Conformal cyclic cosmology (CCC) joins the remote future of each aeon of the universe conformally to the big bang of the next, and requires that the enormous entropy accumulated during an aeon — dominated by supermassive black holes — be effectively reset for the next aeon to begin in a low-entropy state, while black-hole evaporation in the previous aeon should leave localized 'Hawking point' temperature anomalies in the cosmic microwave background (CMB) as a possible observational record. A 2020 loop-quantum-gravity (LQG) analysis of this crossover proposed an entropy-reversal mechanism built from an LQG-modified black-hole entropy and the generalized second law (GSL), and explicitly left open: the validation of that mechanism in a fully quantum-gravitational setting and its consistency with the overall second law; the fate of quantum information across the crossover (information loss versus preservation); and the detailed analysis of Hawking points as observable evidence.

Background

In conformal cyclic cosmology (CCC), proposed by Roger Penrose, the remotely infinite future of an expanding universe is conformally rescaled — the spacetime metric is multiplied by a smooth positive factor, a transformation that leaves light cones and causal structure unchanged — and identified with the big bang of a successor aeon, the two being joined across a spacelike 'crossover' 3-surface; each such universe epoch is called an aeon. The construction rests on Penrose's Weyl curvature hypothesis: the (conformally invariant) Weyl part of the spacetime curvature vanishes at the initial state, so gravitational degrees of freedom are unexcited there, which is taken to encode the low gravitational entropy of the big bang. A central difficulty is that by the end of an aeon the entropy is dominated by supermassive black holes and is enormous, so something must effectively reset it before the next aeon. Penrose's own resolution assumes that information is irreversibly lost when black holes evaporate, so that the fine-grained degrees of freedom are 'renormalized away' and the next aeon starts afresh. This makes CCC's thermodynamics hinge on the black-hole information problem and on Penrose's broader program of the 'gravitization of quantum mechanics', in which quantum state reduction is a real gravitational process. The generalized second law (GSL) — the statement that the fine-grained generalized entropy (matter entropy plus a quarter of the horizon area) does not decrease for suitable causal horizons, established rigorously by Wall for both future and past horizons — is the main rigorous tool available for such questions, but it applies to null causal horizons, and whether a spacelike crossover surface qualifies is unproven. Independently, loop quantum gravity (LQG) — a canonical quantization of general relativity in which area and volume operators have discrete spectra — and its symmetry-reduced version, loop quantum cosmology (LQC), resolve classical singularities through a critical density at which the Hubble expansion bounces; applied to black holes they suggest that collapse ends in a long-lived white-hole-like remnant (a white hole is the time-reverse of a black hole) whose interior volume grows with mass, a picture advanced by Rovelli and Vidotto as a possible origin of past low entropy. Within this landscape, Shriethar and Rathinam (2020) studied the conformal cyclic evolution of a universe whose late stage is dominated by phantom energy (a component with equation-of-state parameter ω<−1\omega<-1 that classically ends in a 'big rip' singularity, which LQC corrections were used to avoid), proposed to identify the huge final volume of an aeon with the interior volume of an LQG white hole so as to bridge the conformal map to the Planck-scale initial volume of the next aeon, and combined an LQG-modified black-hole entropy with the GSL inequalities for past causal horizons to argue that the fine-grained generalized entropy can decrease across the quantum trapped crossover region — a concrete entropy-reversal mechanism. On the observational side, CCC predicts that the final Hawking evaporation of supermassive black holes in the previous aeon, concentrated near a single conformally represented point, should deposit a raised-temperature spot of a few degrees angular diameter in our aeon's cosmic microwave background (CMB) — a 'Hawking point'. Whether such points are statistically present in the Planck and WMAP data is disputed: An, Meissner, Nurowski and Penrose (2020) claimed anomalous spots at high confidence, Jow and Scott (2020) found the significance collapses after marginalizing over the ring size, and the machine-learning search by Bodnia, Isenbaev, Colburn, Swearngin and Bouwmeester (2024) found no statistically significant evidence once anomalously bright or dark pixels are removed. Markwell and Stevens (2023) further showed that even the classical ingredient — the unique choice of the conformal factor at the crossover — remains unsettled, with the earlier competing proposals they compare found to be mutually inconsistent.

Problem Statement

Give a consistent and testable account of the physics of the crossover between two aeons in conformal cyclic cosmology, determining the entropy, information, and observational aspects of the transition. Concretely:

(i) Entropy reset: determine whether an entropy-reversal (entropy-reset) mechanism at the crossover surface can be formulated consistently in a fully quantum-gravitational treatment. This includes establishing whether the generalized second law, with its causal-horizon hypotheses verified or suitably generalized for the crossover surface, permits the fine-grained generalized entropy to decrease across the transition (as the loop-quantum-gravity-based proposal of Shriethar and Rathinam asserts heuristically), and whether such a decrease is compatible with the ordinary second law over a complete aeon-to-aeon cycle.

(ii) Quantum information across aeons: determine the fate of quantum information at the crossover — whether it is lost, as Penrose's CCC assumes when black holes evaporate, or preserved, for example by unitary evolution with entanglement into inaccessible quantum-gravitational degrees of freedom. Any answer must reconcile with, or refute, the argument of Eckstein (2023) that information loss increases the von Neumann entropy and is therefore incompatible with an entropy-decreasing renormalization at the crossover.

(iii) Observable records: determine whether Hawking points — localized raised-temperature anomalies in the cosmic microwave background predicted to arise from the final Hawking evaporation of supermassive black holes in the previous aeon — can be established as statistically significant observational evidence for CCC, with a connection to the crossover mechanism.

These three questions are open validation questions arising from the single crossover proposal of Shriethar and Rathinam (2020); each is neutral as to a positive or negative outcome. A complete resolution requires all three sub-questions to be addressed, each may be answered affirmatively or negatively, and a refutation of any one part is a valid partial result.

References

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