Making waves on CMB power spectrum and inflaton dynamics

We discuss cosmic microwave background anisotropies in models with an unconventional primordial power spectrum. In particular, we consider an initial power spectrum with some “spiky” corrections. Interestingly, such a primordial power spectrum generates “wavy” structure in the CMB angular power spectrum. Some possible models generating such a primordial power spectrum from inflaton dynamics are also briefly discussed. Result of the first year Wilkinson microwave anisotropy probe (WMAP) [1] is almost consistent with the following assumption [2]:the present universe consists of 5 % baryon, 23 % cold dark matter (CDM) and 72 % dark energy. The primordial power spectrum is almost scale invariant with adiabatic fluctuations. These assumptions form so-called the standard scenario of cosmology. Although the fit to the WMAP data with the standard scenario seems to be excellent, there may be some deviations from the standard scenario in the angular power spectrum given by WMAP. One of them is that the angular power spectrum seems to be suppressed at low multipoles compared to the prediction of the standard cosmological scenario. Since the cosmic variance error is very large at low multipole region, we may say that the suppression is just a statistical fluctuation. However, if we take this seriously, it may suggest some new physics. There are many works proposing mechanisms to explain this suppression [3]. The other one is that, if you look at the WMAP angular power spectrum carefully, there is “wavy” structure around multipole region from l ∼ O(10) up to the first peak. In particular, there seems to be a dip around the first peak. Although this feature is not robust at this point, if it is an intrinsic one, it may suggest some unusual physics since this kind of structure cannot be explained by the conventional scenario. There have been some works inspired by this feature. The authors of Refs. [4, 5, 6] considered a primordial power spectrum with oscillatory corrections which can be generated from trans-Planckian physics. They showed that, with such an initial power spectrum, we can improve the fit to the WAMP data compared with the best-fit value of the standard scenario. Although we may not be at the position where we should take this result seriously, it is interesting to consider some models which give the wavy structure on the CMB angular power spectrum. In this letter, we discuss a mechanism which generates such structure in the CMB power spectrum. Here we consider a scenario where the primordial fluctuation is modified from the standard form. If we assume an initial power spectrum with some “spiky” parts, wavy structure of the CMB power spectrum can appear. The initial power spectrum we assume is written as