Correlated adiabatic and isocurvature CMB fluctuations in the wake of the WMAP

TL;DR

The paper investigates correlated adiabatic and cold dark matter isocurvature perturbations in the CMB, relaxing the WMAP constraint $n_{ m ad2}=n_{ m ad1}$ by allowing $n_{ m ad2}$ to vary independently. It parameterizes the initial spectra with $n_{ m ad1}$, $n_{ m ad2}$, $n_{ m iso}$, and $n_{ m cor}$, defines the isocurvature fraction $f_{ m iso}$ and the correlation angle via $oxed{\, ext{cos}\Delta}$, and computes $C_l$ from $C_l^{ m ad1}$, $C_l^{ m ad2}$, $C_l^{ m iso}$ and cross terms $C_l^{ m cor}$, using a modified CAMB. Using a coarse grid around the WMAP9 best fit, they find $f_{ m iso}\, aisebox{0.2ex}{ extcircled{ aisebox{-0.2ex}{}}}\, ext{2}" \sigma

Abstract

In general correlated models, in addition to the usual adiabatic component with a spectral index n_ad1 there is another adiabatic component with a spectral index n_ad2 generated by entropy perturbation during inflation. We extend the analysis of a correlated mixture of adiabatic and isocurvature CMB fluctuations of the WMAP group, who set the two adiabatic spectral indices equal. Allowing n_ad1 and n_ad2 to vary independently we find that the WMAP data favor models where the two adiabatic components have opposite spectral tilts. Using the WMAP data only, the 2-sigma upper bound for the isocurvature fraction f_iso of the initial power spectrum at k_0=0.05 Mpc^{-1} increases somewhat, e.g., from 0.76 of n_ad2 = n_ad1 models to 0.84 with a prior n_iso < 1.84 for the isocurvature spectral index. We also comment on a possible degeneration between the correlation component and the optical depth tau. Moreover, the measured low quadrupole in the TT angular power could be achieved by a strong negative correlation, but then one needs a large tau to fit the TE spectrum.

Figures (2)

• Figure 1: The 68.3%/$1\sigma$ (white), 95.4%/$2\sigma$ (light gray), 99.7%/$3\sigma$ (medium gray), and more than $3\sigma$ (dark gray) confidence levels for our general models. The best-fit model ($\tau$, $\Omega_\Lambda$, $\omega_b$, $\omega_c$, $n_{\rm ad1}$, $n_{\rm ad2}$, $n_{\rm iso}$, $f_{\rm iso}$, $\cos\Delta$) = (0.13, 0.73, 0.025, 0.12, 1.03, 0.64, 1.12, 0.52, -0.08) is marked by an asterisk ($\ast$) and the best-fit $n_{\rm ad2}=n_{\rm ad1}$ model by a circle ($\circ$). The dashed lines in (b) are confidence levels for $n_{\rm ad2}=n_{\rm ad1}$ models and in (c) they indicate $1\sigma$ and $2\sigma$ regions for uncorrelated models, i.e., $\cos\Delta = 0$.
• Figure 2: An example of a model that is within $2\sigma$ from our best-fit model. In the temperature power spectrum (a) the vertical axis is $l(l+1)C_l/2\pi$ and in the TE cross-correlation spectrum (b) the vertical axis is $(l+1)C_l/2\pi$!