The Spectral Index and its Running in Axionic Curvaton

TL;DR

The paper addresses whether a sizable running of the scalar spectral index can be explained in a curvaton scenario rather than single-field inflation. It introduces an axionic curvaton with a potential comprising two sinusoidal terms, leading to oscillations of $n_s-1$ and $\alpha$ as the curvaton evolves, with a generic relation $\alpha \sim \frac{2\pi}{\Delta N}(n_s-1)$. Matching the SPT/WMAP pivot data requires $\Delta N$ of order $20$–$30$ e-folds per modulation, and the model can reproduce the observed negative running $\alpha \approx -0.024$ at the SPT pivot. The mechanism draws support from the string axiverse, where axions obtain masses from multiple instanton contributions, and it remains compatible with red-tilted spectra with negligible running for suitable $\Delta N$, offering a simple, non-large-field inflation realization.

Abstract

We show that a sizable running spectral index suggested by the recent SPT data can be explained in the axionic curvaton model with a potential that consists of two sinusoidal contributions of different height and period. We find that the running spectral index is generically given by d ns/dlnk ~ (2pi/dN)(n_s - 1), where dN is the e-folds during one period of modulations. In the string axiverse, axions naturally acquire a mass from multiple contributions, and one of the axions may be responsible for the density perturbations with a sizable running spectral index via the curvaton mechanism. We note that the axionic curvaton model with modulations can also accommodate the red-tilted spectrum with a negligible running, without relying on large-field inflation.

Figures (2)

• Figure 1: The potential $V(\sigma)$ is shown. We set $m_1 = 0.01 H_{*}$, $m_2 = 0.44 H_*$, and $f_2 = 1.25 \times 10^{-4} f_1$, and the potential and the curvaton field are normalized by $m_1^2 f_1^2$ and $f_1$, respectively. We can see the modulations $\delta V$ is subdominant around the inflection point, but it becomes significant around the origin.
• Figure 2: The evolution of the spectral index $n_s$ and the running $\alpha$. The numerical result is shown by the solid line, while the dashed line represents the analytic solution (\ref{['ana_ns']}) and (\ref{['alc']}). As the curvaton evolves, the predicted $(n_s, \alpha)$ moves clockwise along an oval as indicated by the arrow, and it rotates twice during about $50$ e-folds. We also show the SPT and WMAP pivot scales by the star and the triangle, respectively. The CMB scales $(\ell \lesssim 3000)$ are shown as the thick line.