A spatially homogeneous and isotropic Einstein–Dirac cosmology

Abstract

Abstract. We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree-Fock ansatz where all one-particle wave functions are coherent and have the same momentum. If the scale function is large, the universe behaves like the classical Friedmann dust solution. If however the scale function is small, quantum effects lead to oscillations of the energy-momentum tensor. It is shown numerically and proven analytically that these quantum oscillations can prevent the formation of a big bang or big crunch singularity. The energy conditions are analyzed. We prove the existence of time-periodic solutions which go through an infinite number of expansion and contraction cycles.

Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology

“…Let us briefly discuss the qualitative dependence of the bounce on the free parameters R max , R qu , λ, and φ of our model (for a detailed analysis we refer to [4]). First of all, the probability of preventing the crunch can be increased by choosing |w 1 (R max )| smaller.…”

“…If R min > 0, the big crunch is avoided and R "bounces back," whereas in the case R min = 0 the big crunch appears despite the quantum effects. Considering the phase φ as unknown, one can give the result of Let us briefly discuss the qualitative dependence of the bounce on the free parameters R max , R qu , λ, and φ of our model (for a detailed analysis we refer to [4]). First of all, the probability of preventing the crunch can be increased by choosing |w 1 (R max )| smaller.…”

“…However, the flat and hyperbolic cases are less interesting, since they expand infinitely. We remark that the hyperbolic case allows for solutions with negative energy density where the matter turns to be repulsive (see [4]).…”

“…Substituting the ansatz ( 3) and ( 4) into the ED equations (1), we obtain the following system of ODEs in the spinors (α, β) and the scale function R (for a detailed derivation see [4]),…”

A non-perturbative construction of the fermionic projector on globally hyperbolic manifolds I: Space-times of finite lifetime

“…This assumption is reasonable because we cannot expect the WKB approximation to hold near the singularities (in particular because "quantum oscillations" become relevant; see [15]). Under this assumption, the estimate (5.15) can be translated to a relative error of the order O((mR max ) − 1 5 ).…”