A bound on the cosmic opacity of unparticles from the CMB temperature

Unparticle cosmology gives an unconventional outlook on the dark sector of cosmology, increasingly challenging $\Lambda\mbox{CDM}$ by $H_0$-tension. This model derives from a finite temperature broken conformal symmetry of radiation, described by a non-radiative correction with unknown sign in energy density. This symmetry breaking has a sign ambiguity, in which corrections about the IR fixed point are normal or tachyonic. While the first has been ruled out in a recent study, the latter possesses a late-time temperature $T_c\simeq 4\,T_{CMB}$ associated with $\Omega_{\cal U}\simeq 1$ ($\Omega_{\cal U} \simeq 10^4 \Omega_{CMB}$), where $T_{CMB}$ denotes the temperature of the Cosmic Microwave Background (CMB). Thus exposed to the enormous heat bath of unparticles, $T_{CMB}$ is constrained by the astronomical age of the Universe $T_{u,0}$. The relative temperature shift $\Delta T/T$ in any heat exchange to the CMB is hereby limited to the uncertainty of a few percent in $T_{u,0}$. This bounds the effective cross-section of unparticles interactions with CMB photons to $\sigma _{\gamma \mathcal{U}} \lesssim 10^{-40}\ \mbox{m}^2=10^{-3}\ \mbox{nb}$. Assuming a standard cross-section across the broadband mass and energy spectrum of unparticles, a more stringent bound $\sigma _{\gamma \mathcal{U}} \lesssim 10^{-3}\,\mbox{pb}$ derives from COBE-FIRAS constraints on spectral distortions. The first is midway of photon-neutrino $\sigma_{\gamma\nu}$ and photon-photon cross sections $\sigma_{\gamma\gamma}$, the second is on par with $\sigma_{\gamma\nu}$. These constraints put late-time unparticle cosmology, if present, at the edge of the standard model.