Room for New Physics in the Rayleigh-Jeans Tail of the Cosmic Microwave Background

We show that, despite stringent constraints on the shape of the main part of the cosmic microwave background (CMB) spectrum, there is considerable room for its modification within its Rayleigh-Jeans (RJ) end, $\omega \ll T_{\mathrm{CMB}}$. We construct explicit new physics models that give an order one (or larger) increase of photon count in the RJ tail, which can be tested by existing and upcoming experiments aiming to detect the cosmological 21 cm emission or absorption signal. This class of models stipulates the decay of unstable particles to dark photons $A^{\prime }$ that have a small mass, $m_{A^{\prime }}\sim {10}^{-14}–{10}^{-9}\mathrm{eV}$, nonvanishing mixing angle $\epsilon$ with electromagnetism, and energies much smaller than $T_{\mathrm{CMB}}$. The nonthermal number density of dark photons can be many orders of magnitude above the number density of CMB photons, and even a small probability of $A^{\prime }\to A$ oscillations, for values as small as $\epsilon \sim {10}^{-9}$, can significantly increase the number of RJ photons. In particular, we show that resonant oscillations of dark photons into regular photons in the interval of redshifts $20<z<1700$ can be invoked as an explanation of the recent tentative observation of a stronger-than-expected absorption signal of 21 cm photons. We present a model that realizes this possibility, where meV mass dark matter decays to dark photons, with a lifetime longer than the age of the Universe.

Figure 1

Dark matter $a$ decays to soft massive dark photons $A^{\prime }$, which oscillate into ordinary photons $A$. The conversion happens resonantly at redshift $z_{\text{res}}$ before the formation of the 21 cm absorption signal. The converted photons (red) add to the CMB photon count (green) in the RJ tail.

Figure 2

(Left) Effective photon mass $m_A$ as a function of redshift. When resonant oscillation [$m_A(z)=m_{A^{\prime }}$] occurs between redshift $20\le z\lesssim 1700$ (green) it impacts the 21 cm absorption signal. (Right) Effective conversion probability as a function of redshift. We consider photons with energy $x=\omega /T_{\mathrm{CMB}}=1.4\times {10}^{-3}$, which implies a wavelength of 21 cm at $z=17$.

Figure 3

(Left) (Dark) Photon spectrum (before) after conversion shown in solid black (dashed black, rescaled by ${10}^{-3}$) and compared to the CMB (orange) for $m_a={10}^{-3}\mathrm{eV}$, ${\tau }_a=100\times {\tau }_U$, $m_{A^{\prime }}=5\times {10}^{-12}\mathrm{eV}$ (implying resonance at $z_{\text{res}}=500$) and $\epsilon =2.1\times {10}^{-7}$. (Right) The relevant range of DM mass $m_a$ versus $m_{A^{\prime }}$ for addressing the 21 cm absorption signal; for $m_a/T_{\mathrm{CMB}}<2x_{21}^{\min }$, the produced photons are too soft to impact 21 cm. The region above the dashed purple (green) line are probed by FIRAS (ARCADE 2), constraining $\epsilon$ and ${\tau }_a$. The orange hatched region labelled as BH is possibly disfavored by black hole superradiance [48]. The star shows the example point considered in the left figure.

Figure 4

(Left) Allowed region in DM lifetime versus number ratio of converted-to-original photons $n_{A^{\prime }\to A}/n_{\mathrm{RJ}}$, in the energy window $x_{21}^{\min }<x<x_{21}^{\max }$. The blue region is excluded by stellar energy loss; the purple region would require $P_{A^{\prime }\to A}>1$. (Right) Allowed parameter space in the $(m_{A^{\prime }},\epsilon )$ plane; ${\tau }_a$ is chosen at each point such that $n_{A^{\prime }\to A}/n_{\mathrm{RJ}}=1$ in the 21 cm signal region. In both plots $m_a={10}^3\mu \mathrm{eV}$, the brown region is excluded by a limit on the DM lifetime [12] and the red region (red dashed line) is excluded by FIRAS (would be probed by PIXIE/PRISM) due to $A\to A^{\prime }$ oscillations [15].