[Paper Review] The Big Bang quantum cosmology: The matter-energy production epoch

V.E. Kuzmichev, V. V. Kuzmichev|arXiv (Cornell University)|Dec 4, 2007

Cosmology and Gravitation Theories4 references13 citations

TL;DR

This paper proposes an exactly solvable quantum cosmology model for a closed, homogeneous, and isotropic universe during the matter-energy production epoch, using a primordial scalar field and a perfect fluid as a dynamical reference frame. It derives stationary quantum states and shows that matter-energy arises as a condensate of zero-momentum quanta of the scalar field, with the scale factor linearly related to condensate mass; the nucleation of the universe from a singularity exhibits exponential (explosive) behavior, and evolution occurs via quantum transitions between states of differing condensate mass.

ABSTRACT

The exactly solvable quantum model of the homogeneous, isotropic and closed universe in the matter-energy production epoch is considered. It is assumed that the universe is originally filled with a uniform scalar field and a perfect fluid which defines a reference frame. The stationary state spectrum and the wave functions of the quantum universe are calculated. In this model the matter-energy in the universe has a component in the form of a condensate of massive zero-momentum excitation quanta of oscillations of primordial scalar field. The mean value of the scale factor of the universe in a given state is connected with the mass of a condensate by a linear relation. The nucleation rate of the universe from the initial cosmological singularity point is calculated. It is demonstrated that the process of nucleation of the universe can have an exponential (explosive) nature. The evolution of the universe is described as transitions with non-zero probabilities between the states of the universe with different masses of a condensate.

Motivation & Objective

• To develop a fully quantized model of the early universe during the matter-energy production epoch.
• To resolve the problem of time and spacetime event identification in canonical quantum gravity by using a perfect fluid as a dynamical reference frame.
• To derive exact solutions for the quantum wave functions and energy spectrum of the universe in this framework.
• To investigate the quantum origin of the universe, including nucleation from a singularity and subsequent evolution via quantum transitions.

Proposed method

• Formulate the action for a closed Friedmann-Robertson-Walker universe coupled to a primordial scalar field and a perfect fluid acting as a material reference frame.
• Apply constraint quantization to the system, using the fluid's four-velocity and scalar fields to define spacetime events and break general covariance.
• Solve the Wheeler-DeWitt equation exactly for the wave function of the universe, yielding stationary states and a discrete energy spectrum.
• Identify the physical interpretation of the quantum states as a condensate of massive zero-momentum quanta of the scalar field excitation.
• Calculate the nucleation rate of the universe from the initial singularity using the path integral approach, showing exponential (explosive) behavior.
• Derive transition probabilities between quantum states of different condensate masses, showing Poisson-distributed transitions with mean number ⟨n′⟩ = ξ₀²/2.

Experimental results

Research questions

• RQ1 How can a consistent quantum cosmology be formulated for a closed, homogeneous, and isotropic universe during the matter-energy production epoch?
• RQ2 What is the role of a perfect fluid as a dynamical reference frame in resolving the problem of time in quantum gravity?
• RQ3 How does the universe nucleate from a cosmological singularity in this quantum model, and what is the nature of the nucleation process?
• RQ4 What is the physical interpretation of the quantum states of the universe in terms of scalar field condensates and their relation to the scale factor?
• RQ5 How does the evolution of the universe emerge from quantum transitions between states of different condensate masses?

Key findings

• The stationary quantum states of the universe are described by wave functions that are superpositions of states with different masses of a scalar field condensate.
• The mean value of the scale factor in a given quantum state is linearly related to the mass of the condensate, with the proportionality constant determined by the Planck scale.
• The nucleation rate of the universe from the initial singularity is non-zero and follows an exponential (explosive) law, indicating a quantum tunneling origin of the Big Bang.
• The ground (vacuum) state of the universe with Planck-scale condensate mass has a mean scale factor that closely matches the Planck length.
• Transitions between quantum states of the universe are governed by a Poisson distribution with mean ⟨n′⟩ = ξ₀²/2, and the probability of transitioning from vacuum to non-vacuum states is overwhelmingly high.
• The total probability of vacuum-to-non-vacuum transitions is 1 − e^−⟨n′⟩, which is exponentially large compared to vacuum-to-vacuum transitions, indicating that quantum evolution is dominated by non-vacuum state transitions.