The concept, as explained in wikipedia is more or less clear to me. But the page is not very detailed. How does CCC works?
Also in another question, someone answered
Keep in mind that CCC is a dead theory. It became clear by 2010 that it was not viable because it made predictions about particle physics that were not consistent with what we know about particle physics.
Is this true? What are those predictions?
For the CCC, Roger Penrose considered the physical metric $\hat{g}_{ab}$ in a dying universe by thermal death, and the metric $\check{g}_{ab}$ of a nascent universe with a hot Big Bang. After some physical and mathematical considerations, he appreciated that a continous mathematical transition can be achieved between the end of the first universe and the beginning of the second universe, just considering some kind of conformal invariance (this depends on the dying universe ending up full of massless particles and that the Higgs mechanism is initially disconnected in the Big Bang of the nascent universe). Under these conditions, an abstact conforming metric can be defined as that:
$\hat{g}_{ab} = \hat{\Omega} g_{ab}$, and $\check{g}_{ab} = \check{\Omega} g_{ab}$
Where $\hat{\Omega}$ and $\check{\Omega}$ are conformal factors that multiply the abstract conformal metric $g_{ab}$ to give the physical metrics of the dying universe and the nascent universe. These tensors satisfy Einstein's field equations:
$\hat{R}_{ab} - {1\over 2}\hat{R} \hat{g}_{ab} + \Lambda \hat{g}_{ab} = {8 \pi \text{G} \over \text{c}^4} \hat{T}_{ab}$,
$\check{R}_{ab} - {1\over 2}\check{R} \check{g}_{ab} + \Lambda \check{g}_{ab} = {8 \pi \text{G} \over \text{c}^4} \check{T}_{ab}$
were $\hat{T}_{ab}$ and $\check{T}_{ab}$ are the material content of the ending universe and the beginning universe. In addition, we have that $\hat{T}_a^a = 0$ but $\check{T}_a^a = \mu \neq 0$ and for this reason:
$\hat{R} = 4\Lambda$, but $\check{R} = 4\Lambda + {8 \pi \text{G} \over \text{c}^4} \mu$
The key point is that the conforming factors are given in terms of a new $\omega_g$ "ghost field" that satisfies the equation:
$\left(\square+ \frac{R}{6}\right)\omega_g = \frac{2}{3}\Lambda \omega_g$
and $\hat{\Omega} = \omega_g$ and $\check{\Omega} = -\omega_g^{-1}$ (because $\hat{\Omega}\to\infty$ in the ending universe and $\check{\Omega}\to 0$ in the beginning universe). In this way, the Big Bang is interpreted as an effect the conformal metric transition associated with a drastic change of scale produced by the ghost field $\omega_g$. The virtue of this proposal is that incorporates the Weyl Curvature Hypothesis and explains why our universe began with such an anomalously small entropy state.
Interestingly, the universes or "aeons" would succeed each other in an infinite succession of death and rebirth, in which almost no information from the previous aeon would pass to the next one (our universe initiated in the big bang 13750 million years ago would be only one of those aeons).
I think the primary reason for the end of CCC theory is that the possibility of cycles taking place is by consensus of most cosmologists that CCC is no longer considered feasible since dark energy prevents any cycles from occurring. Of course, some new hypothetically possible future discoveries may change the current strong evidence about dark energy.
Regarding particle physics, I found the following.
https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology#Physical_implications.
This seems to also be another reasonable reason for ending CCC possibilities.
