CMB polarization features from inflation versus reionization

TL;DR

The paper investigates whether the WMAP-detected TT anomalies around $\ell\sim 20-40$ could arise from a step in the inflaton potential and proposes large-scale $E$-mode polarization as a robust cross-check. It models the feature with a step in the potential, computes the resulting primordial power spectrum via numerical mode evolution, and maps it to CMB spectra using transfer functions, highlighting that polarization provides a cleaner probe of such features than temperature. Forecasts show Planck can test the best-fit inflationary feature at about $3\sigma$, while a cosmic-variance-limited experiment could reach $\sim 8\sigma$, though reionization and tensor uncertainties can reduce significance to the $2.5-5\sigma$ level depending on scenario. The work emphasizes that future polarization missions could offer a decisive test of the feature hypothesis and help constrain the shape of a possible step in the inflationary potential, with implications for understanding primordial physics and the reionization history.

Abstract

The angular power spectrum of the cosmic microwave background temperature anisotropy observed by WMAP has an anomalous dip at l~20 and bump at l~40. One explanation for this structure is the presence of features in the primordial curvature power spectrum, possibly caused by a step in the inflationary potential. The detection of these features is only marginally significant from temperature data alone. However, the inflationary feature hypothesis predicts a specific shape for the E-mode polarization power spectrum with a structure similar to that observed in temperature at l~20-40. Measurement of the CMB polarization on few-degree scales can therefore be used as a consistency check of the hypothesis. The Planck satellite has the statistical sensitivity to confirm or rule out the model that best fits the temperature features with 3 sigma significance, assuming all other parameters are known. With a cosmic variance limited experiment, this significance improves to 8 sigma. For tests of inflationary models that can explain both the dip and bump in temperature, the primary source of uncertainty is confusion with polarization features created by a complex reionization history, which at most reduces the significance to 2.5 sigma for Planck and 5-6 sigma for an ideal experiment. Smoothing of the polarization spectrum by a large tensor component only slightly reduces the ability of polarization to test for inflationary features, as does requiring that polarization is consistent with the observed temperature spectrum given the expected low level of TE correlation on few-degree scales. A future polarization satellite would enable a decisive test of the feature hypothesis and provide complementary information about the shape of a possible step in the inflationary potential. (Abridged.)

Figures (15)

• Figure 1: Upper panel, solid black: Inflationary potential with a step [Eq. \ref{['eq:meff']}]. The parameters for the potential are chosen to maximize the WMAP5 likelihood and are listed in Table \ref{['tab:modelparameters']}. The dashed red line shows a smooth $m^2\phi^2$ potential ($c=0$) with $m=7.120\times 10^{-6}$ so that the two models have equal power on small scales ($\phi\ll b$). Middle and lower panels: slow-roll parameters $\epsilon_V$ and $\eta_V$ for the two inflationary potentials.
• Figure 2: Primordial curvature power spectra for the potentials in Fig. \ref{['plot:potential']}.
• Figure 3: Transfer function $T_\ell^X(k)$ for the fiducial model with instantaneous reionization. Upper panel: temperature $X=T$; lower panel: polarization $X=E$. Contours are spaced by factors of $2$. Dashed lines represent the range of $k$-modes where features appear in Fig. \ref{['plot:powspec']}. Polarization is a cleaner probe of features in this range and, for instantaneous reionization, is nearly uncontaminated by secondary effects. The temperature and polarization are also only weakly correlated here due to the transition between the Sachs-Wolfe (SW) and acoustic regimes in temperature.
• Figure 4: Temperature and polarization power spectra for the inflationary power spectra in Fig. \ref{['plot:powspec']}, with solid black curves for the model with a feature and dashed red curves for smooth $\Delta_{{\cal R}}^2(k)$. Dotted curves indicate where $C_{\ell}^{TE}$ is negative. Blue points with error bars show the 5-year WMAP measurements of $C_{\ell}^{TT}$ including sample variance. For both models, the reionization history is assumed to be instantaneous and the cosmological parameters not determined by the inflationary potential are given in Table \ref{['tab:modelparameters']}.
• Figure 5: Transfer function $T_\ell^X(k)$ for the fiducial model with instantaneous reionization for multipoles near the temperature dip ($\ell = 20$) and bump ($\ell = 40$) for temperature and polarization. For temperature, the dip multipoles receive a broad range of contributions from $k \gtrsim 10^{-3}$ and the bump multipoles from $k \gtrsim 3 \times 10^{-3}$. The localization of the transfer function is sharper for polarization, especially for $\ell = 40$ which is immune to reionization effects. The polarization transfer functions have been scaled by $10^4$ and $10^5$ for convenience.