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Suppressing the lower Multipoles in the CMB Anisotropies

Carlo R. Contaldi, Marco Peloso, Lev Kofman, Andrei Linde

TL;DR

This paper addresses why the CMB TT power at the largest angular scales is lower than standard $\\Lambda$CDM predictions. It analyzes two broad mechanisms: late-time ISW effects that could dampen power via the evolution of metric perturbations, and early-universe modifications during the final 65 e-folds of inflation that induce a primordial cutoff in the spectrum, such as a fast-roll (kinetic-dominated) phase. Through a concrete inflationary model and TT-spectrum fits to WMAP data, it shows that a cutoff around $k_c \,\sim\ (4.9-5.3)\\times10^{-4}$ Mpc$^{-1}$ can modestly improve the fit, though the significance is about $2\\sigma$ and depends on the chosen prior. The work highlights horizon-scale features in the primordial spectrum as a plausible explanation and discusses the interpretational challenges, including prior dependence and the possible link to late-time dark energy physics.

Abstract

The Cosmic Microwave Background (CMB) anisotropy power on the largest angular scales observed both by WMAP and COBE DMR appears to be lower than the one predicted by the standard model of cosmology with almost scale free primordial perturbations arising from a period of inflation \cite{cobe,Bennett:2003bz,Spergel,Peiris}. One can either interpret this as a manifestation of cosmic variance or as a physical effect that requires an explanation. We discuss various mechanisms that could be responsible for the suppression of such low $\ell$ multipoles. Features in the late time evolution of metric fluctuations may do this via the integral Sachs-Wolfe effect. Another possibility is a suppression of power at large scales in the primordial spectrum induced by a fast rolling stage in the evolution of the inflaton field at the beginning of the last 65 e-folds of inflation. We illustrate this effect in a simple model of inflation and fit the resulting CMB spectrum to the observed temperature-temperature (TT) power spectrum. We find that the WMAP observations suggest a cutoff at $k_c=4.9^{+1.3}_{-1.6}\times 10^{-4}$Mpc$^{-1}$ at 68% confidence, while only an upper limit of $k_c < 7.4\times 10^{-4}$Mpc$^{-1}$ at 95%. Thus, although it improves the fit of the data, the presence of a cutoff in power spectrum is only required at a level close to $2σ$. This is obtained with a prior which corresponds to equal distribution wrt $k_c$. We discuss how other choices (such as an equal distribution wrt $\ln k_c$ which is natural in the context of inflation) can affect the statistical interpretation.

Suppressing the lower Multipoles in the CMB Anisotropies

TL;DR

This paper addresses why the CMB TT power at the largest angular scales is lower than standard CDM predictions. It analyzes two broad mechanisms: late-time ISW effects that could dampen power via the evolution of metric perturbations, and early-universe modifications during the final 65 e-folds of inflation that induce a primordial cutoff in the spectrum, such as a fast-roll (kinetic-dominated) phase. Through a concrete inflationary model and TT-spectrum fits to WMAP data, it shows that a cutoff around Mpc can modestly improve the fit, though the significance is about and depends on the chosen prior. The work highlights horizon-scale features in the primordial spectrum as a plausible explanation and discusses the interpretational challenges, including prior dependence and the possible link to late-time dark energy physics.

Abstract

The Cosmic Microwave Background (CMB) anisotropy power on the largest angular scales observed both by WMAP and COBE DMR appears to be lower than the one predicted by the standard model of cosmology with almost scale free primordial perturbations arising from a period of inflation \cite{cobe,Bennett:2003bz,Spergel,Peiris}. One can either interpret this as a manifestation of cosmic variance or as a physical effect that requires an explanation. We discuss various mechanisms that could be responsible for the suppression of such low multipoles. Features in the late time evolution of metric fluctuations may do this via the integral Sachs-Wolfe effect. Another possibility is a suppression of power at large scales in the primordial spectrum induced by a fast rolling stage in the evolution of the inflaton field at the beginning of the last 65 e-folds of inflation. We illustrate this effect in a simple model of inflation and fit the resulting CMB spectrum to the observed temperature-temperature (TT) power spectrum. We find that the WMAP observations suggest a cutoff at Mpc at 68% confidence, while only an upper limit of Mpc at 95%. Thus, although it improves the fit of the data, the presence of a cutoff in power spectrum is only required at a level close to . This is obtained with a prior which corresponds to equal distribution wrt . We discuss how other choices (such as an equal distribution wrt which is natural in the context of inflation) can affect the statistical interpretation.

Paper Structure

This paper contains 8 sections, 18 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Late universe case
  3. Early universe case
  4. Changing the Potentials
  5. Kinetic regime
  6. Illustration of the cutoff spectrum
  7. CMB anisotropies with a cutoff
  8. Discussion

Figures (4)

  • Figure 1: Power spectrum for $Q$ from the analytical computation, Eqs. (\ref{['cd']}) and (\ref{['spect']}). This is to be compared with the spectrum of $\Phi$ obtained by the numerical evolution, and reported in the last panel of fig. \ref{['fig:fig2']}.
  • Figure 2: CMB anisotropies with cutoff primordial spectra. The top panel shows a standard $\Omega_{\Lambda}CDM$ model without cutoff, and with $n_s=0.9587$ and $\Omega_{\Lambda}=0.7316$, corresponding to the best--fit values of our model grids. The upper and lower contour show the 1$\sigma$ confidence level for a lognormal distribution appropriate for the sample variance of the observations. The error bars show the experimental noise contributions. The result in the second panel is obtained with the same model, but with an infrared cutoff on the primordial power spectrum, as obtained from an exact evolution of the model described in section \ref{['model']}. The result in the third panel is instead obtained with the power spectrum given in Eq. (\ref{['cutoff']}). The two cutoffs chosen correspond to the best--fit cutoff scales $k_c=4.9\times 10^{-4}$Mpc$^{-1}$ and $k_c=5.3\times 10^{-4}$Mpc$^{-1}$ respectively. The bottom panel shows the two primordial power spectra corresponding to these cutoffs and for the case $n_s=1$.
  • Figure 3: Marginalized distribution in the $n_s$--$k_c$ plane for our grid of models. The left panel is for the exponential cutoff while the right panel is for the toy model discussed in the text. The solid contours show drops in $\chi^2$ corresponding to 68%, 95%, and 99.7% confidence for a two--dimensional Gaussian distribution.
  • Figure 4: The one dimensional marginalized distribution for the cutoff scale $k_c$. The solid (red) curve is for the exponential cutoff while the dashed (blue) curve is for the spectrum obtained in the inflation model discussed in the text. Notice that the sharp drop--off in the likelihood at high $k_c$ is driven mainly by our prior on $\Omega_\Lambda$.