Origin of the arrow of time of the Universe
PT-CERN Call 2022/2
FCUL (Universidade de Lisboa)
IA - Instituto de Astrofísica e Ciências do Espaço
The Energetic Causal Set  (ECS) model and it's quantum counterpart  were pioneered by one of the current supervisors, Marina Cortês, along with Lee Smolin, in the work which won first place in the inaugural Buchalter Cosmology Prize (2014). They introduced a model for the development of space-time that is intrinsically time-asymmetric throughout the emergence of space-time. The model was however implemented in only one spatial dimension. The current masters project  of the student candidate for this project, Vasco Gil Gomes, under the supervision of Cortês and Liddle, extended this to two spatial dimensions successfully replicating the 1d+1 results even though there were no a priori reasons to believe such an extension would be possible. The ECS framework allows the emergence of space-time from irreversible time dynamics, and simulations on 1d+1 ECS models have been shown to lead to emergence of time reversibility . In ECS models new events are created through particle collisions with reversibility tied to emergence of dynamical limit cycles . To ensure collisions in 2d+1 dimensions particles have been assigned a 2d finite cross-section measure. New collisions (events) are selected via a rule that seeks to extremize the distinctions between causal past sets of events. The extension to multi-dimensions which was the largest obstacle in the development of ECS for the past decade. I was able to use algorithmic information theory to solve the numerical challenges successfully replicating the 1d+1 classical results. In this Ph.D. project, I will first extend my ECS simulations to 3+1D, and carry out an extensive parameter-space investigation of both the 2+1D and 3+1D cases, statistically quantifying the transition to emergent time reversibility. The classical version will then be linked to the Hamiltonian formulation of time-asymmetric gravity, while a quantum completion will be studied using the two state vector formalism.