Spectroscopic source redshifts and parameter constraints from weak lensing and the cosmic microwave background

Weak lensing is a potentially robust and model-independent cosmological probe, but its accuracy is dependent on knowledge of the redshift distribution of the source galaxies used. The most robust way to determine the redshift distribution is via spectroscopy of a subsample of the source galaxies. We forecast constraints from combining cosmic microwave background (CMB) anisotropies with cosmic shear using a spectroscopically determined redshift distribution, varying the number of spectra Nspec obtained from 64 to [infinity]. The source redshift distribution is expanded in a Fourier series, and the amplitudes of each mode are considered as parameters to be constrained via both the spectroscopic and weak lensing data. We assume independent source redshifts, and consider in what circumstances this is a good approximation (the sources are clustered and for narrow spectroscopic surveys with many objects this results in the redshifts being correlated). It is found that for the surveys considered and for a prior of 0.04 on the calibration parameters, the addition of redshift information makes significant improvements on the constraints on the cosmological parameters; however, beyond Nspec ~ few × 10^3 the addition of further spectra will make only a very small improvement to the cosmological parameters. We find that a better calibration makes large Nspec more useful. Using an eigenvector analysis, we find that the improvement continues with even higher Nspec, but not in directions that dominate the uncertainties on the standard cosmological parameters

Testing General Relativity in Cosmology

We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the dark energy associated with it. However, with the advent of precision cosmology, it has also become a well-motivated endeavor by itself to test gravitational physics at cosmic scales. We overview cosmological probes of gravity, formalisms and parameterizations for testing deviations from GR at cosmological scales, selected modified gravity (MG) theories, gravitational screening mechanisms, and computer codes developed for these tests. We then provide summaries of recent cosmological constraints on MG parameters and selected MG models. We supplement these cosmological constraints with a summary of implications from the recent binary neutron star merger event. Next, we summarize some results on MG parameter forecasts with and without astrophysical systematics that will dominate the uncertainties. The review aims at providing an overall picture of the subject and an entry point to students and researchers interested in joining the field. It can also serve as a quick reference to recent results and constraints on testing gravity at cosmological scales.Comment: Invited review article for Living Reviews in Relativity. 201 pages, 17 figures. Matches published versio