Figure 1

Modification of the CMB spectrum by decoherence effects. The dots show the residual CMB spectrum measured by COBE/FIRAS [24] ($1\mathrm{Jy}(\mathrm{Jansky})\equiv {10}^{-26}\mathrm{W}{\mathrm{m}}^{-2}{\mathrm{Hz}}^{-1}$). The upper panel shows the effect of $D_{*}=0.01$, 0.1, 1 and the lower panel $D_{*}={10}^{-4}$. The curves show the accumulated deficit in photons compared to the “no decoherence” case. (A different shadowing is included to guide the eye.)Reuse & Permissions

Figure 2

Upper panel: Enhanced SNe dimming by decoherence effects assuming $N=2$, $p=1$, $M_{\mathrm{QD}}=M_{\mathrm{Pl}}$ and $D_{*}={10}^{-6}$, ${10}^{-5}$, ${10}^{-4}$ assuming sources observed in a frequency interval centered at ${\omega }_{\star }=1\mathrm{eV}$. The dots show the SNe Ia “union” compilation from Ref. 28. The luminosity distance $d_L$ is shown by the difference $\Delta (m-M)$ to an empty (${\Omega }_{\mathrm{tot}}=0$) flat universe. The thin lines show the accumulated deficit in photons compared to the “no decoherence” case (standard $\Lambda \mathrm{CDM}$ model) indicated by the thick line. Lower panel: As the upper panel, but now showing also a flat CDM model with ${\Omega }_m=1$ and ${\Omega }_{\Lambda }=0$ (dotted line). For illustration, we consider a hidden photon model with $p=1$, $N=2$, and $D_{*}=6\times {10}^{-6}$ and show the dimming for the B (${\lambda }_{\star }\simeq 440\mathrm{nm}$, upper line) and V (${\lambda }_{\star }\simeq 550\mathrm{nm}$, lower line) bands. Whereas the overall dimming effect is practically indistinguishable from the $\Lambda \mathrm{CDM}$ model, the strong reddening of the starlight from the energy dependence of $D\propto {\omega }^2/M_{\mathrm{Pl}}$ is challenged by the data [34].Reuse & Permissions

Figure 3

Photon survival probability in the presence of decoherence with a single hidden U(1) ($N=2$). The black line shows the photon attenuation, e.g. in the intergalactic photon background via $\gamma +{\gamma }_{\mathrm{BG}}\to e^{+}+e^{-}$, in the absence of decoherence ($D=0$). The dashed curve shows decoherence with $D\lambda =1$ and the dotted curve $D\lambda \gg 1$.Reuse & Permissions