Is a step in the primordial spectral index favored by CMB data ?

TL;DR

The paper investigates whether a localized feature in the primordial power spectrum, induced by a sudden small change in the inflaton potential's second derivative (a mini-waterfall), can better fit the 5-year WMAP data than a smooth, power-law spectrum. It employs an exact solution for the perturbation spectrum within a two-field, hybrid-like inflation model where a rapid transition of an auxiliary heavy field alters the effective inflaton potential, producing a step in the spectral index $n_s$ with damped oscillations and localized running. The CosmoMC analysis shows a modest improvement in fit ($\Delta\chi^2_{eff} \approx -3.05$) at the cost of two extra parameters, with the feature localized at large scales $k_0 \lesssim 0.00355\ \mathrm{Mpc}^{-1}$ ($l \lesssim 40$) and a favored pre/post-transition pair $(n_1, n_2) \approx (0.97, 0.947)$. The results suggest a plausible microphysical origin and motivate future CMB data to confirm the feature, while also highlighting potential non-Gaussian signatures from the two-field dynamics.

Abstract

A sudden small change in the second derivative of the inflaton potential can result in a universal local feature in the spectrum of primordial perturbations generated during inflation. The exact solution describing this feature \cite{minu} is characterized by a step in the spectral index modulated by characteristic oscillations and results in a large running of the spectral index localized over a few e-folds of scale. In this paper we confront this step-like feature with the 5 year WMAP results and demonstrate that it provides a better fit to this data than a featureless initial spectrum. If such a feature exists at all, then it should lie at sufficiently large scales $k_0 \lesssim 0.003 {\rm Mpc}^{-1}$ corresponding to $l \lesssim 40$. The sign of the effect is shown to correspond to the negative running of $n_s$ localized near this scale. This feature could arise as a result of a `mini-waterfall'-type fast second order phase transition experienced by an auxiliary heavy field during inflation, in a model similar to hybrid inflation (though for a different choice of parameters). If this is the case, then the auxiliary field should be positively coupled to the inflaton.

Figures (7)

• Figure 1: Spectral indices for perturbations generated just before ($n_1$) and immediately after ($n_2$) the phase transition are shown for three values of the number of inflationary e-folds occurring during the post-mini-waterfall period: ${\cal N} = 40$ (red, solid), ${\cal N} = 50$ (blue, dotted) and ${\cal N} = 60$ (green, dashed).
• Figure 2: A step in the second derivative of the inflaton potential leads to a step in the spectral index as shown in this figure which plots the primordial spectral index $n_s$ as a function of $x = k/k_0$. The step in $n_s$ at $x \sim 1$ is followed by oscillations with decreasing amplitude. The parameters shown here correspond to $n_1 = 0.97$, $n_2 = 0.95$, which agree well with WMAP5 data.
• Figure 3: Comparison of our model (blue, dashed) with a pure power-law model (red, solid), for the best fit values of parameters. The WMAP5 binned data with related error bars are also plotted for comparison.
• Figure 4: Marginalized posterior distributions for the spectral indices $n_1$ and $n_2$.
• Figure 5: Marginalized posterior distributions for $(n_1 - n_2)$ and also for $(1-(n_1+n_2)/2)$. The right panel gives the marginalized distribution of $[(n_1-n_2) - (1-(n_1+n_2)/2)]$.