Oscillations in the inflaton potential?

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 $3\times {10}^{-5}$. 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.

Figure 1

Primordial power spectrum (top panel) and matter power spectrum (bottom panel) of the smooth inflaton potential (solid line) and oscillating potential (dashed line). The oscillating-potential parameters are $[\alpha ,\beta ]=[5\times {10}^{-4},3\times {10}^{-2}]$. 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. 1. The WMAP5 data are superimposed [18]. 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. 4 for Planck and the cosmic-variance limited experiment.