Quantum nature of the big bang: Improved dynamics

Abstract

An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The scalar field continues to serve as 'emergent time', the big bang is again replaced by a quantum bounce, and quantum evolution remains deterministic across the deep Planck regime. However, while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities, with the new Hamiltonian constraint it occurs only at a Planck-scale density. Thus, the new quantum dynamics retains the attractive features of current evolutions in loop quantum cosmology but, at the same time, cures their main weakness.

Inflationary universe in loop quantum cosmology

“…Intriguingly, one can obtain an modified Friedmann equation from the effective Hamiltonian constraint, which can be used to investigate the role of nonperturbative quantum correction conveniently. It is remarkable that the quantum geometric effects lead to a ρ 2 modification to the Friedmann equation at the scales when ρ becomes comparable to a critical density ρ crit which is close to the Planck density (ρ crit ≈ 0.82ρ Pl ) [13,14,16,17,18]. The modified term in the Friedmann equation is negative definite, which implies a bounce when the energy density hits the critical value; this feature resolves the classical big-bang singularity problem and is in accordance with the result from the quantum evolution in LQC.…”

Loop quantum cosmology evolution operator of an FRW universe with a positive cosmological constant

“…However, although the number of works using the heuristic methods of mimicking the quantum evolution by an appropriately constructed classical mechanics [7] is rapidly growing, not so much effort has been dedicated so far to the investigation on a genuinely quantum level. The rigorous studies of these aspects are in fact restricted just to models either in vacuo [8,9], or admitting massless scalar field as the only matter content [10][11][12][13]. The number of works attempting to include the cosmological constant à is even smaller [14] and the rigorous analysis of the quantum universe dynamics within the precise loop quantum cosmology (LQC) model [15] was done only for negative Ã, a case not favored by the observations.…”

Qualitative study in loop quantum cosmology

“…If ρ 0 = ρ c , at t = 0 we are at the bounce and, by (29), the value ofψ will be the same throughout all the contracting and expanding phase, i.e., the velocity of the scalar field does not change sign, thus reaching the top of the potential. With respect to Type II orbits, the initial point t = 0 will be at (ψ,ψ) = (ψ 0 , 0) where ψ 0 = 0, which corresponds to a change of sign in the velocity of the scalar field, meaning that the orbits do not reach the top of the potential.…”

“…Thus, several types of singularities are avoided (for e.g. Big Rip [27] and Big Crunch [28]) and the Big Bang is replaced by a non-singular bounce (see for instance [29,30]). …”