Estimates of Cosmological Parameters Using the CMB Angular Power Spectrum of ACBAR

TL;DR

This study uses the ACBAR CMB angular power spectrum, together with other CMB measurements, to constrain cosmological parameters within inflation-motivated adiabatic ΛCDM models via Bayesian inference. It demonstrates that including a nonzero cosmological constant ($\\Omega_\\Lambda$) significantly improves fit quality and leverages the damping tail to break degeneracies when combined with priors (LSS, HST-$h$). The authors also model a Sunyaev–Zeldovich component with SZ templates, accounting for non-Gaussian sample variance, and obtain evidence for SZ contributions consistent with a near-unity effective $\\sigma_8^{SZ}$. Overall, ACBar results support a flat ΛCDM framework, refine certain parameter eigenmodes when added to other data, and provide important insights into the high-$$\\ell$$ regime and the SZ amplitude.

Abstract

We report an investigation of cosmological parameters based on the measurements of anisotropy in the cosmic microwave background radiation (CMB) made by ACBAR. We use the ACBAR data in concert with other recent CMB measurements to derive Bayesian estimates of parameters in inflation-motivated adiabatic cold dark matter models. We apply a series of additional cosmological constraints on the shape and amplitude of the density power spectrum, the Hubble parameter and from supernovae to further refine our parameter estimates. Previous estimates of parameters are confirmed, with sensitive measurements of the power spectrum now ranging from \ell \sim 3 to 2800. Comparing individual best model fits, we find that the addition of Ω_Λas a parameter dramatically improves the fits. We also use the high-\ell data of ACBAR, along with similar data from CBI and BIMA, to investigate potential secondary anisotropies from the Sunyaev-Zeldovich effect. We show that the results from the three experiments are consistent under this interpretation, and use the data, combined and individually, to estimate σ_8 from the Sunyaev-Zeldovich component.

Figures (8)

• Figure 1: Top Panel: The Acbar CMB power spectrum, ${\mathcal{C}}_{\ell} \equiv \ell (\ell + 1)C_{\ell}/{(2\pi)}$, plotted over a vacuum energy dominated [$\Omega_k = -0.05$, $\Omega_\Lambda = 0.5$, $\omega_{cdm} = 0.12$, $\omega_b = 0.02$, $H_0 = 50$, $\tau_C = 0.025$, $n_s = 0.925$, amplitude ${\sqrt {\mathcal{C}}_{10}}= 1.11\times 10^{-5}T_{\rm CMB}$] model (black thin line) and a CDM dominated [$\Omega_k = 0.05$, $\Omega_\Lambda = 0$, $\omega_{cdm} = 0.22$, $\omega_b = 0.02$, $H_0 = 50$, $\tau_C = 0$, $n_s = 0.925$, amplitude ${\sqrt {\mathcal{C}}_{10}}= 1.34\times 10^{-5}T_{\rm CMB}$] model (green thick line). These are the best-fit models, for $\Lambda$ and $\Lambda$-free models respectively, found during the Acbar+Others parameter estimation described in the text, with the weak-$h$ prior. Bottom Panel: The top panel with the addition of power spectra from several other experiments. Both models appear to be reasonable fits to the data, with the $\Omega_\Lambda = 0.5$ model statistically being the better of the two.
• Figure 2: Likelihood curves for Acbar+DMR with the $weak$ and $weak$+flat priors. Each prior case is plotted with and without the first Acbar band (centered on $\ell = 187$) included in the analysis. In the upper--right panel, the 1 to 3-$\sigma$ contours are shown for the 2D $\Omega_k$--$\Omega_\Lambda$ likelihood with the $weak$ prior and bands 1-14 (blue) and bands 2-14 (red). The thick black lines define $\Omega_m=0$ and $\Omega_m=1$ and the dotted black line defines $\Omega_m=0.5$. The yellow contours are the 1, 2 and 3-$\sigma$ levels of constraints based on Type 1a Supernovae. The lack of stability of the curves (for $\omega_b$ in particular) indicates that Acbar+DMR alone is not sufficient for robust parameter estimation.
• Figure 3: Likelihood curves for Archeops+B98+CBI+DASI+DMR+MAXIMA+VSA ("Others") with the $weak$, $weak$+LSS, HST-$h$, and strong data priors. The $\Omega_k$--$\Omega_\Lambda$ contours are shown for the $weak$ (blue) and strong data (red) cases. The yellow contours are the 1, 2 and 3-$\sigma$ levels of constraints based on Type 1a Supernovae. CMB estimates of $\Omega_k$, $\omega_{cdm}$, and $\omega_b$ are stable with sensible behavior as additional priors are employed.
• Figure 4: Likelihood curves for Acbar +Archeops+B98+CBI+DASI+DMR+MAXIMA+VSA ( Acbar+"Others") with the $weak$, $weak$+LSS, HST--$h$, and strong data priors. The $\Omega_k$--$\Omega_\Lambda$ contours are shown for the $weak$ (blue) and strong data (red) cases. The yellow contours are the 1, 2 and 3-$\sigma$ levels of constraints based on Type 1a Supernovae. The positions and widths of these curves do not differ significantly from those in Figure \ref{['fig:1DLothers']} despite the addition of the low noise Acbar data through the damping tail. A comparison of the curves here containing the LSS prior ($weak$+LSS and strong data) with those derived using the a lower estimate (discussed in the text) shows only small changes. The most noticeable changes are an upward shift in the lower tail on $\Omega_\Lambda$, and a broader and higher--value $n_s$ peak. Table \ref{['estimatetab']} gives numerical estimates of these parameters, derived by integration of these curves.
• Figure 5: 1, 2, and 3--$\sigma$ contours for various combinations of data sets in the $(q_{2K}^{\rm eff},\sigma_8^{\rm SZ})$ plane. The left panels show fits obtained using the SPH template and the right panels are the equivalent for the analytical model. Both CBI and Acbar data points constrain the upper values of $\sigma_8^{\rm SZ}$ but not the lower values as they are sensitive to the amplitude of the primary spectrum. The higher--$\ell$ BIMA observations are insensitive to the primary component and therefore provide a strong lower bound. The combination of the three datasets (bottom row -- dotted, black contours) show a strong detection of the SZ component. The dashed parallel lines show the width of the Gaussian prior imposed on $q_{2K}^{\rm eff}$. We use a lognormal distribution for the BIMA band powers.