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
Collections this item is in
Note
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Partial requirement for: Ph.D., Arizona State University, 2024
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Field of study: Physics