Quantum Cosmology in the Light of Quantum Mechanics
Abstract
There is a formal analogy between the evolution of the universe, when it is seen as a trajectory in the minisuperspace, and the worldline followed by a test particle in a curved spacetime. The analogy can be extended to the quantum realm, where the trajectories are transformed into wave packets that give us the probability of finding the universe or the particle in a given point of their respective spaces: the spacetime in the case of the particle and the minisuperspace in the case of the universe. The wave function of the spacetime and the matter fields, all together, can then be seen as a superfield that propagates in the minisuperspace and the socalled third quantisation procedure can be applied in a parallel way as the second quantisation procedure is performed with a matter field that propagates in the spacetime. The superfield can thus be interpreted as made up of universes propagating, i.e., evolving, in the minisuperspace. The analogy can also be used in the opposite direction. The way in which the semiclassical state of the universe is obtained in quantum cosmology allows us to obtain, from the quantum state of a field that propagates in the spacetime, the geodesics of the underlying spacetime as well as their quantum uncertainties or dispersions. This might settle a new starting point for a different quantisation of the spacetime.
 Publication:

Galaxies
 Pub Date:
 April 2019
 DOI:
 10.3390/galaxies7020050
 arXiv:
 arXiv:1812.10657
 Bibcode:
 2019Galax...7...50R
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 20 pages, 4 figures. Based on the talk given in the meeting \emph{Travelling through Pedro's universes}, held in Madrid at the Universidad Complutense the days $3^{rd}5^{th}$ of Dec., in the memory of Prof. Pedro F. Gonz\'{a}lezD\'{\i}az