Running Spectral Index from Large-field Inflation with Modulations Revisited

TL;DR

The paper addresses how to reconcile a sizable tensor signal with a suppressed small-scale CMB power by invoking a negative running of the scalar spectral index. It develops a framework of modulated large-field inflation, focusing on multi-natural inflation where multiple sinusoidal terms in the potential can generate a notable running without disrupting overall slow-roll dynamics. The authors show that a negative running compatible with current constraints can arise in a two-sinusoid realization, while also yielding viable predictions for the tensor-to-scalar ratio r. This approach links the B-mode results to microphysical features of the inflaton potential and makes testable predictions for upcoming CMB and gravitational-wave measurements of r, n_s, and the running.

Abstract

We revisit large field inflation models with modulations in light of the recent discovery of the primordial B-mode polarization by the BICEP2 experiment, which, when combined with the Planck + WP + highL data, gives a strong hint for additional suppression of the CMB temperature fluctuations at small scales. Such a suppression can be explained by a running spectral index. In fact, it was pointed out by two of the present authors (TK and FT) that the existence of both tensor mode perturbations and a sizable running of the spectral index is a natural outcome of large inflation models with modulations. We find that this holds also in the recently proposed multi-natural inflation, in which the inflaton potential consists of multiple sinusoidal functions and therefore the modulations are a built-in feature.

Figures (2)

• Figure 1: Evolution of the spectral index $n_s$, its running $d n_s/d \ln k$, and the tensor-to-scalar ratio for $f = 100M_p$, $A = 4 \times 10^{-3}$, $B = 1\times10^{-4}$, and $\theta = -1$. The red diamond denotes $N = 60$ e-folds before the end of inflation, whereas the black (white) star corresponds to $N = 63 (55)$.
• Figure 2: Same as Fig. \ref{['fig:running1']} but for $f = 10M_p$, $A=4.5\times 10^{-2}$, $B = 1.24\times 10^{-2}$ and $\theta = 2$. The red diamond denotes $N=60$ e-folds before the end of inflation, whereas the black (white) star corresponds to $N = 62 (54)$.