Negative Running of the Spectral Index, Hemispherical Asymmetry and the Consistency of Planck with Large $r$

Abstract

Planck favours a negative running of the spectral index, with the likelihood being dominated by low multipoles $l \lesssim 50$ and no preference for running at higher $l$. A negative spectral index is also necessary for the 2-$\sigma$ Planck upper bound on the tensor-to-scalar ratio $r$ to be consistent with values significantly larger than 0.1. Planck has also observed a hemispherical asymmetry of the CMB power spectrum, again mostly at low multipoles. Here we consider whether the physics responsible for the hemispherical asymmetry could also account for the negative running of the spectral index and the consistency of Planck with a large value of $r$. A negative running of the spectral index can be generated if the hemispherical asymmetry is due to a scale- and space-dependent modulation which suppresses the CMB power spectrum at low multipoles. We show that the observed hemispherical asymmetry at low $l$ can be generated while satisfying constraints on the asymmetry at higher $l$ and generating a negative spectral index of the right magnitude to account for the Planck observation and to allow Planck to be consistent with a large value of $r$.