Arrows of time and the beginning of the universe

Abstract

I examine two cosmological scenarios in which the thermodynamic arrow of time points in opposite directions in the asymptotic past and future. The first scenario, suggested by Aguirre and Gratton, assumes that the two asymptotic regions are separated by a de Sitter-like bounce, with low-entropy boundary conditions imposed at the bounce. Such boundary conditions naturally arise from quantum cosmology with Hartle-Hawking wave function of the universe. The bounce hypersurface breaks de Sitter invariance and represents the beginning of the universe in this model. The second scenario, proposed by Carroll and Chen, assumes some generic initial conditions on an infinite spacelike Cauchy surface. They argue that the resulting spacetime will be non-singular, apart from black holes that could be formed as the initial data is evolved, and will exhibit eternal inflation in both time directions. Here I show, assuming the null convergence condition, that the Cauchy surface in a non-singular (apart from black holes) universe with two asymptotically inflating regions must necessarily be compact. I also argue that the size of the universe at the bounce between the two asymptotic regions cannot much exceed the de Sitter horizon. The spacetime structure is then very similar to that in the Aguirre-Gratton scenario and does require special boundary conditions at the bounce. If cosmological singularities are allowed, then an infinite Cauchy surface with `random' initial data will generally produce inflating regions in both time directions. These regions, however, will be surrounded by singularities and will have singularities in their past or future.

References added; some minor fine-tuning of the text

References in corpus (6)

• Properties of the scale factor measure
• Eternal inflation, bubble collisions, and the persistence of memory
• Boltzmann babies in the proper time measure
• Observer dependence of bubble nucleation and Schwinger pair production
• Rest frame of bubble nucleation
• No-Bang Quantum State of the Cosmos

Cited by in corpus (17)

• Conceptual Problems in Quantum Gravity and Quantum Cosmology
• Emergent scenario in the Einstein-Cartan theory
• Emergent universe in spatially flat cosmological model
• On the initial singularity and extendibility of flat quasi-de Sitter spacetimes
• Cosmological singularity theorems and black holes
• Stability of Einstein static universe in gravity theory with a non-minimal derivative coupling
• Understanding Gravitational Entropy of Black Holes: A New Proposal via Curvature Invariants
• Thermodynamics of Shearing Massless Scalar Field Spacetimes is Inconsistent With the Weyl Curvature Hypothesis
• Hysteresis in the Sky
• Emergent scenario in mimetic gravity
• CPTM symmetry, closed time paths and cosmological constant problem in the formalism of extended manifold
• Analytical approximations for primordial power spectra in a spatially closed emergent universe
• Implications of the singularity theorem for the size of a nonsingular universe
• Possible relationship between initial conditions for inflation and past geodesic incompleteness of the inflationary spacetime
• The nucleation of false vacuum bubbles with compact geometries
• Arrows of time in bouncing cosmologies
• On the Carroll-Chen Model