Non-Gaussianity from Axion Monodromy Inflation

TL;DR

This work analyzes primordial non-Gaussianity in axion monodromy inflation, where a linear potential is superimposed with oscillations. Using both analytic approximations and a numerical solver for single-field inflation, the authors show that resonant effects can produce a large, oscillatory bispectrum with $f_{NL}$ of order tens (up to ∼50) while the power spectrum remains nearly featureless, and they provide a simple analytic fitting formula for the bispectrum accurate to ~5%. They also estimate the trispectrum in the squeezed and counter-collinear limits, finding $ au_{NL}$ scales as $(f_{NL}^{(sq)})^2$, suggesting potential Planck-level detectability in certain configurations. The results offer a testable, string-inspired inflationary scenario with a distinctive non-Gaussian signature that complements the standard chaotic-inflation predictions of a sizable tensor-to-scalar ratio and a red spectral index.

Abstract

We study the primordial non-Gaussinity predicted from simple models of inflation with a linear potential and superimposed oscillations. This generic form of the potential is predicted by the axion monodromy inflation model, that has recently been proposed as a possible realization of chaotic inflation in string theory, where the monodromy from wrapped branes extends the range of the closed string axions to beyond the Planck scale. The superimposed oscillations in the potential can lead to new signatures in the CMB spectrum and bispectrum. In particular the bispectrum will have a new distinct shape. We calculate the power spectrum and bispectrum of curvature perturbations in the model, as well as make analytic estimates in various limiting cases. From the numerical analysis we find that for a wide range of allowed parameters the model produces a feature in the bispectrum with fnl ~ 50 or larger while the power spectrum is almost featureless. This model is therefore an example of a string-inspired inflationary model which is testable mainly through its non-Gaussian features. Finally we provide a simple analytic fitting formula for the bispectrum which is accurate to approximately 5% in all cases, and easily implementable in codes designed to provide non-Gaussian templates for CMB analyses.

Figures (4)

• Figure 1: The power- and bispectra for the models in table
• Figure 2: The shape function $x_1^2x_2^2F(x_1,x_2)$ as defined in Eq. (\ref{['eq:sf']}) for the general $\alpha_{\textrm{g}}$ model. Note that by definition $F$ is normalised to one for the equilateral form $x_1=x_2=x_3=1$, and that we only plot unique triangles, i.e. triangles with $x_1>x_2$ have been suppressed in the figure for clarity.
• Figure 3: The bispectrum for isosceles triangles for the $\alpha_{\textrm{s}}$ and $\Lambda_{\textrm{s}}$ models as a function of side ratio $k/m$ together with the analytic model
• Figure 4: Comparison of the analytic estimates of the amplitudes $f_A$ of $f_{\mathrm{NL}}$ to the numerical results.