Oscillations in the inflaton potential?

TL;DR

This work investigates whether small sinusoidal modulations atop a simple quadratic inflaton potential can leave detectable oscillatory signatures in the primordial power spectrum and CMB. Using a horizon-crossing framework, the authors show that such modulations induce oscillations that are periodic in $\log k$ and map to $C_\ell$ with a characteristic logarithmic pattern. An analysis of WMAP5 data yields no evidence for these features and sets an upper bound of $\alpha \lesssim 3\times10^{-5}$; forecasts indicate Planck could reach sensitivities around $\alpha \sim 10^{-6}$, with a cosmic-variance-limited experiment offering further gains, especially when polarization data are used. The study highlights robustness caveats related to the horizon-crossing approximation and notes that full perturbation calculations could further attenuate the observable signal, pointing to avenues for refined theory and data analysis.

Abstract

We consider a class of inflationary models with small oscillations imprinted on an otherwise smooth inflaton potential. These oscillations are manifest as oscillations in the power spectrum of primordial perturbations, which then give rise to oscillating departures from the standard cosmic microwave background power spectrum. We show that current data from the Wilkinson Microwave Anisotropy Probe constrain the amplitude of a sinusoidal variation in the inflaton potential to have an amplitude less than 3 x 10^{-5}. We anticipate that the smallest detectable such oscillations in Planck will be roughly an order of magnitude smaller, with slight improvements possible with a post-Planck cosmic-variance limited experiment.

Figures (5)

• Figure 1: Primordial power spectrum (top) and matter power spectrum (bottom) of the smooth inflaton potential (solid) and oscillating potential (dashed). The oscillating-potential parameters are [$\alpha,\beta$]=[$5\times10^{-4},3\times10^{-2}$]. The amplitude is chosen to be large to clearly show the effect of the oscillations.
• Figure 2: The CMB power spectrum corresponding to the models shown in Fig. \ref{['f:primordial']}. The WMAP5 data are superimposed wmap5. The error bars include both the cosmic variance and instrumental noise.
• Figure 3: The best-fit amplitude $\alpha$ and its standard error, considering WMAP5 data, for our range of frequencies $\beta$.
• Figure 4: From the top to the bottom, by pairs, the smallest detectable amplitude $\sigma_\alpha$ as a function of $\beta$, for WMAP, Planck and a cosmic-variance limited experiment. The upper part of each pair includes the temperature data only, and the lower one the polarization data as well. Note that the temperature and temperature--polarization curves for WMAP and Planck are effectively degenerate and thus appear to be one curve.
• Figure 5: Magnification of Fig. \ref{['f:alpharesults_a']} for Planck and the cosmic-variance limited experiment.