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We forecast the main cosmological parameter constraints achievable with the CORE space mission which is dedicated to mapping the polarisation of the Cosmic Microwave Background (CMB). CORE was recently submitted in response to ESAs fifth call for medium-sized mission proposals (M5). Here we report the results from our pre-submission study of the impact of various instrumental options, in particular the telescope size and sensitivity level, and review the great, transformative potential of the mission as proposed. Specifically, we assess the impact on a broad range of fundamental parameters of our Universe as a function of the expected CMB characteristics, with other papers in the series focusing on controlling astrophysical and instrumental residual systematics. In this paper, we assume that only a few central CORE frequency channels are usable for our purpose, all others being devoted to the cleaning of astrophysical contaminants. On the theoretical side, we assume LCDM as our general framework and quantify the improvement provided by CORE over the current constraints from the Planck 2015 release. We also study the joint sensitivity of CORE and of future Baryon Acoustic Oscillation and Large Scale Structure experiments like DESI and Euclid. Specific constraints on the physics of inflation are presented in another paper of the series. In addition to the six parameters of the base LCDM, which describe the matter content of a spatially flat universe with adiabatic and scalar primordial fluctuations from inflation, we derive the precision achievable on parameters like those describing curvature, neutrino physics, extra light relics, primordial helium abundance, dark matter annihilation, recombination physics, variation of fundamental constants, dark energy, modified gravity, reionization and cosmic birefringence. (ABRIDGED)
We forecast the scientific capabilities to improve our understanding of cosmic inflation of CORE, a proposed CMB space satellite submitted in response to the ESA fifth call for a medium-size mission opportunity. The CORE satellite will map the CMB an
We examine the cosmological constraints that can be achieved with a galaxy cluster survey with the future CORE space mission. Using realistic simulations of the millimeter sky, produced with the latest version of the Planck Sky Model, we characterize
We present an analysis of the main systematic effects that could impact the measurement of CMB polarization with the proposed CORE space mission. We employ timeline-to-map simulations to verify that the CORE instrumental set-up and scanning strategy
We demonstrate that, for the baseline design of the CORE satellite mission, the polarized foregrounds can be controlled at the level required to allow the detection of the primordial cosmic microwave background (CMB) $B$-mode polarization with the de
We describe a space-borne, multi-band, multi-beam polarimeter aiming at a precise and accurate measurement of the polarization of the Cosmic Microwave Background. The instrument is optimized to be compatible with the strict budget requirements of a m