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.
Can we have inflation with Omega > 1?
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abstract
It is very difficult to obtain a realistic model of a closed inflationary universe. Even if one fine-tunes the total number of e-folds to be sufficiently small, the resulting universe typically has large density perturbations on the scale of the horizon. We describe a class of models where this problem can be resolved. The models are unattractive and fine-tuned, so the flatness of the universe remains a generic prediction of inflationary cosmology. Nevertheless one should keep in mind that with the fine-tuning at the level of about one percent one can obtain a semi-realistic model of a closed inflationary universe. The spectrum of density perturbations in this model may have a cut-off on the scale of the horizon. Similar approach may be valid in application to a compact inflationary universe with a nontrivial topology.
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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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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
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.