WMAP constraints on inflationary models with global defects

TL;DR

The paper investigates whether global defects, specifically textures from $O(4)$ symmetry breaking, can meaningfully contribute to cosmic structure formation within an inflationary framework by adding a defect component to the inflationary perturbations. It computes the defect CMB and matter spectra using the unequal-time correlator (UETC) approach and performs an eight-parameter MCMC fit to the first-year WMAP data, allowing the defect strength to be characterized by the fractional contribution $f_{\rm d}$ at $\ell=10$. A strong degeneracy with cosmological parameters such as $\Omega_{\rm b}h^{2}$, $h$, $A_{\rm s}^{2}$ and $n_{\rm s}$ means that WMAP data alone cannot decisively constrain defects; when Big Bang Nucleosynthesis and Hubble parameter priors are included, the allowed defect fraction tightens to $f_{\rm d}<0.13$ (95% C.L.). The study highlights the model-dependent nature of CMB-based parameter inferences and suggests that future CMB polarization data and Planck measurements could further limit or reveal sub-dominant defect contributions.

Abstract

We use the cosmic microwave background angular power spectra to place upper limits on the degree to which global defects may have aided cosmic structure formation. We explore this under the inflationary paradigm, but with the addition of textures resulting from the breaking of a global O(4) symmetry during the early stages of the Universe. As a measure of their contribution, we use the fraction of the temperature power spectrum that is attributed to the defects at a multipole of 10. However, we find a parameter degeneracy enabling a fit to the first-year WMAP data to be made even with a significant defect fraction. This degeneracy involves the baryon fraction and the Hubble constant, plus the normalization and tilt of the primordial power spectrum. Hence, constraints on these cosmological parameters are weakened. Combining the WMAP data with a constraint on the physical baryon fraction from big bang nucleosynthesis calculations and high-redshift deuterium abundance, limits the extent of the degeneracy and gives an upper bound on the defect fraction of 0.13 (95% confidence).

Figures (6)

• Figure 1: The temperature power spectrum contributions from the global defects compared to that from primordial tensor perturbations and to the more dominant primordial scalar contribution. The defect and tensors contributions are scaled such that their contributions at $\ell=10$ are 13% and 19% respectively of a scalar-only fit to the WMAP data. (Note that the ordinate axis has linear scaling below $300\: \mu \rm K^2$ but logarithmic scaling above this value so as to show the slowly-varying defect contribution well on the same plot as the scalar contribution.) The dotted line indicates the 2$\sigma$ uncertainty in the WMAP data, including cosmic variance.
• Figure 2: The change in the temperature power spectrum from a model without defects, when defects are added and degeneracy direction followed to maintain the fit to data. The WMAP first-year binned data are over-plotted, with the zero-defect model subtracted from them, demonstrating the inability of the data to readily distinguish between the models. The error bars include cosmic variance. (Note that multipole axis is linear for $\ell>200$ and logarithmic below this in order to show both regions clearly.)
• Figure 3: The marginalized likelihood function for the defect fraction when using only the WMAP data (top) and when additionally incorporating the BBN and HKP constraints (bottom). The horizontal lines show the 68% and 95% confidence levels.
• Figure 4: A plot of the likelihood from the fit to WMAP data projected onto the $\Omega_{\rm b}h^{2}$-$f_{\rm d}$ plane. The contours show the 68% and 95% confidence levels and highlight the degeneracy between the two parameters. The vertical lines show the 68% and 95% confidence limits of the determination of $\Omega_{\rm b}h^{2}$ of Kirkman et al.
• Figure 5: The changes to the temperature power spectrum for the same cases as in Fig. \ref{['fig:degen']}, but shown at higher multipoles and compared to the VSA data. The changes in the parameters follow the degeneracy present in the WMAP data but the changes in these previously unconstrained scales are too small for the VSA data to readily distinguish between the curves. The error bars do not include the 3% calibration uncertainty, which allows the power spectra values to be scaled up or down in unison. On this difference plot, this uncertainty is shown by the dashed zig-zags.