WMAP 3-year primordial power spectrum

TL;DR

This work uses Bayesian model selection with nested sampling to constrain the primordial power spectrum from WMAP3 plus Ly-$\alpha$ and LSS data, testing seven parameterizations including Harrison–Zel'dovich, power-law, running, large-scale cutoff, broken spectra, eight-bin reconstructions, and the Lasenby–Doran (L-D) model. Parameter constraints come from MCMC analyses, while model comparison relies on evidence differences $\Delta\ln Z$ to quantify preference. The results indicate that a scale-invariant spectrum is disfavoured and that a tilted spectrum with a cutoff or an L-D-like form provides the strongest evidence, with the L-D model delivering a decisive improvement in the primordial-parameter space and a consistent tilt of $n_s\approx 0.96$; Ly-$\alpha$ and LRG data generally reduce the inferred running. Overall, the study demonstrates that incorporating large-scale suppression and non-standard boundary-condition-inspired spectra can yield substantially better fits to the data, informing inflationary physics and early-universe scenarios.

Abstract

We constrain the form of the primordial power spectrum using Wilkinson Microwave Anisotropy Probe (WMAP) 3-year cosmic microwave background (CMB) data (+ other high resolution CMB experiments) in addition to complementary large-scale structure (LSS) data: 2dF, SDSS, Ly-alpha forest and luminous red galaxy (LRG) data from the SDSS catalogue. We compute the comparative Bayesian evidence in addition to parameter estimates for a collection of seven models: (i) a scale invariant Harrison-Zel'dovich (H-Z) spectrum; (ii) a power-law; (iii) a running spectral index; (iv) a broken spectrum; (v) a power-law with an abrupt cutoff on large-scales; (vi) a reconstruction of the spectrum in eight bins in wavenumber; and (vii) a spectrum resulting from a cosmological model proposed by Lasenby & Doran (L-D). Using a basic dataset of WMAP3 + other CMB + 2dF + SDSS our analysis confirms that a scale-invariant spectrum is disfavoured by between 0.7 and 1.7 units of log evidence (depending on priors chosen) when compared with a power-law tilt. Moreover a running spectrum is now significantly preferred, but only when using the most constraining set of priors. The addition of Ly-alpha and LRG data independently both suggest much lower values of the running index than with basic dataset alone and interestingly the inclusion of Ly-alpha significantly disfavours a running parameterisation by more than a unit in log evidence. Overall the highest evidences, over all datasets, were obtained with a power law spectrum containing a cutoff with a significant log evidence difference of roughly 2 units. The natural tilt and exponential cutoff present in the L-D spectrum is found to be favoured decisively by a log evidence difference of over 5 units, but only for a limited study within the best-fit concordance cosmology.

Figures (9)

• Figure 1: Marginalised parameter constraints with dataset I (black) for the H-Z, single-index and running models compared with our WMAP1 (Bridges06) analysis (red).
• Figure 2: Comparison of parameter constraints using dataset I (black) for the H-Z, single-index and running models with dataset II (red) and dataset III (blue).
• Figure 3: Marginalised parameter constraints for dataset I (black) for abrupt cutoff model compared with our WMAP1 (Bridges06) analysis (red).
• Figure 4: Comparison of cutoff constraints using dataset I (black), dataset II (red) and dataset III (blue).
• Figure 5: Marginalised 1D and 2D probability constraints for the broken spectrum model, for $k_s$, $\ln(k_e/k_s)$ and $A/B$ for our WMAP1 (Bridges06) analysis (red) and dataset I (black). 2D constraints plotted with $1\sigma$ and $2\sigma$ confidence contours.