Quantum Initial Conditions Research Articles

Oscillatory universes in loop quantum cosmology and initial conditions for inflation

Positively curved oscillatory universes are studied within the context of loop quantum cosmology subject to a consistent semiclassical treatment. The semiclassical effects are reformulated in terms of an effective phantom fluid with a variable equation of state. In cosmologies sourced by a massless scalar field, these effects lead to a universe that undergoes ever-repeating cycles of expansion and contraction. The presence of a self-interaction potential for the field breaks the symmetry of the cycles and can enable the oscillations to establish the initial conditions for successful slow-roll inflation, even when the field is initially at the minimum of its potential with a small kinetic energy. The displacement of the field from its minimum is enhanced for lower and more natural values of the parameter that sets the effective quantum gravity scale. For sufficiently small values of this parameter, the universe can enter a stage of eternal self-reproduction.

Classical physics and Hamiltonian quantum mechanics as relics of the Big Bang

In a fundamental formulation of the quantum mechanics of a closed system, such as the universe as a whole, three forms of information are needed to make predictions of the probabilities of alternative histories. These are the action functional of the elementary particles, the quantum initial condition of the universe, and the information about our specific history. We discuss the origin of the "quasiclassical domain" of familiar experience and Hamiltonian quantum mechanics with its preferred time in such a formulation of quantum cosmology. It is argued that these features of the universe are not general properties of quantum theory, but rather approximate features emergent after the Planck time because of the character of the specific initial condition and dynamics of our universe.

Quantum probability distributions in the early Universe. IV. Stochastic dynamics in de Sitter space.

Using the Smoluchowski equation, we investigate the stochastic evolution of the horizon-averaged or coarse-grained scalar field (inflaton) in a pure de Sitter background. We clarify the effect quantum fluctuations have on the classical dynamics of relaxation. We consider two types of nonlinear potentials [V(\ensuremath{\varphi})=(1/2\ensuremath{\gamma}${\ensuremath{\varphi}}^{2}$+ 1) / 4 g${\ensuremath{\varphi}}^{4}$ and V(\ensuremath{\varphi})=-(1/2\ensuremath{\lambda}${\ensuremath{\varphi}}^{2}$+ 1) / 4 g${\ensuremath{\varphi}}^{4}$] with inflaton probability distributions initially displaced from equilibrium. In the former case quantum fluctuations have only a minor effect on the classical inflaton dynamics. In the latter case the situation is different. Quantum fluctuations play a crucial part in the early-time behavior of the inflaton probability distribution. Using techniques borrowed from nonequilibrium statistical mechanics, we show how [for V(\ensuremath{\varphi})=-(1/2\ensuremath{\lambda}${\mathrm{\ensuremath{\varphi}}}^{2}$+ 1) / 4 g${\mathrm{\ensuremath{\varphi}}}^{4}$] macroscopic (classical) order originates from stochastic (quantum) initial conditions. We estimate the time scale at which this transition takes place. The work here extends and validates the conclusion of Guth and Pi that the long-time behavior of f(\ensuremath{\varphi};t) can be described by a classical probability distribution.

Quantum initial conditions in quasi-classical trajectory calculations

The quantum distribution of initial conditions suggested recently by Careless and Hyatt as a means of “phase-averaging” classical trajectories is shown to lead to reaction probabilities which depend on the initial distance between the reagents even when this distance is sufficiently large for the corresponding interaction energy to vanish. We used that distribution to calculate reaction probabilities for the collinear H + H 2 exchange reaction on a potential energy surface for which quasi-classical and exact quantum results had been previously obtained. The dependence of the resulting reaction probabilities on the arbitrarily chosen value of the initial atom-molecule separation was substantial. We conclude that the use of such quantum distributions for initial conditions is physically unacceptable.