Exploring the Superimposed Oscillations Parameter Space

TL;DR

This work investigates potential features in the CMB from a primordial power spectrum with superimposed oscillations arising from new physics at a scale $M_c$. To manage computational cost, it analyzes the fast parameter space described by the oscillation amplitude $|x|\sigma_0$, phase $\psi$, and $\sigma_0=H/M_c$, with frequency controlled by $2\epsilon_1/\sigma_0$ using Monte Carlo sampling in a modified CAMB/COSMOMC framework. They derive a 2$\sigma$ bound $|x|\sigma_0<0.11$ and a 1$\sigma$ bound $H/M_c<6.6\times10^{-4}$, while the mean likelihood favors oscillations near $|x|\sigma_0\approx0.1$, indicating volume effects play a substantial role. The study emphasizes that marginalized probabilities and mean likelihoods can lead to different conclusions about the presence of oscillatory features, suggesting future data are needed to decisively test these models. Overall, current data mildly prefer oscillatory features in a mean-likelihood sense but remain compatible with standard slow-roll when marginalized over parameter volume.

Abstract

The space of parameters characterizing an inflationary primordial power spectrum with small superimposed oscillations is explored using Monte Carlo methods. The most interesting region corresponding to high frequency oscillations is included in the analysis. The oscillations originate from some new physics taking place at the beginning of the inflationary phase and characterized by the new energy scale Mc. It is found that the standard slow-roll model remains the most probable one given the first year WMAP data. At the same time, the oscillatory models better fit the data on average, which is consistent with previous works on the subject. This is typical of a situation where volume effects in the parameter space play a significant role. Then, we find the amplitude of the oscillations to be less than 22% of the mean amplitude and the new scale Mc to be such that H/Mc < 6.6 x 10^(-4) at 1-sigma level, where H is the scale of inflation.

Figures (4)

• Figure 1: $1D$ marginalized probabilities (solid curve) and normalized mean likelihoods (dashed curve) for the slow-roll parameters $\epsilon_{_1}$, $\epsilon_{_2}$ and the scalar amplitude $P_\mathrm{scalar}$, in the case of the reference model. The three-dimensional plots show the normalized mean likelihoods and the corresponding $1\sigma$ and $2\sigma$ contours of the $2D$ marginalized probabilities.
• Figure 2: $1D$ marginalized probabilities (solid curves) and normalized mean likelihoods (dashed curves) for the oscillatory model.
• Figure 3: $1\sigma$ and $2\sigma$ contours of the $2D$ marginalized probabilities and normalized mean likelihoods (see also Fig. \ref{['fig:tpl3Db']}).
• Figure 4: $1\sigma$ and $2\sigma$ contours of the $2D$ marginalized probabilities and normalized mean likelihoods (see also Fig. \ref{['fig:tpl3Da']}). Strong correlations appear between the amplitude and the frequency of the oscillations (on the left).