Description
In this opus, I challenge the claim that inflationary spacetimes must be past geodesi-cally incomplete. To do this, I utilize the warped product formalism of Bishop and
O’Neill and build upon the venerable Friedmann Robertson Walker (FRW) space-
time formalism to the Generalized Friedmann Robertson Walker (GFRW) spacetime
formalism, where the achronal spacelike sections can be any geodesically complete
Riemannian manifold (Σ, gΣ ). I then solve the GFRW geodesic equation in generality
as a functional of the scale factor f , and derive a main theorem, which characterizes
the geodesic completeness in GFRW spacetimes. After offering a definition of infla-
tion which enumerates the topological requirements which permit a local foliation of
a scale factor, I discuss a cohort of geodesically complete inflationary GFRWs which
have averaged expansion quantity Havg > 0, proving that classical counter-examples
to the theorem of Borde, Guth, and Vilenkin do exist. I conclude by introducing
conjectures concerning the relationship between geodesic completeness and inflation:
in particular, I speculate that if a spacetime is geodesically complete and non-trivial,
it must inflate!
Details
Title
- Geodesic Completeness of Inflationary Spacetimes
Contributors
- Lesnefsky, Joseph Edward (Author)
- Easson, Damien A (Thesis advisor)
- Davies, Paul C (Thesis advisor)
- Parikh, Maulik (Committee member)
- Kotschwar, Brett (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2024
Subjects
Resource Type
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Note
- Partial requirement for: Ph.D., Arizona State University, 2024
- Field of study: Physics