Towards a measurement of the spectral runnings

Single-field slow-roll ination 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 1- n _s ) ∼ 0:04. A direct consequence of this tilt are nonvanishing runnings α _s = dn _s =d log k, and β _s = dα _s =d log k, which in the minimal inationary 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 inationary prediction for α _s , although not for β _s . 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 α ^s = 10 ^-3 , required to probe the single-field slow-roll inationary paradigm. We show that only a very-futuristic interferometer targeting the dark ages will be capable of measuring the minimal inationary 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 β ^s , 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.