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Abstract Local measurements of the Hubble constant ( $$H_0$$ H 0 ) based on Cepheids e Type Ia supernova differ by $$\approx 5 \sigma $$ ≈ 5 σ from the estimated value of $$H_0$$ H 0 from Planck CMB observations under $$\Lambda $$ Λ CDM assumptions. In order to better understand this $$H_0$$ H 0 tension, the comparison of different methods of analysis will be fundamental to interpret the data sets provided by the next generation of surveys. In this paper, we deploy machine learning algorithms to measure the $$H_0$$ H 0 through a regression analysis on synthetic data of the expansion rate assuming different values of redshift and different levels of uncertainty. We compare the performance of different regression algorithms as Extra-Trees, Artificial Neural Network, Gradient Boosting, Support Vector Machines, and we find that the Support Vector Machine exhibits the best performance in terms of bias-variance tradeoff in most cases, showing itself a competitive cross-check to non-supervised regression methods such as Gaussian Processes.

Abstract Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.