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arXiv · 1010.3054

n-Dimensional FLRW Quantum Cosmology

P. S. Letelier·J. P. M. Pitelli
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Abstract

We introduce the formalism of quantum cosmology in a Friedmann-Lemaître-Robertson-Walker (FLRW) universe of arbitrary dimension filled with a perfect fluid with $p=αρ$ equation of state. First we show that the Schutz formalism, developed in four dimensions, can be extended to a n-dimensional universe. We compute the quantum representant of the scale factor $a(t)$, in the Many-Worlds, as well as, in the de Broglie-Bohm interpretation of quantum mechanics. We show that the singularities, which are still present in the n-dimensional generalization of FLRW universe, are excluded with the introduction of quantum theory. We quantize, via the de Broglie-Bohm interpretation of quantum mechanics, the components of the Riemann curvature tensor in a tetrad basis in a n-dimensional FLRW universe filled with radiation ($p=\frac{1}{n-1}ρ$). We show that the quantized version of the Ricci scalar are perfectly regular for all time $t$. We also study the behavior of the energy density and pressure and show that the ratio $ _L/<ρ>_L$ tends to the classical value $1/(n-1)$ only for $n=4$, showing that $n=4$ is somewhat privileged among the other dimensions. Besides that, as $n\to\infty$, $ _L/<ρ>_L\to 1$.

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BibTeXRIS

P. S. Letelier, J. P. M. Pitelli. 2011-07-28. n-Dimensional FLRW Quantum Cosmology. https://doi.org/10.1103/physrevd.82.104046

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