Drifting Oscillations in Axion Monodromy

TL;DR

This work investigates oscillatory features in the primordial power spectrum from axion monodromy inflation, emphasizing slow drift of the oscillation period caused by moduli backreaction and related UV completions. It develops drifting-frequency templates that extend beyond fixed-frequency analyses and demonstrates their relevance across string-inspired scenarios, including power-law and nonperturbative moduli stabilization. Through analytic-template reasoning and Planck data tests, the authors show that drifting effects can be significant for high oscillation frequencies or strong drift, and they provide a practical framework for incorporating such drift into data analyses. The study offers a pathway to constrain or discover rich microphysical structure in inflation by enabling more robust searches for oscillatory features in cosmological data.

Abstract

We study the pattern of oscillations in the primordial power spectrum in axion monodromy inflation, accounting for drifts in the oscillation period that can be important for comparing to cosmological data. In these models the potential energy has a monomial form over a super-Planckian field range, with superimposed modulations whose size is model-dependent. The amplitude and frequency of the modulations are set by the expectation values of moduli fields. We show that during the course of inflation, the diminishing energy density can induce slow adjustments of the moduli, changing the modulations. We provide templates capturing the effects of drifting moduli, as well as drifts arising in effective field theory models based on softly broken discrete shift symmetries, and we estimate the precision required to detect a drifting period. A non-drifting template suffices over a wide range of parameters, but for the highest frequencies of interest, or for sufficiently strong drift, it is necessary to include parameters characterizing the change in frequency over the e-folds visible in the CMB. We use these templates to perform a preliminary search for drifting oscillations in a part of the parameter space in the Planck nominal mission data.

Figures (5)

• Figure 1: Comparison of a numerical power spectrum and an analytic template after a small shift in $f$ in the analytic template to maximize the overlap. Top row: $C_0=0$, $p_f=-\frac{1}{3}$, $f=4\times 10^{-4}\,M_p$, and $b=0.01$. Bottom row: $C_0=0$, $p_f=-\frac{1}{3}$, $f=10^{-3}\,M_p$, and $b=0.05$. The top row is best viewed after zooming in.
• Figure 2: Results for a search for oscillations in simulated data. The simulations are based on the template \ref{['eq:temp1']} with $p_f=-1/3$, $f=10^{-3}M_p$, and amplitudes $\delta n_s$ ranging from $\delta n_s=0.02$ to $\delta n_s=0.05$, as indicated by the labels. Points included in the plot lead to an improvement over the best-fit with $\delta n_s=0$ of $\Delta\chi^2\geq4$. The sizes of the dots and their color indicate the amount of improvement. The orange cross indicates the input values of $f$ and $p_f$, and the red line represents the corresponding value of $\alpha=\omega/H$ as defined in equation \ref{['eq:alpha']}. As the amplitude $\delta n_s$ increases the significance of the improvements grows.
• Figure 3: Points that lead to an improvement over $\Lambda$CDM of $\Delta\chi^2\geq4$ for the first template, \ref{['eq:temp1']}. The left panel shows the results for the public Planck likelihood Ade:2013kta, and the right panel shows the results for the likelihood discussed in Spergel:2013rxa. The sizes of the dots and their color indicate the amount of improvement. Larger blue points represent larger values of $\Delta\chi^2$. The solid lines indicate constant $\alpha=\omega/H$. The red solid line represents $\omega/H=28.8$, the best-fit frequency found by the Planck collaboration PlanckInf. A significant contribution to the improvement derives from the region around $\ell=1800$ in the 217 GHz data. This range of multipoles of the 217 GHz data is known to be affected by interference between the 4K cooler and the read-out electronics Spergel:2013rxaAde:2013kta.
• Figure 4: Marginalized posterior in the $\delta n_s - f$ plane for the template \ref{['eq:temp1']}, for the run in which only the power spectrum parameters are varied. The left panel shows the results for the public Planck likelihood, and the right panel shows the results for the likelihood described in Spergel:2013rxa.
• Figure 5: Results for the second template, \ref{['eq:lnn']}. As before, points included in the plot lead to an improvement over $\Lambda$CDM of $\Delta\chi^2\geq4$, and the sizes of the dots and their color indicate the amount of improvement. The orange dot indicates the best-fit point. The top panels shows the results for the public Planck likelihood, and the bottom panels show the results for the likelihood described in Spergel:2013rxa. While especially for higher frequency there is a dependence on $c_1$, indicating that a drift in frequency leads to a better fit, the dependence on $c_2$ is weak.