Separating the Early Universe from the Late Universe: cosmological parameter estimation beyond the black box

Abstract

We present a method for measuring the cosmic matter budget without assumptions about speculative Early Universe physics, and for measuring the primordial power spectrum P*(k) non-parametrically, either by combining CMB and LSS information or by using CMB polarization. Our method complements currently fashionable ``black box'' cosmological parameter analysis, constraining cosmological models in a more physically intuitive fashion by mapping measurements of CMB, weak lensing and cluster abundance into k-space, where they can be directly compared with each other and with galaxy and Lyman alpha forest clustering. Including the new CBI results, we find that CMB measurements of P(k) overlap with those from 2dF galaxy clustering by over an order of magnitude in scale, and even overlap with weak lensing measurements. We describe how our approach can be used to raise the ambition level beyond cosmological parameter fitting as data improves, testing rather than assuming the underlying physics.

Figures (18)

• Figure 1: Measurements of the linear matter power spectrum $P(k)$ computed as described in the text, using the concordance model of Efstathiou02 (solid curve) to compute window functions. The locations of the CMB points depend on the matter budget and scales with the reionization optical depth as $e^{2\tau}$ for $k\mathrel{\hbox{$\mathchar"218$} \hbox{$\mathchar"13E$}} 0.002$. Correcting for bias shifts the 2dF galaxy points 2df vertically ($b=1.3$ assumed here) and should perhaps blue-tilt them slightly. The cluster point scales vertically as $(\Omega_m/0.3)^{-1.2}$, and its error bars reflects the spread in the literature. The lensing points are based on Hoekstra02. The Ly$\alpha$F points are from a reanalysis GnedinHamilton01 of Croft00 and have an overall calibration uncertainty around 17%.
• Figure 2: CMB data used in our analysis. Error bars in the plot do not include calibration or beam errors which allow substantial vertical shifting and tilting for some experiments (these effects were included in our analysis).
• Figure 3: Combination of data from Figure \ref{['cmb_experimentsFig']}. These error bars include the effects of beam and calibration uncertainties, which cause long-range correlations of order 5%-10% over the peaks. In addition, points tend to be anti-correlated with their nearest neighbors, typically at the level of a few percent. The horizontal bars give the characteristic widths of the window functions (see text). The curves show the flat $\Lambda$CDM concordance models from consistent (green/light gray) and Efstathiou02 (blue/dark gray).
• Figure 4: The curves $k W_\ell(k)$ whose integral give ${\cal C}_\ell$ for a scale-invariant spectrum, all rescaled to have unit area. From left to right, the curves are for multipoles $\ell=2$, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
• Figure 5: The correspondence between $\ell$-space and $k$-space for CMB. For each $\ell$, the shaded bands indicates the $k$-range from the 20th to 80th percentile of the distribution $k W_\ell(k)$ (Figure \ref{['kernelsFig']}), and the black curve shows the median. From top to bottom, the three bands are for the E-polarization, cross-polarization (X) and unpolarized (T) cases, respectively. To avoid clutter, the E and X bands have been multiplied by 10 and 100, respectively.