Is the number of energetic CMB Photons (produced due to Sunyaev-Zel'dovich effect) abundant in the whole universe now ?

The Sunyaev–Zel'dovich effect is the distortion of the cosmic microwave background radiation (CMB) by high energy electrons in galaxy clusters, in which the low energy CMB photons receive an average energy boost during collision with the high energy cluster electrons.

Observed distortions of the cosmic microwave background spectrum are used to detect the density perturbations of the universe. Using the Sunyaev–Zel'dovich effect, dense clusters of galaxies have been observed.

So is this effect still in occurence? Is the universe filled abundantly by these photons or they are in a very small amount ?


No. This is because the effect of the Sunyaev-Zel'dovich Effect is very weak in general. A good point to note is that Galaxy cluster formation is a relatively 'recent' event. With most of them occurring around a redshift of $z<1$. So much that if we manage to discover a high redshift $z>3$ galaxy cluster, it would imply a different model of the Epoch of Large Scale Structure Formation

The average number of scatterings that occur when a given photon passes through a cluster is $1$ or less. This is because the average value of the Comptonization Parameter $y\approx 10^{-4}$.

\begin{equation} y = \int \frac{k_B T_e}{mc^2} \sigma_T n_e c dt \end{equation} Where the terms $\tau=\sigma_T n_e c$ describes the optical depth.

The Thermal SZ Effect, would be in principle always be in occurrence as long as there are regions of hot plasma/electrons. Additionally, there is also the non-Thermal SZ Effect due to relativistic electrons, kinematic SZ Effect due to the large scale relative motion of the cluster to the CMB photons.

Another interesting point to note about galaxy clusters, the principle agent responsible for the SZ Effect, is that it is predominantly comprised of webs of dark matter and the Intracluster Medium (hot plasma) only comprise about 9% of its mass, further highlighting the extent of the effects.


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