Evidence for a non-zero Lambda and a low matter density from a combined analysis of the 2dF Galaxy Redshift Survey and Cosmic Microwave Background Anisotropies

TL;DR

This paper tackles the degeneracies that hinder cosmological parameter estimation from the CMB by performing a joint likelihood analysis with the 2dFGRS galaxy power spectrum, under adiabatic Gaussian initial conditions with power-law spectra and allowing tensor modes through $n_s$ and $n_t$. The authors develop a nine-parameter CMB likelihood and a 2dFGRS likelihood, then combine them to break the geometrical and tensor degeneracies, yielding tight constraints on $\omega_b$, $\omega_c$, $\Omega_\Lambda$, $h$, and related quantities. They find strong evidence for a positive cosmological constant, with $0.65<\Omega_\Lambda<0.85$ at $2\sigma$, and their results are consistent with primordial nucleosynthesis and direct $H_0$ measurements, supporting a concordance cosmology independent of Type Ia supernovae. Tensor modes remain weakly constrained, and certain high-$\omega_b$ solutions are disfavored by nucleosynthesis priors, underscoring the value of combining CMB and large-scale structure data to robustly infer cosmological parameters.

Abstract

We perform a joint likelihood analysis of the power spectra of the 2dF Galaxy Redshift Survey (2dFGRS) and the cosmic microwave background (CMB) anisotropies under the assumptions that the initial fluctuations were adiabatic, Gaussian and well described by power laws with scalar and tensor indices of n_s and n_t. On its own, the 2dFGRS sets tight limits on the parameter combination Omega_m h, but relatively weak limits on the fraction of the cosmic matter density in baryons Omega_b/Omega_m. The CMB anisotropy data alone set poor constraints on the cosmological constant and Hubble constant because of a `geometrical degeneracy' among parameters. Furthermore, if tensor modes are allowed, the CMB data allow a wide range of values for the physical densities in baryons and cold dark matter. Combining the CMB and 2dFGRS data sets helps to break both the geometrical and tensor mode degeneracies. The values of the parameters derived here are consistent with the predictions of the simplest models of inflation, with the baryon density derived from primordial nucleosynthesis and with direct measurements of the Hubble parameter. In particular, we find strong evidence for a positive cosmological constant with a pm 2sigma range of 0.65 < Omega_Lambda < 0.85, completely independently of constraints on Omega_Λderived from Type Ia supernovae.

Figures (4)

• Figure 1: Contours ($1$, $2$ and $3 \sigma$) of the pseudo-marginalized likelihood functions (see text for details) for various pairs of parameters computed by fitting to the galaxy power spectrum of the 2dFGRS. These contours correspond to changes in the likelihood of $2 \Delta {\rm ln} ({\cal L})$ of $2.3$, $6.0$ and $9.2$. The crosses show the position of maximum likelihood.
• Figure 2: The points show band-averaged observational estimates of the CMB power spectrum from Wang et al. (2001) together with $\pm 1 \sigma$ errors. The lines shows the CMB power spectra for the adiabatic fiducial inflationary models that provide the best fit to the CMB and 2dFGRS power spectra. The parameters of these model are listed in Table 1. The solid line shows the best fit without a tensor component (fit B). The dashed line shows the best fit (fit C) including a tensor component (shown by the dotted line).
• Figure 3: Results of the nine parameter likelihood analysis. Figs 3a and 3b show approximate $1$, $2$ and $3\sigma$ likelihood contours for various parameter pair combinations computed from an analysis of the CMB data alone. Figs 3a use variables natural to the CMB analysis and illustrate the geometrical and tensor degeneracies. Figs 3b use the variables natural to the analysis of the galaxy power spectrum (as used in Fig. 1). Figs 3c and 3d show the likelihood contours of CMB and 2dFGRS data combined. The crosses in each panel show the position of the maximum likelihood.
• Figure 4: The points show the galaxy power spectrum of the 2dFGRS measured by P01 divided by the power spectrum of a scale-invariant CDM model with $\omega_b=0$, $\Omega_mh =0.2$. The error bars are computed from the diagonal components of the covariance matrix. The lines show the linear matter power spectra of the maximum likelihood fits to the combined CMB and 2dFGRS power spectra after convolution with the spherically averaged window function of the survey. The solid line shows fit B from Table 1 (no tensor component). The dashed line shows fit C (including a tensor component).