Oscillations in the inflaton potential: Complete numerical treatment and comparison with the recent and forthcoming CMB datasets

Abstract

Amongst the multitude of inflationary models currently available, models that lead to features in the primordial scalar spectrum are drawing increasing attention, since certain features have been found to provide a better fit to the CMB data than the conventional, nearly scale invariant, primordial spectrum. In this work, we carry out a complete numerical analysis of two models that lead to oscillations over all scales in the scalar power spectrum. We consider the model described by a quadratic potential which is superposed by a sinusoidal modulation and the recently popular axion monodromy model. Since the oscillations continue even on to arc minute scales, in addition to the WMAP data, we also compare the models with the small scale data from ACT. Though, both the models, broadly, result in oscillations in the spectrum, interestingly, we find that, while the monodromy model leads to a considerably better fit to the data in comparison to the standard power law spectrum, the quadratic potential superposed with a sinusoidal modulation does not improve the fit to a similar extent. We also carry out forecasting of the parameters using simulated Planck data for both the models. We show that the Planck mock data performs better in constraining the model parameters as compared to the presently available CMB datasets.

Figures (6)

• Figure 1: The difference in $\chi_{\rm eff}^{2}$ with respect to the reference model, i.e. $\Delta\chi_{\rm eff}^{2} =[\chi_{\rm eff}^{2}({\rm model})-\chi_{\rm eff}^{2}({\rm power\; law})]$, in the case of the axion monodromy model has been plotted as a function of the multipole moment for the WMAP seven year data, after binning in the multipole space with $\ell_{\mathrm{bin}}=10$. While the figure on top corresponds to the WMAP seven year $TT$ data (for $\ell>32$), the lower one is for the $TE$ data (for $\ell>24$).
• Figure 2: The scalar power spectra corresponding to the best fit values of the WMAP seven year data for the two inflationary models that we have considered. The solid red and the solid blue lines describe the scalar power spectra in the cases of the chaotic model with a sinusoidal modulation and the axion monodromy model, respectively. The spectrum corresponding to the best fit power law model would essentially be the same as in the chaotic model with sinusoidal modulations, but without any oscillations. The inset highlights the extraordinary extent of persistent oscillations in the case of the monodromy model.
• Figure 3: The CMB $TT$ angular power spectra corresponding to the best fit values of the different models for the WMAP seven year data. The solid red, solid green and the black curves correspond to the power law model, the chaotic model with sinusoidal modulation and the axion monodromy model, respectively. The gray circles with error bars denote the WMAP seven year unbinned data. The inset highlights the difference in the angular power spectrum between the monodromy model and the power law case. In the case of the axion monodromy model, the tiny and continued oscillations in the power spectrum lead to small improvements in the fit to the data over a wide range of multipoles, which eventually add up to a good extent.
• Figure 4: The CMB $TE$ and the $EE$ angular power spectra corresponding to the best fit values of the different models for the WMAP seven year data. The solid red, green and black curves represent the $TE/EE$ spectrum (in fact, magnitude of TE spectrum) in the power law case, the chaotic model with sinusoidal modulations and the axion monodromy model, respectively. As in the earlier figure, the insets highlight the difference in the $TE/EE$ spectrum between the monodromy model and the power law case.
• Figure 5: One dimensional distributions of the inflationary model parameters from the WMAP-$7$, WMAP-$7$$+$ ACT and the Planck simulated data. We have plotted the constraints on the parameters $m$, $\alpha$, $\beta$ and $\delta$ of the chaotic model with sinusoidal modulations (on the left column) and the parameters $\lambda$, $\alpha$, $\beta$ and $\delta$ for the axion monodromy model (on the right column). It is evident that the simulated Planck data tightens the bounds on the parameters substantially.