  Circles of low-variance and Hawking points in the Cosmic Microwave Background
(CMB), resulting from black hole mergers and black hole evaporation,
respectively, in a previous cycle of the universe, have been predicted as
possible evidence for the Conformal Cyclic Cosmology model (CCC) introduced by
R. Penrose. We present a high-resolution search for such low-variance circles
in the Planck and WMAP CMB data, and introduce HawkingNet, our machine learning
open-source software based on a ResNet18 algorithm, to search for Hawking
points in the CMB. We find that spots consisting of a few unusually bright
(high-temperature) or dark (low-temperature) pixels, erroneously lead to
regions with many low-variance circles, and consequently sets of
near-concentric low-variance circles, when applying the search criteria used in
previous work [V.G. Gurzadyan, R. Penrose]. After removing those spots from the
data, no statistically significant low-variance circles can be found.
Concerning Hawking points, also no statistically significant evidence is found
when using a Gaussian temperature amplitude model over 1 degree opening angle
and after accounting for spots of unusual brightness. That the unusual spots in
the data are themselves remnants of Hawking points is not supported by
low-variance and/or low-temperature circles around them. The absence of such
statistically-significant distinct features in the currently available CMB data
does not disprove the CCC model, but implies that higher resolution CMB data
and/or refined CCC based predictions are needed to pursue the search for CCC
signatures further
