n-Dimensional FLRW Quantum Cosmology

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 $p=\alpha \rho$ 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 ($p=\frac{1}{n-1}\rho$). 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 $<p{>}_L/<\rho {>}_L$ 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 $n\to \infty$, $<p{>}_L/<\rho {>}_L\to 1$.

12 pages, revtex, minor modifications

References in corpus (2)

• Does the Big Rip survive quantization?
• Quantum singularities in FRW universe revisited