How does plasm affect the speed of light? 99% of the universe is made of plasma according to Imperial College London. I understand that the plasma is made of charged particles and photons are easily absorbed and re-emit photons. So how does the plasma affect the speed of light? 
 A: It's not that simple. Plasma affects things, but the effect on the speed of light can be ignored to some extent.
The intergalactic plasma density average is about 1 particle per cubic meter, and most of the cosmic microwave radiation CMB has come through space with no interaction with it. The last time the CMB was scattered was at the surface of last scattering, when the electrons and protons recombined Into hydrogen atoms and made the universe mostly transparent to photons,about 380,000 years after the Big Bang. All we have seen of the universe so far is from after that. 
The main effect on those photons has been due to cosmological expansion and thus the redshift of about a factor of 1000. The speed has been c, locally. For the most part the major effect on cosmological distance that changes that is from gravitational lensing, with the Wolfe-Sachs effect. 
The astrophysical effects from plasma interactions have been relevant but different, and mostly from regions or areas where the plasma density is higher, such as near stars, in their coronas or atmospheres, and in hot interstellar or galactic regions where collisions or explosions have heated up the gases. In those case it is important, and not a simple single effect. See the different effects summarized at 
https://en.m.wikipedia.org/wiki/Plasma_(physics), and much more detailed at 
http://www.sp.ph.imperial.ac.uk/~sjs/APmaster.pdf as well as 
some in https://en.m.wikipedia.org/wiki/Astrophysical_plasma. 
And how it can have some effect in disturbing slightly the CMB spectrum, at https://en.m.wikipedia.org/wiki/Sunyaev–Zel'dovich_effect
But it does have effects in determining luminosities from galactic clusters and nebula at https://arxiv.org/abs/1605.08333, and can have a small effect in the determinations of the cosmic distance scale. Also redshift relationships such as in https://arxiv.org/abs/1404.0870. 
So, mostly the issue has been how does the plasma absorption of some of the EM radiation or how much does it emit so one can determine distances. I.e., luminosities, spectra of absorption or emission, thus some density or distance measurements using those luminosities or spectra. Since those bodies of plasma overall are a small part of the distances travelled the speed of light can be taken to be c. 
The detailed research continues, but it's just one aspect of the astrophysics and cosmology of the universe. 
