Measuring the spectral running from cosmic microwave background and primordial black holes

TL;DR

This paper combines CMB, BAO, and primordial black hole data to constrain the spectral running, finding that PBH constraints significantly influence the scalar spectral index's running and that a power-law spectrum without running fits the data well.

Contribution

It demonstrates the significant impact of PBH constraints on spectral running and shows that a power-law spectrum without running is consistent with current observations.

Findings

PBH constraints strongly affect spectral running limits

Power-law spectrum without running fits observational data

Tensor spectral index is very small and difficult to measure

Abstract

We constrain the spectral running by combining cosmic microwave background (CMB) data, baryon acoustic oscillation (BAO) data and the constraint from primordial black holes (PBHs). We find that the constraint from PBHs has a significant impact on the running of running of scalar spectral index, and a power-law scalar power spectrum without running is consistent with observational data once the constraint from PBHs is taken into account. In addition, from the constraints on the slow-roll parameters, the derived tensor spectral index in the single-field slow-roll inflation model is quite small, namely $|n_t|\lesssim 9.3\times 10^{-3}$ which will be very difficult to be measured by CMB data only in the future, and the absolute value of derived running of tensor spectral index is not larger than $2.1\times 10^{-4}$ at 95% confidence level.