Constraining Monodromy Inflation

TL;DR

This work tests monodromy inflation, characterized by a linear potential with a periodic modulation, against the WMAP9 CMB data using Mode-Code and nested sampling to compute power spectra and Bayesian evidence. It identifies two modulated parameter combinations that modestly improve the fit (\\Delta\\chi^2 on the order of 10–20) but does not yield decisive model discrimination against the unmodulated case, with a total evidence difference of about \Delta\\log E \sim +0.6. The modulated potentials also predict resonant non-Gaussianity with a specific form, quantified by $f_{\\mathrm{NL}} = {3 \sqrt{2\\pi} b}/{8 (f \phi_\\star / M_{\\rm Pl}^2)^{3/2}}$, and the inferred $f_{\\mathrm{NL}}$ distribution has a non-negligible tail that could be probed by future CMB bispectrum measurements. If future data confirm such modulation, it would provide a nontrivial consistency check for monodromy inflation and its stringy origins, while also predicting a detectable gravitational-wave background from the inflationary epoch.

Abstract

We use cosmic microwave background (CMB) data from the 9-year WMAP release to derive constraints on monodromy inflation, which is characterized by a linear inflaton potential with a periodic modulation. We identify two possible periodic modulations that significantly improve the fit, but it is unclear whether this improvement is associated with a "signal" or with the scatter in the measured angular power spectrum. The unmodulated potential is mildly favored by standard model selection criteria. A modulated inflationary potential can generate substantial primordial non-Gaussianity, of a specific and characteristic form. For the best-fit parameters to the WMAP angular power spectrum, the corresponding non-Gaussianity might be detectable in upcoming CMB data, allowing nontrivial consistency checks on the predictions of a modulated inflationary potential.

Figures (6)

• Figure 1: Marginalized posterior distributions for inflationary parameters.
• Figure 2: Reference angular power spectrum with $b=0$ and difference for the best fit spectrum with $\log_{10}{(f/M_{\rm Pl})}\approx -3.38$ in blue and with $\log_{10}{(f/M_{\rm Pl})}\approx -3.18$ in orange.
• Figure 3: The difference in $\Delta \chi^2_\mathrm{eff}$ given by the WMAP9 MASTER TTTT likelihood for the reference and best-fit modulated models as a function of $\ell$, binned as indicated by the labels.
• Figure 4: Marginalized 2D-joint posterior for $b$ and $\log_{10}{(f/M_{\rm Pl})}$ -- the intensity is a function of the posterior, and shows that the peaks are narrow and well-defined. Note that the color scale is qualitative.
• Figure 5: Posterior distribution for $f_\mathrm{NL}$.