Stochastic Inflation and the Lower Multipoles in the CMB Anisotropies

TL;DR

The paper addresses the lack of power at the largest CMB scales by formulating stochastic inflation with colored (non-Markovian) noise produced by a smooth window function. By enforcing a homogeneity constraint at $\tau_*$ and deriving the colored-noise correlations, it derives the power spectrum of curvature perturbations $\mathcal{P}_{\mathcal{R}}(k)$ to first order in slow-roll and shows that a blue tilt emerges on the largest scales. The main result is that the suppression of low multipoles can arise naturally from the non-Markovian noise and the choice of coarse-graining without introducing new physics, with the effect controlled by $\tau_*$ and the window shape $W_\sigma$. This links stochastic-inflationary non-Markovian dynamics to observable CMB features and provides a minimal explanation for the WMAP observations. $\mathcal{P}_{\mathcal{R}}(k)$ and related quantities are expressed in terms of $|I_1(k)|^2$, reflecting how the noise filtering shapes the primordial spectrum.

Abstract

We generalize the treatment of inflationary perturbations to deal with the non-Markovian colored noise emerging from any realistic approach to stochastic inflation. We provide a calculation of the power-spectrum of the gauge-invariant comoving curvature perturbation to first order in the slow-roll parameters. Properly accounting for the constraint that our local patch of the Universe is homogeneous on scales just above the present Hubble radius, we find a blue tilt of the power-spectrum on the largest observable scales, in agreement with the WMAP data which show an unexpected suppression of the low multipoles of the CMB anisotropy. Our explanation of the anomalous behaviour of the lower multipoles of the CMB anisotropies does not invoke any ad-hoc introduction of new physical ingredients in the theory.

Figures (2)

• Figure 1: Conditional power-spectrum obtained with the Gaussian window \ref{['window']} in the limit $\tau_*/\tau_{in}\simeq\infty$, for different values of $\sigma$ varying from 0.1 (left curve) to 0.9 (right curve).
• Figure 2: . Angular power spectra of the CMB temperature anisotropies obtained with the Gaussian window \ref{['window']} and different values of the constraint time $\tau_*$. The cosmological parameters used in the computation of the radiation transfer functions are $\Omega_b = 0.046$, $\Omega_{CDM} = 0.224$, $\Omega_\Lambda = 0.730$ and $h = 0.72$, corresponding to the best fit of the WMAP data hinshaw. Dots represent the WMAP Binned Combined TT Power Spectrum, obtained from the LAMBDA website: http://lambda.gsfc.nasa.gov/.