CMB Constraints on WIMP Annihilation: Energy Absorption During the Recombination Epoch

Abstract: We compute in detail the rate at which energy injected by dark matter annihilation heats and ionizes the photon-baryon plasma at z ~ 1000, and provide accurate fitting functions over the relevant redshift range for a broad array of annihilation channels and DM masses. The resulting perturbations to the ionization history can be constrained by measurements of the CMB temperature and polarization angular power spectra. We show that models which fit recently measured excesses in 10-1000 GeV electron and positron cosmic rays are already close to the 95% confidence limits from WMAP. The recently launched Planck satellite will be capable of ruling out a wide range of DM explanations for these excesses. In models of dark matter with Sommerfeld-enhanced annihilation, where sigma v rises with decreasing WIMP velocity until some saturation point, the WMAP5 constraints imply that the enhancement must be close to saturation in the neighborhood of the Earth.

• The paper presents a rigorous analysis of how dark matter annihilations modify the CMB angular power spectra during the recombination epoch.
• It employs semi-analytical methods and numerical simulations to accurately track energy deposition across various annihilation channels.
• The results tighten constraints on Sommerfeld-enhanced WIMP models by comparing observed CMB data from WMAP and Planck with theoretical predictions.

Analyzing Constraints on WIMP Annihilation During the Recombination Epoch Through CMB Observations

This paper presents a rigorous analysis of the constraints on Weakly Interacting Massive Particles (WIMPs) with respect to their annihilations during the recombination epoch, and the resultant impact on Cosmic Microwave Background (CMB) observations. The authors, Slatyer, Padmanabhan, and Finkbeiner, explore the energy deposition mechanisms from dark matter annihilations, closely examining how these mechanisms influence the ionization history and thereby affect the CMB angular power spectra. The primary focus is to utilize the precise measurements from existing CMB datasets, such as WMAP and the recently launched Planck satellite, to explore and potentially constrain WIMP models, especially those with enhancements stemming from mechanisms like Sommerfeld effect.

The document begins by elucidating that dark matter annihilations can modify the observed temperature and polarization fluctuations of the CMB. This is primarily due to additional ionization and heating of the primordial plasma, caused by high-energy particles injected through annihilation events occurring at redshifts around 1000. In particular, the broadened last scattering surface implies specific alterations in the angular power spectra, which can serve as a probe for indirect astrophysical constraints on dark matter physics.

The study examines different annihilation channels and energies, particularly focusing on models that align with observed cosmic-ray excesses in the GeV to TeV range, previously noted by experiments such as PAMELA and ATIC. The results indicate that models fitting these cosmic-ray excesses are already nearing the exclusion threshold defined by WMAP data at 95% confidence, indicating a tight testing field for such models with the advent of the Planck results.

A key exploration within the paper is the support for Sommerfeld-enhanced annihilation models where the cross-section, 〈σv〉, increases with decreasing WIMP velocity. This is particularly interesting as it implies a historically higher cross-section during the recombination epoch and could lead to significant changes in CMB properties if not close to saturation near the Earth’s velocity dispersions.

The authors meticulously calculate the energy deposition from these annihilations, incorporating semi-analytical methods and numerical simulations across different energy bands and interaction channels. They address multiple energy loss processes, such as inverse Compton scattering, ionization, and electron cooling mechanisms, refining previous estimates significantly. Where conventional analyses might have assumed an "on-the-spot" deposition approximation, this work advances by tracking energy across epochs, considering redshift phenomena and delayed deposition impacts.

Numerical results and fits are provided for energy absorption efficiencies, denoted as the function f(z), across a wide redshift range and various channels. The fitting functions and parameter extractions presented are poised to serve as a critical resource for researchers attempting to constrain annihilation cross-sections against CMB data.

Ultimately, this paper provides a richly calculated foundation for advanced analyses of dark matter properties, leveraging the backdrop of the CMB as an indirect but potent probe. It not only consolidates and updates the understanding of the ionization history perturbations due to WIMP activities but also provides a roadmap for future constraints on non-standard dark matter scenarios. While Planck and future missions are anticipated to confirm or refute many of these models, the techniques and results from this work lay a crucial groundwork for understanding WIMP annihilation impacts on early-universe cosmology. Thus, this research represents a meticulous, data-driven inquiry into the longstanding mystery of dark matter through the lens of cosmic epochs rich with transformative physics.