We derive cosmological constraints using a galaxy cluster sample selected from the 2500 deg 2 SPT-SZ survey. The sample spans the redshift range 0.25<z<1.75 and contains 343 clusters with SZ detection significance ξ>5. The sample is supplemented with optical weak gravitational lensing measurements of 32 clusters with 0.29<z<1.13 (from Magellan and Hubble Space Telescope) and X-ray measurements of 89 clusters with 0.25<z<1.75 (from Chandra). We rely on minimal modeling assumptions: (i) weak lensing provides an accurate means of measuring halo masses, (ii) the mean SZ and X-ray observables are related to the true halo mass through power-law relations in mass and dimensionless Hubble parameter E(z) with a priori unknown parameters, and (iii) there is (correlated, lognormal) intrinsic scatter and measurement noise relating these observables to their mean relations. We simultaneously fit for these astrophysical modeling parameters and for cosmology. Assuming a flat νΛCDM model, in which the sum of neutrino masses is a free parameter, we measure Ω m =0.276±0.047, σ 8 =0.781±0.037, and σ 8 (Ω m /0.3) 0.2 =0.766±0.025. The redshift evolutions of the X-ray Y X-mass and M gas-mass relations are both consistent with self-similar evolution to within 1σ. The mass slope of the Y X-mass relation shows a 2.3σ deviation from self-similarity. Similarly, the mass slope of the M gas-mass relation is steeper than self-similarity at the 2.5σ level. In a νwCDM cosmology, we measure the dark energy equation-of-state parameter w=−1.55±0.41 from the cluster data. We perform a measurement of the growth of structure since redshift z∼1.7 and find no evidence for tension with the prediction from general relativity. This is the first analysis of the SPT cluster sample that uses direct weak-lensing mass calibration and is a step toward using the much larger weak-lensing data set from DES. We provide updated redshift and mass estimates for the SPT sample.

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 anisotropies in temperature and polarization in 19 frequency channels spanning the range 60-600 GHz. CORE will have an aggregate noise sensitivity of 1.7µK• arcmin and an angular resolution of 5' at 200 GHz. We explore the impact of telescope size and noise sensitivity on the inflation science return by making forecasts for several instrumental configurations. This study assumes that the lower and higher frequency channels suffice to remove foreground contaminations and complements other related studies of component separation and systematic effects, which will be reported in other papers of the series "Exploring Cosmic Origins with CORE." We forecast the capability to determine key inflationary parameters, to lower the detection limit for the tensor-to-scalar ratio down to the 10 −3 level, to chart the landscape of single field slow-roll inflationary models, to constrain the epoch of reheating, thus connecting inflation to the standard radiation-matter dominated Big Bang era, to reconstruct the primordial power spectrum, to constrain the contribution from isocurvature perturbations to the −3 level, to improve constraints on the cosmic string tension to a level below the presumptive GUT scale, and to improve the current measurements of primordial non-Gaussianities down to the f local NL < 1 level. For all the models explored, CORE alone will improve significantly on the present constraints on the physics of inflation. Its capabilities will be further enhanced by combining with complementary future cosmological observations.

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 ESA's fifth call for mediumsized 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 ΛCDM 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 ΛCDM, 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. In addition to assessing the improvement on the precision of individual parameters, we also forecast the post-CORE overall reduction of the allowed parameter space with figures of merit for various models increasing by as much as ∼ 10 7 as compared to Planck 2015, and 10 5 with respect to Planck 2015 + future BAO measurements.