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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abstract
We present a wide class of models which realise a bounce in a spatially flat Friedmann universe in standard General Relativity. The key ingredient of the theories we consider is a noncanonical, minimally coupled scalar field belonging to the class of theories with Kinetic Gravity Braiding / Galileon-like self-couplings. In these models, the universe smoothly evolves from contraction to expansion, suffering neither from ghosts nor gradient instabilities around the turning point. The end-point of the evolution can be a standard radiation-domination era or an inflationary phase. We formulate necessary restrictions for Lagrangians needed to obtain a healthy bounce and illustrate our results with phase portraits for simple systems including the recently proposed Galilean Genesis scenario.
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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.
Bouncing solutions in quadratic curvature gravity with a scalar field satisfy null, weak, and dominant energy conditions but violate the strong one when using the scalar-field energy-momentum tensor, while all four conditions are violated near the bounce in the effective tensor formulation.
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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.