matter power spectra
This work addresses the challenge of probing beyond-ΛCDM models in cosmology, offering a framework that could inform survey design and provide theoretical insights, though it is incremental as it builds on existing VAE methods.
The paper tackles the problem of searching for dynamical dark energy models in cosmological data by developing DE-VAE, a variational autoencoder that compresses matter power spectra boosts into a lower-dimensional representation. The result shows that a single latent parameter can predict 95% (99%) of DE power spectra within 1σ (2σ) errors for a Stage IV-like survey, with high mutual information to DE parameters.
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 $1σ$ ($2σ$) 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-$Λ$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-$Λ$CDM models.