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On the past-completeness of inflationary spacetimes
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On the past-completeness of inflationary spacetimes
abstract
We discuss the question of whether or not inflationary spacetimes can be geodesically complete in the infinite past. Geodesic completeness is a necessary condition for averting an initial singularity during eternal inflation. It is frequently argued that cosmological models which are expanding sufficiently fast (having average Hubble expansion rate $H_{avg}>0$) must be incomplete in null and timelike past directions. This well-known conjecture relies on specific bounds on the integral of the Hubble parameter over a past-directed timelike or null geodesic. As stated, we show this claim is an open issue. We show that the calculation of $H_{avg}$ yields a continuum of results for a given spacetime predicated upon the underlying topological assumptions. We present an improved definition for $H_{avg}$ and introduce an uncountably infinite cohort of cosmological solutions which are geodesically complete despite having $H_{avg}>0$. We discuss a standardized definition for inflationary spacetimes as well as quantum (semi-classical) cosmological concerns over physically reasonable scale factors.
Forward citations
Cited by 9 Pith papers
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Obstructions to Minimal Regular Black Hole Cosmologies
Obstructions from matching conditions and completeness theorems prevent minimal regular black hole models from hosting unbounded FRW daughter cosmologies.
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The BGV Theorem and the Null Convergence Condition
NCC plus ³R≤0 imply BGV for shear-free geodesic orthogonal foliations, but shear and non-geodesic threading make the BGV expansion directional and can evade that guarantee.
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Affine ANEC selects the closed FRW branch for geodesically complete cosmology
Affine ANEC obstructs non-static flat and open FRW from being null geodesically complete while ANEC-satisfying, but allows explicit scalar-field realizations for closed FRW with NEC-respecting matter.
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Geodesically Complete Curvature-Bounce Inflation
Constructs an explicit closed FRW curvature-supported bounce-inflation model with a canonical scalar field that remains geodesically complete, NEC-compliant, and yields standard slow-roll predictions.
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Open case for a closed universe
A no-go theorem proves flat and open FRW universes cannot be nonsingular, geodesically complete and ANEC-consistent while closed universes can, with positive curvature mimicking phantom dark energy at the 1% level.
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Obstructions to Minimal Regular Black Hole Cosmologies
A minimal FRW 'daughter universe' matched without a shell to an asymptotically flat regular black hole is either bounded (closed) or geodesically incomplete (flat/open), so a regular core alone cannot supply a viable ...
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Obstructions to Minimal Regular Black Hole Cosmologies
No-shell FRW daughters matched to asymptotically flat regular black holes are bounded if closed and past-incomplete if flat or open; a regular core alone cannot yield a viable daughter cosmology.
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Geodesically Complete Curvature-Bounce Inflation
A closed k=+1 FRW universe with curvature-driven bounce and canonical scalar inflation remains sub-Planckian, satisfies the null energy condition, and produces ns=0.9617-0.9650 and r=0.0037-0.0045 consistent with data.
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Non-Gaussianity and Strong-Coupling Problem in a Two-Field DHOST Bouncing Model
Refines two-field DHOST bouncing model to match observed f_NL and keep strong-coupling scale above background energy, claiming full viability at linear and non-linear levels.
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