Towards a measurement of the spectral runnings

Abstract

Single-field slow-roll inflation predicts a nearly scale-free power spectrum of perturbations, as observed at the scales accessible to current cosmological experiments. This spectrum is slightly red, showing a tilt (1−ns)∼ 0.04. A direct consequence of this tilt are nonvanishing runnings αs= d ns/ d log k, and βs= dαs/ d log k, which in the minimal inflationary scenario should reach absolute values of 10−3 and 10−5, respectively. In this work we calculate how well future surveys can measure these two runnings. We consider a Stage-4 (S4) CMB experiment and show that it will be able to detect significant deviations from the inflationary prediction for αs, although not for βs. Adding to the S4 CMB experiment the information from a WFIRST-like or a DESI-like survey improves the sensitivity to the runnings by ∼ 20%, and 30%, respectively. A spectroscopic survey with a billion objects, such as the SKA, will add enough information to the S4 measurements to allow a detection of αs=10−3, required to probe the single-field slow-roll inflationary paradigm. We show that only a very-futuristic interferometer targeting the dark ages will be capable of measuring the minimal inflationary prediction for βs. The results of other probes, such as a stochastic background of gravitational waves observable by LIGO, the Ly-α forest, and spectral distortions, are shown for comparison. Finally, we study the claims that large values of βs, if extrapolated to the smallest scales, can produce primordial black holes of tens of solar masses, which we show to be easily testable by the S4 CMB experiment.