$Euclid$ preparation: XV. Forecasting cosmological constraints for the $Euclid$ and CMB joint analysis

TL;DR

This paper forecasts how combining Euclid and CMB data will significantly improve constraints on cosmological parameters, especially for extended models, emphasizing the importance of their joint analysis.

Contribution

It provides detailed forecasts for Euclid and CMB joint analysis, including both standard and extended cosmological models, using Fisher and posterior-fitting methods.

Findings

CMB data enhances Euclid constraints up to tenfold for standard parameters.

Extended model parameters see two to three times improvement, exceeding ten in some cases.

Joint analysis is crucial for robust cosmological constraints.

Abstract

The combination and cross-correlation of the upcoming $Euclid$ data with cosmic microwave background (CMB) measurements is a source of great expectation since it will provide the largest lever arm of epochs, ranging from recombination to structure formation across the entire past light cone. In this work, we present forecasts for the joint analysis of $Euclid$ and CMB data on the cosmological parameters of the standard cosmological model and some of its extensions. This work expands and complements the recently published forecasts based on $Euclid$-specific probes, namely galaxy clustering, weak lensing, and their cross-correlation. With some assumptions on the specifications of current and future CMB experiments, the predicted constraints are obtained from both a standard Fisher formalism and a posterior-fitting approach based on actual CMB data. Compared to a $Euclid$-only analysis, the addition of CMB data leads to a substantial impact on constraints for all cosmological parameters of the standard $\Lambda$-cold-dark-matter model, with improvements reaching up to a factor of ten. For the parameters of extended models, which include a redshift-dependent dark energy equation of state, non-zero curvature, and a phenomenological modification of gravity, improvements can be of the order of two to three, reaching higher than ten in some cases. The results highlight the crucial importance for cosmological constraints of the combination and cross-correlation of $Euclid$ probes with CMB data.