The Cosmic Microwave Background and the Ionization History of the Universe

TL;DR

This paper addresses how uncertainties in the recombination history and the ionization history during reionization affect cosmological parameter inference from the CMB. It introduces a crude four-parameter model to capture residual recombination uncertainties and a redshift-bin approach to reconstruct $x_e(z)$, then uses MCMC forecasting to assess Planck-like constraints. The findings show that recombination uncertainties can bias parameters if unaccounted, but can be mitigated by marginalization over the extra parameters, at the cost of larger errors; reionization constraints from CMB polarization are feasible in principle with ideal data, but Planck-like data yield limited, prior-dependent inferences. Overall, combining such flexible histories with future observations and complementary probes (e.g., 21 cm) will be crucial for robustly constraining the ionization history and preserving unbiased parameter estimates.

Abstract

Details of how the primordial plasma recombined and how the universe later reionized are currently somewhat uncertain. This uncertainty can restrict the accuracy of cosmological parameter measurements from the Cosmic Microwave Background (CMB). More positively, future CMB data can be used to constrain the ionization history using observations. We first discuss how current uncertainties in the recombination history impact parameter constraints, and show how suitable parameterizations can be used to obtain unbiased parameter estimates from future data. Some parameters can be constrained robustly, however there is clear motivation to model recombination more accurately with quantified errors. We then discuss constraints on the ionization fraction binned in redshift during reionization. Perfect CMB polarization data could in principle distinguish different histories that have the same optical depth. We discuss how well the Planck satellite may be able to constrain the ionization history, and show the currently very weak constraints from WMAP three-year data.

Figures (8)

• Figure 1: The ionization fraction as a function of redshift during recombination. The solid line is computed using recfastSeager:1999km, the dashed line includes a model of additional transitions from Dubrovich:2005fc. The bottom panel shows the several-percent fractional difference.
• Figure 2: Forecast Planck constraints on recombination and cosmological parameters. There are two fiducial models, one using recfast (thin lines) and one using recfast with extra transitions following Dubrovich:2005fc (thick lines). Each simulated data set is analysed in two ways: dashed curves show the constraints using recfast and no additional recombination parameters; solid lines show the constraints allowing for four extra effective recombination parameters, as described in the text. The dotted lines show that using a fixed wrong recombination model can give biased parameter constraints; allowing for extra parameters (solid lines) broadens the errors bars but gives consistent results for both fiducial models.
• Figure 3: Ionization history for standard recfast (fudge parameter $F=1.14$, solid), recfast with $F=1$ (dash-dotted), and recfast with $F=1.14$ and an input of $3\times 10^{-24}\rm{eV} s^{-1}$ per proton today from homogeneous dark matter annihilation (dashed; see Padmanabhan:2005es, equivalent to $F_{26}=0.06$ of Zhang:2006fr).
• Figure 4: WMAP (solid line) and simulated PLANCK (dashed line) constraints on the parameter $T_{\rm h}$ as a function of redshift $\bar{z}$. Shading corresponds to the marginalized probability for the WMAP constraint and contours are at $68\%$ and $95\%$.
• Figure 5: CMB anisotropies and ionization histories for the fiducial models used in this analysis: sharp (solid), dashed (double reionization) and dragged (dash-dotted). The total optical depth for all three models is $\tau = 0.1$. The top left panel is the ionization fraction $x_e$, top right is the visibility (with respect to $z$). Bottom left are the temperature-polarization cross-correlation power spectra, bottom right the $E$-polarization power spectra. Error bars on the bottom plots show the noise plus cosmic variance from our simple model of Planck in the sharp reionization model.