COrE (Cosmic Origins Explorer) is a fourth-generation full-sky, microwave-band satellite recently proposed to ESA within Cosmic Vision 2015-2025. COrE will provide maps of the microwave sky in polarization and temperature in 15 frequency bands, ranging from 45 GHz to 795 GHz, with an angular resolution ranging from 23 arcmin (45 GHz) and 1.3 arcmin (795 GHz) and sensitivities roughly 10 to 30 times better than PLANCK (depending on the frequency channel). The COrE mission will lead to breakthrough science in a wide range of areas, ranging from primordial cosmology to galactic and extragalactic science. COrE is designed to detect the primordial gravitational waves generated during the epoch of cosmic inflation at more than $3sigma $ for $r=(T/S)>=10^{-3}$. It will also measure the CMB gravitational lensing deflection power spectrum to the cosmic variance limit on all linear scales, allowing us to probe absolute neutrino masses better than laboratory experiments and down to plausible values suggested by the neutrino oscillation data. COrE will also search for primordial non-Gaussianity with significant improvements over Planck in its ability to constrain the shape (and amplitude) of non-Gaussianity. In the areas of galactic and extragalactic science, in its highest frequency channels COrE will provide maps of the galactic polarized dust emission allowing us to map the galactic magnetic field in areas of diffuse emission not otherwise accessible to probe the initial conditions for star formation. COrE will also map the galactic synchrotron emission thirty times better than PLANCK. This White Paper reviews the COrE science program, our simulations on foreground subtraction, and the proposed instrumental configuration.
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