The Big Bang, CPT, and neutrino dark matter (1803.08930v2)

Abstract: We investigate the idea that the universe before the Big Bang is the $CPT$ reflection of the universe after the bang, both classically and quantum mechanically, so that the universe does {\it not} spontaneously violate $CPT$. We show how $CPT$ symmetry selects a preferred vacuum state for quantum fields on a $CPT$-invariant cosmological background spacetime. The universe before the bang and the universe after the bang may be viewed as a universe/anti-universe pair, emerging directly into the hot, radiation-dominated era we observe in our past. This, in turn, leads to a remarkably economical explanation of the cosmological dark matter. With no additional fields beyond Einstein gravity and the standard model of particle physics (including right-handed neutrinos), a $\mathbb{Z}_{2}$ symmetry stabilizes one of the right-handed neutrinos. We calculate its abundance in detail and show that, in order to match the observed dark matter density, its mass must be $4.8\times10^{8}~{\rm GeV}$. We obtain several further predictions, including: (i) that the three light neutrinos are majorana; (ii) that one of these is exactly massless; and (iii) that, in the absence of an epoch of cosmic inflation, there should be no primordial, long-wavelength gravitational waves. We also briefly discuss the natural origin of the matter-antimatter asymmetry within this picture and possibilities for explaining the cosmological perturbations.

• The paper proposes that a CPT-invariant universe naturally leads to the selection of a right-handed neutrino, with an estimated mass of 4.8×10^8 GeV, as a viable dark matter candidate.
• The study extends CPT symmetry to curved FRW spacetimes using canonical quantization, providing a framework that aligns with the observed absence of long-wavelength gravitational waves.
• The paper further predicts that two light neutrinos are Majorana particles—with one remaining massless—and offers a mechanism for explaining the matter-antimatter asymmetry via thermal leptogenesis.

CPT-Symmetric Universe and Neutrino Dark Matter: Theoretical Considerations

The paper "The Big Bang, CPT, and Neutrino Dark Matter" by Latham Boyle, Kieran Finn, and Neil Turok presents an exploration of the implications that a CPT-invariant universe would have on our understanding of cosmology, particularly regarding the nature of dark matter and the initial conditions of the universe. Grounded in theoretical physics, the authors propose an intriguing framework wherein the universe before the Big Bang is conceived as a CPT reflection of the universe post-Big Bang. This symmetry opens pathways to significant cosmological predictions, including the viability of neutrinos as dark matter candidates.

Central Thesis and Methodology

At the heart of this paper is CPT symmetry—a fundamental symmetry of the laws of physics, incorporating charge conjugation (C), parity transformation (P), and time reversal (T). The authors suggest that under a CPT-invariant framework, the universe may inherently possess a symmetric structure across the temporal divide of the Big Bang, leading to a scenario where the universe and an "anti-universe" emerge simultaneously.

The methodology involves extending the analysis of CPT symmetry to curved spacetimes, specifically Friedmann-Robertson-Walker (FRW) models, thereby generalizing the standard Minkowski treatment. Through a canonical quantization approach, the authors identify a CPT-invariant vacuum state, which, they propose, naturally aligns with the large-scale structure of the universe without additional field assumptions.

Predictions and Implications

1. Neutrino as Dark Matter: The paper posits that one of the right-handed neutrinos, if stabilized by a discrete Z2 symmetry, serves as a compelling dark matter candidate. This requires no exotic particles beyond those already posited by extensions of the Standard Model. The mass of the dark matter neutrino is predicted to be 4.8 × 10^8 GeV, which fits the observed dark matter density.
2. Absence of Long-Wavelength Gravitational Waves: The framework predicts the absence of primordial, long-wavelength gravitational waves, a result that aligns with the lack of such detections in current astrophysical observations.
3. Majorana Nature of Light Neutrinos: Another significant prediction is that two of the light neutrinos are Majorana particles, with one being massless—an assertion that can be tested with upcoming neutrino experiments.
4. Matter-Antimatter Asymmetry: The CPT framework offers a natural explanation for the matter-antimatter asymmetry in the universe. It suggests that the decays of heavy neutrinos early in the universe could establish the observed imbalance via thermal leptogenesis.

Theoretical and Practical Import

The paper's implications are profound, challenging traditional views of cosmological inflation and primordial conditions. By offering a symmetric origin of the universe, it bypasses several issues inherent to inflationary models, such as the fine-tuning problems and the nature of the inflationary potential. Practically, these insights motivate searches focused on neutrino properties and emphasize gravitational observations to falsify or verify the absence of long-wavelength gravitational waves.

Future Directions

The work sets the stage for further exploration of cosmological phenomena through the lens of fundamental symmetries. It provides a framework that bridges particle physics and cosmology, with potential directions including a detailed paper of how neutrino interactions might deviate from standard cosmological predictions and how these deviations can be observed. Additionally, this line of inquiry invites further mathematical development to rigorously test the implications of a two-sheeted universe model.

In summary, this paper offers a compelling picture of the universe's origins and the nature of dark matter through the robust application of CPT symmetry. Its blending of cosmological and particle physics insights illuminates promising avenues for discovery, making it a valuable contribution to theoretical physics.