Bouncing and coasting universe with exact quantum-classical correspondence

Abstract

When the scale factor of expansion of the universe is written as $a(t)\equiv A{e}^{\alpha (t)}$, with $A$ as some real constant and $\alpha (t)$ a real function, the gravitational action $I_G$ appears in the same form as the matter action $I_M$ for a homogeneous and isotropic scalar field with a specific scale factor-dependent potential. We observe that by making analytic continuation of the Lagrangian function in this $I_G$ to the complex plane of $\alpha$, one can obtain terms corresponding to both parts of a total action that describes a viable cosmological model. The solution gives a bouncing and coasting universe, which first contracts and then expands linearly, with a smooth bounce in between them. Such a bounce, called a Tolman wormhole, is due to a Casimir-like negative energy that appears naturally in the solution. In a novel approach to quantum cosmology, we perform canonical quantization of the above model using the operator method and show that it can circumvent the operator ordering ambiguity in the conventional formalism. It leads to a quantum wave equation for the universe, solving which we get the interesting result that the universe is in a ground state with nonzero energy. This solution is different from the Wheeler-DeWitt wave function and possesses exact quantum-classical correspondence during all epochs.

arXiv commentThis preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in International Journal of Theoretical Physics, and is available online at https://doi.org/10.1007/s10773-021-04956-0

References in corpus (25)

• Lecture Notes on General Relativity
• The R_h = ct Universe
• Generalized energy conditions in Extended Theories of Gravity
• Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
• Energy conditions in modified gravity
• The Cosmic Horizon
• Minimal conditions for the creation of a Friedman-Robertson-Walker universe from a "bounce"
• Cosmographic evaluation of deceleration parameter using SNe Ia data
• Modified de Broglie-Bohm approach to quantum mechanics
• Generalized Chen-Wu type cosmological model
• Probability and complex quantum trajectories
• $R_h=ct$ and the eternal coasting cosmological model
• Cosmography, Decelerating Past, and Cosmological Models: Learning the Bayesian Way
• Dear Qubitzers, GR=QM
• A Low Matter Density Decaying Vacuum Cosmology from Complex Metric
• A modified Ozer-Taha type cosmological model
• The dimensionless age of the Universe: a riddle for our time
• Tomographic Representation of Minisuperspace Quantum Cosmology and Noether Symmetries
• Probability and complex quantum trajectories: Finding the missing links
• Exact Classical Correspondence in Quantum Cosmology
• A tomographic description for classical and quantum cosmological perturbations
• A comparison of the R_h=ct and LCDM cosmologies based on the observed halo mass function
• Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories
• Tunneling in energy eigenstates and complex quantum trajectories
• Interfering Quantum Trajectories Without Which-Way Information