What is the energy spectrum of all photons in the observable universe? Does anyone know what the energy spectrum for the entire universe looks like? In other words, what would the graph look like if you plotted the number of photons on the $y$-axis and frequency on the $x$-axis? Would it look like a blackbody spectrum, what would the peak temperature be?
 A: 
What is the energy spectrum of all photons in the observable universe?

All photons means:

*

*photons from the cosmic microwave background. It is the best black body radiation spectrum known at very low temperature.

2)photons radiated by stars in galaxies. The approximate black body spectrum of stars is in the thousands of kelvin, similar to our sun, the yellow curve here.


*transient radiations from mergers of stars to neutron stars, black holes etc  making gamma ray bursts.


*Continuous radiation of magnetized plasma in galaxies and around galaxies, due to the expulsion of matter from a star,
So if one had a detector that could detect from very low to very high photon energies, there would be a big bump near zero from the CMB, since all of empty space contains it, and then smaller bumps at higher energy corresponding to 2 , 3, 4 and maybe more cases.
It will not be one black body, nor meaningful to look for one peak.
For example look at this study A GeV-TeV Measurement of the Extragalactic Background Light, EBL

Figure 3.The spectral intensity of the EBL from UV to far-IR. The constraints from this work are shown as a 68% confidence region and median (blue).  A corresponding region from (The Fermi-LAT Collaboration2018) that relies on GeV data only is shown in orange.  Various measurements in the literature are shown in gray:  direct measurements (open symbols), integrated galaxy counts (filled symbols).


The CMB is not included in the measurement, as it needs a different technique to measure its very high wavelength content.
A combined plot of all possible measurements needs a specialist in the subject.
