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The matter-energy intensity distribution in a quantum gravitational system

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Abstract

The influence of the quantum nature of gravity on the distribution of matter-energy in a gravitational system with the maximally symmetric geometry is studied. The state vector of the quantum gravitational system (QGS) satisfies the set of wave equations which describes the time evolution of a quantum system in the space of quantum fields. It is shown that this state vector can be normalized to unity. The generalization of the wave equations to the domain of negative values of the cosmic scale factor is made. For the arrow of time from past to future, the state vector describes the QGS contracting for the negative values of the scale factor and expanding for its positive values. The intensity distributions of matter are calculated for two exactly solvable models of spatially closed and flat QGSs formed by dust and radiation. The analogies with the motion in time of minimum wave packet for spatially closed QGS and with the phenomenon of diffraction in optics for flat QGS are drawn.

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Notes

  1. It is convenient to formulate quantum theory in terms of dimensionless variables and parameters, in which length is measured in modified units of Planck length \(l_\mathrm{P} = \sqrt{2 G \hbar / (3 \pi c^{3})}\), proper time is expressed in Planck time units \(t_\mathrm{P} = l_\mathrm{P} / c\), and mass-energy is taken in Planck mass units \(m_\mathrm{P} = \hbar / (l_\mathrm{P} c)\). The Planck density \(\rho _\mathrm{P} = 3 c^{4} / (8 \pi G l_\mathrm{P}^{2})\) is used as a unit of energy density and pressure. The scalar field is taken in \(\phi _\mathrm{P} = \sqrt{3 c^{4} / (8 \pi G)}\). Here G is Newton’s gravitational constant.

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  1. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, 03680, Ukraine

    V. E. Kuzmichev & V. V. Kuzmichev

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  1. V. E. Kuzmichev
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Kuzmichev, V.E., Kuzmichev, V.V. The matter-energy intensity distribution in a quantum gravitational system. Quantum Stud.: Math. Found. 5, 245–255 (2018). https://doi.org/10.1007/s40509-017-0115-0

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