Eur. Phys. J. C (2018) 78: 980
https://doi.org/10.1140/epjc/s10052-018-6471-z

Regular Article - Theoretical Physics

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

¹ CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China
² School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, 100049, China
³ Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou, 225009, China
⁴ Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, China

^* e-mail: lijun@itp.ac.cn

Received: 11 August 2018
Accepted: 20 November 2018
Published online: 27 November 2018

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 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 at 95% confidence level.