Describe the collapse phase of Penrose cyclic universe, Conformal cyclic cosmology I read about Penrose's idea of Conformal cyclic cosmology, he suggested that mostly everything at the end of the universe is black holes and empty space and that eventually the black holes evaporate at which time there is only light going through the universe.
Then why does the universe collapse? What does collapse mean in this circumstance? I wish to understand in a realistic physical sense of what is happening in his model at this time.
 A: There is no collapse. The black holes evaporate, the particles get indefinitely diluted, space expands indefinitely, and time continues to $t=\infty$. Then the state is equivalent to the big bang state, if one rescales the whole thing conformally. 
This is probably not a model in "a realistic physical sense" for most people.
A: The universe, in Penrose's view, doesn't collapse all at once, or all in one place:  Its material components evaporate (very slowly), turning into Hawking radiation, over an enormous duration of time.  Evaporation, which involves expansion of the space between particles and often results from heating, is different from collapse:  Collapse actually resembles condensation, which generally results from cooling.
For instance, large stars collapse when their consumption of their nuclear fuel leaves them without radiation pressure sufficient to resist their own gravity. As at least half of all stars are generally considered to be in binary pairs, their collapse into black holes remains evident through the elliptical orbit still followed by their surviving partner.
The completion of the slow collapse or absorption of stars into black holes, and of the evaporation of black holes into Hawking radiation, would leave a universe consisting entirely of radiation, which would comprise the Big Bang of a subsequent temporal iteration of that universe, presumably on a vastly larger spatial scale. However, as the formation of such a "Big Bang" would be completed only when all matter would have turned into radiation, the duration of each iteration would remain unknown, as the formation of every form of natural or artificial clock would require fermions (matter particles), and there would have been an interval during which none would exist.
The long and short of it is, that the "collapse phase" of Penrose's single universe would be divided between many collapses of stars into black holes, just as its phase of expansion would be experienced locally as being divided between the absorption of smaller black holes by larger ones and an overall evaporation of the mass of all black holes into radiation:  To some extent, these processes might be happening on vastly different scales, as the formation of a very large black hole by the gravitational collapse of dust in Sagittarius A has been witnessed (well after the fact) by us, even while the large proportion of empty space within molecular structures has remained a generally accepted fact.
A factor in Penrose's receipt of a 2020 Nobel Prize in Physics may have been his publication, earlier that year, of the final version of a paper (written in collaboration with such major physicists as An and Meissner) whose preprints are freely visible at
https://arxiv.org/abs/1808.01740. That paper identified "spots of anomalously raised temperature" in the Cosmic Microwave Background radiation, which the paper had identified as Hawking radiation.
Prior to that paper, Penrose's Cyclic Conformal Cosmology (written in 2010) had been very controversial, because, although the evaporation of other subatomic particles had been observed (often in stages, through their disintegration into particles whose effects were less easily observed), such evaporation or disintegration of protons had NOT been observed (and still has not been observed), in spite of many years of observation of them deep within an Asian mine, where the confusing influence of cosmic rays is less likely to affect it.
