Open and closed universes, initial singularities, and inflation

Abstract

The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a) previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b) the timelike convergence condition is known to be violated in inflationary spacetimes. An immediate consequence of this theorem is that a recent result on initial singularities in open, future-eternal, inflating spacetimes may now be extended to include many closed universes. Also, as a fringe benefit, the time-reverse of the theorem may be applied to gravitational collapse.

Minimal conditions for the creation of a Friedman–Robertson–Walker universe from a “bounce”

“…More surprisingly, for universes with positive spatial curvature, none of the other energy conditions need be violated. We shall present a model-independent analysis of the bounce similar to the model-independent analysis applied to the Morris-Thorne traversable wormholes [10][11][12][13][14][15], and also show with specific examples how the various cosmological singularity theorems [3,4] and their modern extensions [16][17][18][19][20] can be evaded. Finally we discuss the extent to which SEC violations are compatible with known physics, and exhibit an inflation-inspired model for which a big-bounce is "natural".…”

“…The closed universe singularity theorem of [18] uses a very strong technical requirement (compact localized past light cones) explicitly violated by our models. The more recent results in [19,20] are also compatible with our results in that the theorems either apply to open universes, or make additional technical assumptions violated by our analysis.…”

“…On the other hand, it is rather easy to violate the SEC, leading some researchers to refer to the SEC as "the unphysical energy condition". Violations of the SEC are generic to classical scalar fields [3,11], to inflationary spacetimes [16][17][18][19][20], to spacetimes with (cosmologically large) positive cosmological constants [21][22][23], to certain mean-field quantum field theories [25,26] and other quantum mechanical situations [8], and significantly, to classical relativistic fluids with two body interactions [9,27]. A particularly wide class of Tolman wormholes can also be constructed by Wick rotating Euclidean wormholes back to Lorentzian signature [28]; the Wick rotated Euclidean wormholes typically satisfying all energy conditions except the SEC.…”

Localization of energy for a regular black hole solution in an asymptotically de Sitter spacetime geometry

“…The attempt for singularity avoidance in the context of black hole solutions has led to the quest for so-called regular black holes, which do not exhibit physical singularities; the first regular model was proposed already in 1968 by Bardeen [67]. Ayón-Beato and García [68] managed to construct an exact, static and spherically symmetric, globally non-singural, electrically charged black hole solution, whose behavior, asymptotically, resembles that of the Reissner-Nordström solution.…”

Value of H, space-time patterns, vacuum, matter, expansion of the Universe, alternative cosmologies

“…As early as 1993, Borde and Vilenkin argued [74,75] thar "a physically reasonable spacetime that is eternally inflating to the future must possess an initial singularity". Work on the initial singularity also concerns information and dynamics contained in imaginary time [76][77][78][79].…”