Cosmological parameters from CMB measurements and the final 2dFGRS power spectrum

TL;DR

This paper combines the final 2dFGRS galaxy power spectrum with a compilation of CMB temperature, polarization, and cross-spectrum data to constrain cosmological parameters across multiple model spaces. Using a Markov Chain Monte Carlo approach with CAMB, the authors quantify how including the large-scale structure data tightens constraints on Ω_m, Ω_b, h, σ_8, and the scalar spectral index n_s, while also probing extensions such as massive neutrinos, curvature, dark energy equation of state, and tensor modes. They find a relatively tight, flat-universe-compatible solution with Ω_m ≈ 0.24, Ω_b ≈ 0.041, H0 ≈ 74, σ_8 ≈ 0.77, and n_s ≈ 0.95, with f_ν < 0.105 (Σm_ν < 1.2 eV) at 95% confidence; allowing w_DE to float yields w_DE ≈ -0.85, consistent with a cosmological constant. The work also discusses the influence of priors, model complexity, and cross-dataset consistency, highlighting the importance of clear parameter-space definitions when comparing cosmological constraints across studies.

Abstract

We derive constraints on cosmological parameters using the power spectrum of galaxy clustering measured from the final two-degree field galaxy redshift survey (2dFGRS) and a compilation of measurements of the temperature power spectrum and temperature-polarization cross-correlation of the cosmic microwave background radiation. We analyse a range of parameter sets and priors, allowing for massive neutrinos, curvature, tensors and general dark energy models. In all cases, the combination of datasets tightens the constraints, with the most dramatic improvements found for the density of dark matter and the energy-density of dark energy. If we assume a flat universe, we find a matter density parameter of $Ω_{\rm m}=0.237 \pm 0.020$, a baryon density parameter of $Ω_{\rm b} = 0.041 \pm 0.002$, a Hubble constant of $H_{0}=74\pm2 {\rm kms}^{-1}{\rm Mpc}^{-1}$, a linear theory matter fluctuation amplitude of $σ_{8}=0.77\pm0.05$ and a scalar spectral index of $n_{\rm s}=0.954 \pm 0.023$ (all errors show the 68% interval). Our estimate of $n_{\rm s}$ is only marginally consistent with the scale invariant value $n_{\rm s}=1$; this spectrum is formally excluded at the 95% confidence level. However, the detection of a tilt in the spectrum is sensitive to the choice of parameter space. If we allow the equation of state of the dark energy to float, we find $w_{\rm DE}= -0.85_{-0.17}^{+0.18}$, consistent with a cosmological constant. We also place new limits on the mass fraction of massive neutrinos: $f_ν < 0.105$ at the 95% level, corresponding to $\sum m_ν < 1.2$ eV.

Figures (18)

• Figure 1: Marginalized posterior likelihoods for the cosmological parameters in the basic-five model determined from CMB information only (dashed lines) and CMB+2dFGRS $P(k)$ (solid lines). The diagonal shows the likelihood for individual parameters; the other panels show the likelihood contours for pairs of parameters, marginalizing over the other parameters. The contours show $-2\Delta \ln(L/L_{\rm max}) = 2.3$ and $6.17$.
• Figure 2: Marginalized posterior likelihoods for the cosmological parameters in the basic-six model determined from CMB information only (dashed lines) and CMB plus 2dFGRS $P(k)$ (solid lines).
• Figure 3: The marginalized posterior likelihood in the $f_{\nu}-\omega_{\rm dm}$ plane for the basic-six+$f_{\nu}$ parameter set. The dashed lines show the 68% and 95% contours obtained in the CMB only case. The solid contours show the corresponding results obtained in the CMB plus 2dFGRS $P(k)$ case.
• Figure 4: The marginalized posterior likelihood in the $f_{\nu}-\Omega_{\rm DE}$ plane for the basic-six+$f_{\nu}$ parameter set. The dashed lines show the 68% and 95% contours obtained in the CMB only case. The solid contours show the parameter constraints obtained for combined CMB and 2dFGRS $P(k)$ datasets.
• Figure 5: The one dimensional marginalized posterior likelihood for $\Omega_{k}$ for CMB data only (dashed line), CMB plus 2dFGRS $P(k)$ (solid line), and CMB plus 2dFGRS $P(k)$, with a prior on the optical depth of $\tau<0.3$ (dot-dashed line). Closed models have $\Omega_{k}<0$.