[Paper Review] Quantum Cosmological Origin of Universes

V. N. Pervushin, V.A. Zinchuk|ArXiv.org|Apr 25, 2005

Cosmology and Gravitation Theories3 references3 citations

TL;DR

This paper proposes a quantum cosmological origin of universes and particles via a Hilbert-Dirac-Bogoliubov pathway from General Relativity to quantum gravity, treating the cosmological scale factor as a zero mode of momentum constraints. By avoiding double counting in Hamiltonian reduction, it derives a new cosmological perturbation theory that explains the CMB primordial power spectrum through the creation of W± and Z bosons from Bogoliubov vacuum when their Compton wavelength matches the horizon size.

ABSTRACT

A direct pathway from Hilbert's ``Foundation of Physics'' to Quantum Gravity is established through Dirac's Hamiltonian reduction of General Relativity and Bogoliubov's transformation by analogy with a similar pathway passed by QFT in 20th century. The cosmological scale factor appears on this pathway as a zero mode of the momentum constraints treated as a global excitation of the Landau superfluid liquid type. This approach would be considered as the foundation of the well--known Lifshitz cosmological perturbation theory, if it did not contain the double counting of the scale factor as an obstruction to the Dirac Hamiltonian method. After avoiding this ``double counting'' the Hamiltonian cosmological perturbation theory does not contain the time derivatives of gravitational potentials that are responsible for the CMB ``primordial power spectrum'' in the inflationary model. The Hilbert -- Dirac -- Bogoliubov Quantum Gravity gives us another possibility to explain this ``spectrum'' and other topical problems of cosmology by the cosmological creation of both universes and particles from Bogoliubov's vacuum. We listed the set of theoretical and observational arguments in favor of that the CMB radiation can be a final product of primordial vector W-, Z- bosons cosmologically created from the vacuum when their Compton length coincides with the universe horizon. The equations describing longitudinal vector bosons in SM, in this case, are close to the equations of the inflationary model used for description of the ``power primordial spectrum'' of the CMB radiation.

Motivation & Objective

• To establish a direct quantum gravity pathway from Hilbert’s 1915 geometric formulation of GR to quantum cosmology.
• To resolve the double counting of the scale factor in standard cosmological perturbation theory using Dirac’s Hamiltonian reduction.
• To explain the CMB primordial power spectrum not via inflation, but via cosmological creation of longitudinal vector bosons (W±, Z) from vacuum.
• To unify quantum gravity with the Standard Model by identifying the Bogoliubov vacuum as the origin of primordial particles and universes.
• To propose a new principle of relativity based on measurement units, linking conformal invariance to observable quantities.

Proposed method

• Apply Dirac’s Hamiltonian reduction to General Relativity, treating the cosmological scale factor as a zero mode of momentum constraints.
• Use Lichnerowicz’s transformation to separate the zero mode and eliminate double counting of canonical momenta.
• Employ Bogoliubov’s transformation to describe quantum creation of universes and particles from vacuum, analogous to superfluidity.
• Construct a reduced Hamiltonian action using gauge-invariant variables derived from Zel’manov’s class of gauge functions.
• Apply Einstein’s correspondence principle to connect conformal quantities to measurable physical observables.
• Derive equations for longitudinal vector bosons in the Standard Model that closely resemble inflationary model equations for the CMB power spectrum.

Experimental results

Research questions

• RQ1 Can a consistent quantum gravity theory be derived from Hilbert’s geometric formulation of GR via Dirac reduction and Bogoliubov transformation?
• RQ2 How does the cosmological scale factor emerge as a zero mode in the Hamiltonian framework, and what is its role in avoiding double counting?
• RQ3 Can the CMB primordial power spectrum be explained without inflation, via quantum creation of W± and Z bosons from vacuum?
• RQ4 What is the role of the Bogoliubov vacuum in initiating geometric time and the cosmological creation of universes?
• RQ5 How does the proposed framework resolve the horizon, homogeneity, and dark matter problems in cosmology?

Key findings

• The cosmological scale factor arises as a zero mode of the momentum constraints, analogous to a global excitation in Landau superfluidity.
• Double counting of the scale factor in standard Lifshitz perturbation theory invalidates its consistency with GR; removing it leads to a new Hamiltonian cosmological perturbation theory.
• The new theory does not contain time derivatives of gravitational potentials, which are responsible for the primordial power spectrum in inflationary models.
• The equations for longitudinal vector bosons in the Standard Model closely match those used in inflationary models to describe the CMB power spectrum.
• The CMB radiation can be interpreted as the final product of cosmologically created W± and Z bosons when their Compton wavelength equals the universe horizon size.
• The framework introduces a new principle of relativity based on measurement units, where equations of motion depend on both data and units, suggesting a deeper unification of GR and QFT.