Penrose's basic construction[2] is to connect a countable sequence of open Friedmann–Lemaître–Robertson–Walker metric (FLRW) spacetimes, each representing a Big Bang followed by an infinite future expansion.
Penrose suggests this extra gravitational radiation may be enough to explain the observed cosmic acceleration without appeal to a dark energy field.
In 2010, Penrose and Vahe Gurzadyan published a preprint of a paper claiming that observations of the cosmic microwave background (CMB) made by the Wilkinson Microwave Anisotropy Probe (WMAP) and the BOOMERanG experiment contained an excess of concentric circles compared to simulations based on the standard Lambda-CDM model of cosmology, quoting a 6-sigma significance of the result.
[12] In a paper published on August 6, 2018, authors Daniel An, Krzysztof Antoni Meissner, Pawel Nurowski, and Penrose presented a continued analysis of the CMB data as it seemed to them that “…anomalous points provide an important new input to cosmology, irrespective of the validity of CCC.” They also suggested that those anomalies could be "Hawking points", remnant signals from the "Hawking evaporation of supermassive black holes in the aeon prior to ours".
[13] A 2020 analysis found that the ostensibly anomalous "Hawking points" were actually consistent with the standard inflationary picture once the look-elsewhere effect is taken into account, therefore arguing that they could not be used as evidence for CCC.
[14] In 2022, another group published [15] a preprint on CMB anomalies, consisting of a single or a few bright pixels, erroneously lead to regions with many low-variance circles when applying the search criteria used in previous works.
Concerning Hawking points, they also state no statistically significant evidence when using a Gaussian temperature amplitude model over 1 degree opening angle and after accounting for CMB anomalies.
In 2015, Gurzadyan and Penrose also discussed the Fermi paradox, the apparent contradiction between the lack of evidence but high probability estimates for the existence of extraterrestrial civilizations.