New CMB spectral distortion constraints on decaying dark matter with full evolution of electromagnetic cascades before recombination

Current constraints on energy injection in the form of energetic particles before the epoch of recombination using CMB spectral distortions assume that all energy goes into $y$ and $\mu$-type distortions. We revisit these constraints with exact calculations of the spectral distortions by evolving the electromagnetic cascades. The actual spectral distortion differs in shape and amplitude from the $y$-type distortion and depends on the energy and nature of injected particles. The constraints on the energy injection processes such as dark matter decay can be relaxed by as much as a factor of 5.

Figure 1

Ratio of energy density deposited as heat with respect to CMB energy density for varying $z_X$ and $f_X=0.0003$ for 20 GeV dark matter decay into monochromatic electron-positron pairs.

Figure 2

Spectral distortions for dark matter decay into monochromatic photons for different $m_X$ and $z_X$ and constant $f_X=0.0003$.

Figure 3

Best thermal distortion fit to actual distortion spectral and corresponding residual for decaying dark matter of lifetime $z_X=20000$.

Figure 4

95% COBE-FIRAS upper limits on $f_X$ for different $m_X$ as a function of decay redshift $z_X$. Also shown is the constraint in the $yim$-approximation.

Figure 5

95% COBE-FIRAS limits on $f_X$ for decay into electron-positron pairs (left) and photons (right).