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Inflationary cosmology is notoriously past geodesically incomplete in many situations. However, it is generally unknown whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be extended beyond its null past boundary. In homogeneous and isotropic cosmology with flat spatial sections, we classify which past inflationary histories have a scalar curvature singularity and which might be extendible/non-singular. We derive rigorous extendibility criteria of various regularity classes for quasi-de Sitter spacetimes that evolve from infinite proper time in the past. Beyond homogeneity and isotropy, we show that continuous extensions respecting the Einstein field equations with a perfect fluid must have the equation of state of a de Sitter universe asymptotically. An interpretation of our results is that past-eternal inflationary scenarios are most likely physically singular, except in very special situations.

Zoom link:  https://pitp.zoom.us/j/98334550627?pwd=UnR3eUxZRFZpeEZoOGEwNkJuc0M0UT09

We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with cosmological constant. The construction of spinfoam amplitudes uses the state-integral model of PSL(2,C) Chern-Simons theory and the implementation of simplicity constraint. The formulation has 2 key features: (1) spinfoam amplitudes are all finite, and (2) With suitable boundary data, the semiclassical asymptotics of the vertex amplitude has two oscillatory terms, with phase plus or minus the 4-dimensional Lorentzian Regge action with cosmological constant for the constant curvature 4-simplex.

Zoom link:  https://pitp.zoom.us/j/92219187641?pwd=RUsvcWo2SHFmVTE3NmxDMUZlVEV2UT09