Searching for Dark Matter in the CMB: A Compact Parameterization of Energy Injection from New Physics

TL;DR

This work develops a model-independent framework to constrain energy deposition during recombination by decomposing arbitrary redshift histories into principal components. Using a Fisher-misher transfer-matrix formalism and marginalization over standard cosmological parameters, the authors identify a small set of orthogonal redshift-weighting functions that capture most of the CMB sensitivity to energy injection. They show that for generic annihilation-like histories Planck can measure a few components, while a cosmic-variance-limited experiment could measure more, and that a universal PC e_WIMP(z) suffices to describe conventional WIMP annihilation histories. The analysis is validated with CosmoMC, yielding consistent constraints and providing a practical mapping from physical models to PC coefficients for robust, model-independent limits on new-physics energy deposition in the early universe.

Abstract

High-precision measurements of the temperature and polarization anisotropies of the cosmic microwave background radiation have been previously employed to set robust constraints on dark matter annihilation during recombination. In this work we improve and generalize these constraints to apply to energy deposition during the recombination era with arbitrary redshift dependence. Our approach also provides more rigorous and model-independent bounds on dark matter annihilation and decay scenarios. We employ principal component analysis to identify a basis of weighting functions for the energy deposition. The coefficients of these weighting functions parameterize any energy deposition model and can be constrained directly by experiment. For generic energy deposition histories that are currently allowed by WMAP7 data, up to 3 principal component coefficients are measurable by Planck and up to 5 coefficients are measurable by an ideal cosmic variance limited experiment. For WIMP dark matter, our analysis demonstrates that the effect on the CMB is described well by a single (normalization) parameter and a "universal" redshift dependence for the energy deposition history. We give WMAP 7 constraints on both generic energy deposition histories and the universal WIMP case.

Figures (24)

• Figure 1: Rate of Hydrogen ionization from energy deposition, relative to the number density of ionized Hydrogen ($n_{ion}^0$) when there is no energy deposition. The lines shown are the cases of constant $p_\mathrm{ann}$ and $p_\mathrm{dec}$, corresponding to on-the-spot energy deposition from dark matter annihilation and dark matter decay, respectively.
• Figure 2: The effect of the number of included $\ell$'s, and the number of included frequency bands, on the constraint on a constant-$p_\mathrm{ann}$ energy deposition history; here we show the value of $p_\mathrm{ann}$ corresponding to a $2 \sigma$ signal.
• Figure 3: The degree of nonlinearity in the computed significance of a sample energy deposition history, for $p_\mathrm{ann}$ constant, using WMAP 7 noise parameters. We show the ratio of (1) the S/N estimated by a linear extrapolation from small energy deposition to (2) the "true" S/N (estimated as in § \ref{['subsec:sensitivity_discussion']}), as a function of $p_\mathrm{ann}$. The solid, dashed and dotted lines indicate the WMAP 7 2$\sigma$ upper limit on $p_\mathrm{ann}$, the value of $p_\mathrm{ann}$ for which the nonlinearity is $10\%$, and the value for which the nonlinearity is $1\%$, respectively. The red dot-dashed line indicates the 2$\sigma$ upper limit on $p_\mathrm{ann}$ that would be obtained by linearly extrapolating the significance from small energy deposition, which overestimates the significance and hence leads to a too-strong constraint.
• Figure 4: The first three principal components for WMAP 7, Planck and a CVL experiment, both before and after marginalization over the cosmological parameters.
• Figure 5: The first six principal components for Planck after marginalization, in the case of (left) annihilation-like redshift dependence with linear binning, (center) annihilation-like redshift dependence with log binning, and (right) decay-like redshift dependence with log binning. Note that for decay-like energy deposition histories, the redshift range is extended down to $z=10$ in order to fully capture the effect on the CMB - see §\ref{['sec:fisher']}. This larger redshift range makes linear binning impractical.