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

Abstract

In this Letter we investigate the minimal conditions under which the creation of our universe might arise due to a "bounce" from a previous collapse, rather than an explosion from a big-bang singularity. Such a bounce is sometimes referred to as a Tolman wormhole. We subject the bounce to a general model-independent analysis along the lines of that applied to the Morris-Thorne traversable wormholes, and show that there is always an open temporal region surrounding the bounce over which the strong energy condition (SEC) must be violated. On the other hand, all the other energy conditions can easily be satisfied. In particular, we exhibit an inflation-inspired model in which a big bounce is "natural".Oscillating universes [1,2] are alternatives to standard big bang cosmology [3][4][5][6]. They avoid the big-bang singularity and replace it with a cyclical evolution from a previous incarnation of our present universe. Unfortunately, many of the older discussions of oscillating universes leave the nature of the turnaround quite ambiguous (cusp? angular-momentum barrier?). Interest in oscillating universes largely declined after the development of the first cosmological singularity theorem [3,4], but we feel that the time is ripe for a reassessment of the situation. In this Letter, we model the turnaround by a Friedman-Robertson-Walker (FRW) universe undergoing a "bounce" and ask what the absolute minimum requirements are for such a bounce to occur. Not too surprisingly, the strong energy condition (SEC) of classical gravity must be violated [7][8][9]. (SEC-violation is a necessary but not sufficient condition.) 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".A bouncing baby universe, or Tolman wormhole, is simply a FRW universe that undergoes a collapse, instant of maximum compression, and subsequent expansion (as opposed to undergoing a big crunch singularity or exhibiting a big-bang singularity). In a model-independent analysis, the key idea is to extract as much information as possible from the energy conditions without making any particular commitment to the equation of state for the matter content of the universe [10][11][12][13][14][15]. The utility of such an approach has recently been demonstrated in a different context: applying the energy conditions to the epoch of galaxy formation [21][22][23].The FRW cosmology is described by the metric [3-6]with k = +1, 0, or −1 for hyperspherical, flat, or hyperbolic spatial sections, respectively....

A simple harmonic universe

“…Two questions have recurred often in theoretical cosmology [1][2][3][4][5][6][7][8][9]: 1) is the Universe eternal or did it have a beginning at some definite time in the past?, and 2) is it possible to make Universes with one or more "bounces" where the scale factor crunches and then bangs? 1 The answers to these two questions are deeply intertwined with the subject matter of the singularity theorems of Penrose and Hawking (discussed comprehensively in [10]).…”

Primordial perturbations in a nonsingular bouncing universe model

“…This means, given that there is already some radiation present, that, in the context of GR, there must exist some other fluid having negative energy. In particular, for the special case at hand for which the spatial curvature K = 0, this means that the Null Energy Condition (NEC) must be violated at some time near the bounce [14].…”

“…In its latest version [11], moreover, the model also * Electronic address: peter@iap.fr † Electronic address: nelsonpn@cbpf.br contains a supposedly actual singularity [12]. Quantum cosmology, in the framework of the Wheelerde-Witt (WdW) equation, exhibits bouncing solutions [13] which can be interpreted as truly avoiding the singularity, even for flat (K = 0) spatial sections, a possibility strictly forbidden in classical General Relativity (GR), unless [14] some exotic material, with negative energy density violating the Null Energy Condition (NEC) [15], is introduced, which most cosmologists are reluctant on doing. Such a bouncing universe model provides a solution to the horizon problem by geodesically completing the manifold in the past, and avoids the monopole formation if the bounce takes place at a temperature below that of Grand Unification (GUT); this class of models does not however address the question of flatness and one must assume K = 0 from the outset.…”

Nonsingular big bounces and the evolution of linear fluctuations

“…(4) to c 2 A ≡ 1 − 3(1 − c 2 s )K/k 2 , [10]; as eqs. (3)(4)(5) are complete set for single component, this prescription applies always in the single scalar field case. It is convenient to have…”

“…Specific realizations of the bounce and the conditions required to have the FLRW (Friedmann-Lemaître-Robertson-Walker) world model from a bounce were studied in [4,5].…”