Deep learning reconstruction of the large scale structure of the Universe from luminosity distance observations

Abstract

Supernovae Ia (SN) are among the brightest objects we can observe and can provide a unique window on the large scale structure of the Universe at redshifts where other observations are not available. The photons emitted by SNe are in fact affected by the density field between the source and the observer, and from the observed luminosity distance it is possible to solve the inversion problem (IP), i.e. to reconstruct the density field which produced those effects.So far the IP was only solved assuming some restrictions about the geometry of the problem, such as spherical symmetry for example, and the approach was based on solving complicated systems of differential equations which required smooth function as inputs, while observational data is not smooth, due to its discrete nature. In order to overcome these limitations we develop for the first time an inversion method which is not assuming any symmetry, and can be applied directly to observational data, without the need of any data smoothing procedure.The method is based on the use of convolutional neural networks (CNN) trained on simulated data, and it shows quite accurate results. The training data set is obtained by first generating random density and velocity profiles, and then computing their effects on the luminosity distance. The CNN is then trained to reconstruct the density field from the luminosity distance. The CNN is a modified version of U-Net to account for the tridimensionality of the data, and can reconstruct the density and velocity fields with a good level of accuracy.The use of neural networks to analyze observational data from future SNe catalogues will allow to reconstruct the large scale structure of the Universe to an unprecedented level of accuracy, at a redshift at which few other observations are available.

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“…In order to extract the most of cosmological information from the tantalising amount of data to come, the deployment of machine learning (ML) algorithms on Physics and Astronomy [20,21] is becoming crucial to accelerate data processing and improve statistical inference. Some recent applications of ML on Cosmology focuses on reconstructing the latetime cosmic expansion history to test fundamental hypothesis of the standard model and constrain its parameters [22][23][24][25][26][27][28][29][30][31][32][33][34][35], cosmological model discrimination with LSS and WL [36][37][38][39][40][41][42][43][44][45][46], predicting structure formation [47][48][49][50][51][52][53][54][55][56][57], probing the era of reionisation [58][59][60][61][62][63][64], photometric redshift estimation …”

Machine Learning the Hubble Constant

“…In order to extract the most of cosmological information from the tantalizing amount of data to come, the deployment of machine learning (ML) algorithms on Physics and Astronomy [20,21] is becoming crucial to accelerate data processing and improve statistical inference. Some recent applications of ML on Cosmology focuses on reconstructing the latetime cosmic expansion history to constrain dark energy models [22][23][24][25][26][27][28][29][30][31], cosmological model discrimination with LSS and WL [32][33][34][35][36][37][38][39][40][41][42], predicting structure formation [43][44][45][46][47][48][49][50][51][52][53], probing the era of reionisation [54][55][56][57][58][59][60], photometric redshift estimation [61][62][63][64][65]…”