[Paper Review] Correlated adiabatic and isocurvature CMB fluctuations in the wake of the WMAP

J. Väliviita, Vesa Muhonen|arXiv (Cornell University)|Apr 10, 2003

Cosmology and Gravitation Theories8 citations

TL;DR

This paper investigates correlated adiabatic and isocurvature fluctuations in the cosmic microwave background (CMB), relaxing the WMAP assumption that two adiabatic components have identical spectral indices. Allowing independent spectral indices for the two adiabatic components, the authors find that WMAP data favor models with opposite spectral tilts and a slightly higher upper bound on the isocurvature fraction (f_iso < 0.84 at 2σ), with correlation playing a key role in fitting the low CMB quadrupole and high TE spectrum simultaneously.

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 &lt; 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.

Motivation & Objective

• To investigate whether correlated adiabatic and isocurvature CMB fluctuations can better explain WMAP data than uncorrelated models.
• To relax the WMAP assumption that two adiabatic components have equal spectral indices, allowing independent evolution of n_ad1 and n_ad2.
• To assess the impact of spectral index degeneracy and correlation on cosmological parameter constraints, particularly f_iso and τ.
• To examine the degeneracy between correlation amplitude and optical depth τ in fitting the TT and TE power spectra.
• To determine whether the low CMB quadrupole and high TE quadrupole can be simultaneously explained by correlated models.

Proposed method

• The study uses a two-field inflation model with inflaton φ and entropy field χ, modeling the evolution of curvature and entropy perturbations via transfer functions T_RS and T_SS during inflation and reheating.
• The initial power spectra are assumed to follow power laws with independent spectral indices: n_ad1, n_ad2, n_iso, and n_cor = (n_ad2 + n_iso)/2 for the correlation component.
• The angular power spectra (TT, TE) are computed numerically using transfer functions derived from solving the equations of motion for adiabatic and entropy perturbations.
• A Bayesian likelihood analysis is performed using WMAP data only, marginalizing over cosmological parameters including τ, Ω_Λ, ω_b, ω_c, and f_iso.
• The analysis includes constraints on f_iso and cosΔ (correlation amplitude) by varying spectral indices independently and comparing to observed TT and TE spectra.
• The model allows for non-Gaussian marginalized likelihoods and confidence regions to assess parameter degeneracies and constraints.

Experimental results

Research questions

• RQ1 Can a correlated mixture of adiabatic and isocurvature fluctuations better explain the WMAP CMB data than uncorrelated models?
• RQ2 What are the constraints on the isocurvature fraction f_iso when the two adiabatic spectral indices are allowed to differ?
• RQ3 How does the correlation between adiabatic and isocurvature components affect the fitting of the low TT quadrupole and high TE quadrupole?
• RQ4 To what extent does the correlation degeneracy with optical depth τ influence cosmological parameter estimation?
• RQ5 Does allowing independent spectral indices for the two adiabatic components significantly alter the constraints on n_ad1 compared to pure adiabatic models?

Key findings

• The WMAP data favor models where the two adiabatic components have opposite spectral tilts, with n_ad1 ≈ 1.03 and n_ad2 ≈ 0.64 in the best-fit model.
• The 2σ upper bound for the isocurvature fraction f_iso increases from 0.76 (under the WMAP assumption of equal n_ad1 and n_ad2) to 0.84 when n_ad2 and n_ad1 are allowed to vary independently.
• A strong negative correlation (cosΔ ≈ -0.08) helps cancel excess power in the TT spectrum, enabling a low quadrupole while still fitting the high TE quadrupole.
• The correlation component adds power to the TE spectrum, which explains why correlated models prefer slightly smaller optical depth τ (τ ≈ 0.13) than pure adiabatic models.
• The degeneracy between the isocurvature fraction and baryon density ω_b is significantly worsened in correlated models, making ω_b unconstrained by CMB alone.
• The marginalized spectral index for the primary adiabatic component is n_ad1 = 0.98 ± 0.07 in correlated models, only slightly different from the pure adiabatic case (n_ad1 = 0.97 ± 0.06).