Predicting spatial curvature in globally CPT-symmetric universes
PhD student Wei-Ning Deng from the group recently presented her latest work at the Cambridge-LMU cosmology meeting. The meeting, part of the strategic partnership between the cosmology groups at Cambridge and LMU Munich, brought together experts in theory, simulation and observation of the large-scale structure of the universe. Attendees included researchers from both Cambridge and LMU, with the aim to deepen ties between the two cosmology communities and stimulate discussion about the future of the field. With a mixture of short talks and longer presentations, the meeting provided an opportunity to discuss a variety of cosmological topics.
Wei-Ning’s talk focused on the results of her recent paper 2407.18225, which explores the implications of global $CPT$ symmetry on the spatial curvature of the universe.
The $CPT$ symmetric universe model, as originally proposed by Boyle and Turok 1803.08928, posits that the universe began in a $CPT$-symmetric state at the Big Bang. This model elegantly addresses several outstanding problems in both cosmology and particle physics, without the need to introduce new physics.
Separately, Lasenby and collaborators 2104.02521 have explored the consequences of imposing symmetry conditions at the end of the universe, on a hypersurface known as the future conformal boundary. They found that these boundary conditions impose constraints on the allowed modes of cosmological perturbations, which could lead to observable effects on the Cosmic Microwave Background (CMB).
This new work combines these two approaches, extending Lasenby’s future conformal boundary framework to include spatial curvature and extending the $CPT$-symmetric universe of Boyle and Turok to include future boundary conditions. The research finds that requiring the universe to be both $CPT$-symmetric and possess a future conformal boundary places tight constraints on the allowed spatial curvature of the universe.
In a closed universe, spatial compactness requires that cosmological perturbations can only exist with specific wavelengths, corresponding to integer wave vectors. However, the future conformal boundary imposes a different set of constraints, which are generally incompatible with integer wave vectors. This conflict can only be resolved if the curvature of the universe takes on specific discrete values.
Using their simplified universe model, which includes only dark energy, radiation and curvature, Wei-Ning and her supervisor Will Handley found that the curvature density is constrained to be $\Omega_K \in {-0.014, -0.009, -0.003, \ldots}$. Remarkably, these values are consistent with the latest observations from the Planck satellite 1807.06209, which suggest that the universe is either flat or slightly closed.
This work provides a tantalising hint that global $CPT$ symmetry and future conformal boundary conditions could play a crucial role in shaping the large-scale structure of our universe. Future work will explore the implications of this model in greater detail, by incorporating matter into the perturbation analysis and generating predictions for the CMB power spectrum.