Future Probes of the Primordial Scalar and Tensor Perturbation Spectra: Prospects from the CMB, Cosmic Shear and High-Volume Redshift Surveys

Abstract

Detailed study of the scalar and tensor perturbation spectra can provide much information about the primordial fluctuation-generator, be it inflation or something else. The tensor perturbation spectrum may be observable through its influence on CMB polarization, but only if the tensor-to-scalar ratio, r = T/S, is greater than about 10^{-5}. The tensor tilt can be measured with an error of sigma(n_T) that decreases with r from 0.1 at r=0.001 to 0.02 at r = 0.1. Current CMB constraints on the scalar perturbation spectrum can be improved by higher--resolution CMB observations and/or by tomographic cosmic shear observations. These can both shrink errors on the tilt (n_S) and running (n_S'= dn_S/d\ln k) to the 10^{-3} level. Stunning as these results would be, it may become very desirable to improve upon them an order of magnitude further in order to study the expected departures from n_S' = 0. Such improvements are likely to require observation of three--dimensional clustering over very large volumes. Unfortunately, to get down to the 10^{-4} level will require a sparse spectroscopic redshift survey with about 10^9 galaxies spread over a volume less than but comparable to that of the observable Universe.