Sir Roger Penrose is an
Oxford
University
superstar-theorist whose ideas have spanned an amazing breadth of territory,
ranging from geometrical tiling to the nature of human consciousness to the
structure of space-time.At age 87
he is still going strong, and for thel last decade has been promoting and
investigating a radical new theory, Conformal Cyclic Cosmology (or CCC), which
is based on general relativity and which concerns itself with the origins of our
universe and its predecessors.I
find CCC to be a very interesting take on cosmology, but I'm afraid that it
has some fatal flaws.

Basically, Penrose observes that during the
evolution of an open Friedmann-Lemaître-Robertson-Walker universe like ours,
starting from the initial singularity of the Big Bang and ending with infinite
expansion to timelike infinity, there are two distinct eras in which the
universe lacks any way of "building a clock" to measure time, and so time
itself becomes meaningless.One of
these eras is the initial singularity of the early universe, in which time is
infinitely dilated by gravity. The
other is the exponential expansion to toward timelike infinity of the very late
universe, the era after all protons have decayed to leptons, all black holes
have evaporated into Hawking radiation, and all that remain in the expanding
universal blackness are massless photons and gravitational radiation travelling
at the speed of light.Massless
wave-particles like electromagnetic and gravitational waves do not have "clocks" because they travel at light speed, so that in their rest fames
time is completely halted.As we say
in physics, if you travel at the speed of light, everything happens at once.

Because of this similarity in the "clocklessness" of these two eras, general relativity theorist Paul Tod
pointed out in 2003 that the initial singularity of the Big Bang can be
conformably mapped into the very late stages of infinite expansion populated
only by massless particles.In some
sense the two eras, even though vastly different in scale, represent the same
timeless conditions.Penrose has
extended Tod's idea by taking the conceptual leap of asserting that this
conformal mapping is not just an interesting similarity.Rather, it is a real and actual
transition.This allows him to
hypothesize the existence of an infinite "daisy chain" of universes, the
very late stage of each predecessor universe transitioning into the initial Big
Bang stage of the next universe in the chain.

It's well known in cosmology that there
is a severe entropy problem with all recycling universe models.This is because the 2^{nd} Law of Thermodynamics requires that
the entropy of the overall system must always progressively increase with time.That implies that every successive universe in such a cyclic chain must
have more entropy and be more disordered than its predecessors.

In the early Big Bang stage of our universe
the gravitational degrees of freedom were very small and restricted, leading to
great uniformity in all regions and very small initial entropy.Penrose argues that the enormous rescaling compression that occurs in the
conformal remapping across the boundary from late infinite expansion to initial
Big Bang singularity resets the entropy of the emerging universe to a very small
value and also accounts for the remarkable uniformity of the early universe.Interestingly, this scenario eliminates the need for assuming an
inflationary phase in the early universe, as is hypothesized by the current LCDM Standard Model of cosmology to account for that uniformity.In other words, the conformal transition of CCC resets the entropy to a
very low value.

Penrose assumes that the massless
speed-of-light "clockless" particles of each previous universe cycle are
carried over to the next cycle, while any massive particles (those with internal
clocks) are removed by decay, particle-antiparticle annihilation, or capture by
black holes, so that they do not participate in the transition to the next
cycle.The transferred
massless particles (photons, gravitons) are integer-spin bosons, while the
non-transferred particles with mass (electrons, neutrinos) are fractional-spin
fermions.I see some serious
problems with Penrose's assumption of the vanishing fermions, which will be
discussed below.

The big problem with most attempts to construct any general theory of
cosmology, particularly one as extrapolative as CCC, is that there are typically
no experimental or observational tests that can be used to check on validity.Rather remarkably, this is not
the case for CCC.One CCC test is
that there should be no great outburst of gravitational radiation, as the
standard-model inflation scenario in the early Big Bang would produce.The BICEP2 experiment in
Antarctica
is presently searching for the polarization signature of such gravitational
radiation from inflation but, consistent with CCC, has not observed it.In a sense, CCC also includes inflation, but its inflation occurs late in
the previous cycle of the universe, before the conformal remapping occurs and
before the first stages of the Big Bang, and thus it leaves no gravitational
wave signature.

Further, in the late stages of the hyper-expanded previous universe, the
very massive black holes from the centers of dead galaxies would collide, making
gravitational radiation, and ultimately would evaporate into Hawking-radiation
photons, producing clumps of leftover photons and gravitational waves.The resulting clumps would be carried into the next cycle of the universe
chain, producing a clumping that Penrose calls "Hawking points" that cause
disturbances in the cosmic microwave radiation.These Hawking points are supposed to appear in the temperature variations
of the cosmic microwave background as a pattern of concentric circles.

Penrose and his colleagues claim that their analysis of WMAP and Planck
data has found such concentric circles in with significance of 6-sigma or more,
as compared to simulations based on standard LCDM
cosmology (cold dark matter with cosmological constant L).However, several other groups have attempted to reproduce this analysis
and have found no statistically significant indication of the Hawking-point
circles.The difference seems to
revolve around the way in which the individual groups did the LCDM
simulations.In a recent
publication, Penrose and collaborators further claim that the
polarization-dependent B-mode observations of the BICEP2 experiment provides an
additional indication of Hawking points in the cosmic microwave background.The controversy about the presence or absence of Hawking points in the
cosmic microwave background radiation continues, and we will have to wait for
some time to see if the physics community accepts Penrose's analysis as
supporting his CCC description of the universe.

To make CCC work, Penrose needs to introduce some specific assumptions
about the dark matter in the universe: what it is and how it dissipates in the
late stages.He assumes that our
universe's dark matter is formed of previously unknown massive particles that
he calls erebons, which are purely
gravitational, have no strong, weak, or electromagnetic interactions, have a
rest mass on the order of a Planck mass (21.8 mg =
1.22×10^{28}
eV), a lifetime of around 10^{11} years, and ultimately decay into
Planck-energy gravitational waves.Penrose depends on these hypothetical dark matter leftovers to provide
just the right amount of temperature variation, as observed in the cosmic
microwave background.

There are problems with the CCC scenario.In order for the late phase in which the universe undergoes infinite
expansion to timelike infinity to match the "clocklessness" of the initial
Big Bang singularity so that one can be conformably mapped into the other, the
late-stage universe must be completely empty of all massive particles.In particular, one must assume that all protons eventually decay into
leptons. Further, Penrose's
late-stage universe must somehow have also eliminated all of the electrons,
positrons, neutrinos, anti-neutrinos, and dark matter particles that were
previously present in great numbers.

Neutrinos are among the most plentiful
particles in the universe because there was a weak-interaction flash of
neutrinos created in the early Big Bang in analogy with the flash that created
the cosmic microwave background.These
very low energy cosmic background neutrinos are everywhere around us in great
numbers, and there is no established mechanism for getting rid of them as the
universe ages.Penrose proposes to
deal with them by hypothesizing a fourth species of neutrinos that is massless.He requires that the three species of massive neutrinos should decay into
the massless neutrino variety as the late-stage universe ages to timelike
infinity.

The large population of electrons and
positrons in our present universe represents a more serious problem for
Penrose's CCC.Along the path to
timelike infinity, many of these electrons and positrons will pair off and
annihilate into photons, but as Penrose points out, many will be trapped at or
near the event horizons of black holes.Further,
the Hawking evaporation of black holes with a net electrical charge will produce
even more electrons or positrons.One
cannot get away with hypothesizing that over the long haul all the electrons and
positrons decay into some hypothetical massless particles because such particles
would have an electric charge.There
are no known stable massless charged particles.They cannot exist because an electric charge moving through space at the
speed of light would radiate away all its energy into Cherenkov radiation.

Penrose has this to say about the electron
problem: "There are various possible
ways out of this, none of which is part of conventional particle physics.One possibility is that electric charge is not exactly conserved, so that
within the span of eternity electric charge would eventually disappear.A much more satisfying possibility, from
my own perspective, is that the electron's mass would eventually decay away
– and again there is all eternity for this to happen, so the possibility may
not be too outrageous to contemplate."

I find Penrose's attempts to wriggle out of the electron problem
curious and unacceptable.Most
physicists would certainly choose to retain electric charge conservation and to
dump Penrose's CCC model, rather than the other way around.Further, the suggested fix to CCC of decaying away the electron's mass
does not solve the charge problem; it only converts electrons to massless
light-speed charged particles, which as noted above cannot exist.

In summary, Sir Roger Penrose's Conformal
Cyclic Cosmology is certainly provocative, offers much food for thought, and
solves some of the problems of standard cosmology, e.g., inflation and dark
matter, in interesting ways.It may
or may not be supported by the observation of concentric circular patterns in
the temperature variations of the cosmic microwave background.However, it has problems of its own, e.g., the electron problem, and
these make it very difficult for me to take CCC seriously as a model of the
universe.

References:

Conformal
Cyclic Cosmology:

Roger
Penrose, "Before the big bang: An outrageous new perspective and its
implications for particle physics", Proceedings
of EPAC 2006,
Edinburgh
,
Scotland
, 2759-2767 (June 2006); available at http://accelconf.web.cern.ch/accelconf/e06/PAPERS/THESPA01.PDF

Concentric
Circles in CMB:

V.
G. Gurzadyan and R. Penrose "Concentric circles in WMAP data may provide
evidence of violent pre-Big-Bang activity", (2010-11-16);
arXiv:1011.37061486 [astro-ph.CO].

V.
G. Gurzadyan and R. Penrose "More on the low variance circles in CMB
sky", (2010-12-07), arXiv:1012.1486 [astro-ph.CO].

I.
K. Wehus and H. K. Eriksen, "A search for concentric circles in the 7-year
WMAP temperature sky maps". The Astrophysical Journal 733 (2), L29 (2010); arXiv:1012.1268 [astro-ph.CO].

A.
Moss, D. Scott and J.P. Zibin, "No evidence for anomalously low variance
circles on the sky". Journal of Cosmology and Astroparticle Physics, 2011
(4), 033 (2010); arXiv:1012.1305 [astro-ph.CO].

A.
Hajian "Are There Echoes From The Pre-Big Bang Universe? A Search for Low
Variance Circles in the CMB Sky". The Astrophysical Journal. 740
(2), 52 (2010). arXiv:1012.1656 [astro-ph.CO].

A.
DeAbreu, et al, "Searching for
concentric low variance circles in the cosmic microwave background",
Journal of Cosmology and Astroparticle Physics 2015 (12), 031 (2015); arXiv:1508.05158 [astro-ph.CO].

John Cramer's book on
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