Dark matter and dark energy from pockets of gravity created by quantum tunneling of the inflaton potential

Max Chaves

Published 2013-09-17, updated 2013-12-13Version 3

It is usually assumed that during the reheating period of inflation the inflaton field behaves coherently and follows a classical path. It is pointed out that a background inflaton field \phi_0 falling down a potential density V(\phi) can and frequently should undergo a quantum tunneling effect involving an energy \DeltaV<<V, so that it becomes possible to create perturbative inflatons \phi's, which, in turn, can disintegrate into other particles. We argue for this scenario using large field inflation assumed during a typical slow-roll regime, and typical values for the physical quantities associated with the tunneling effect are worked out. It is shown how, as a result of these highly energetic and localized processes, the components of the metric receive strong gradients within a small volume. These pockets of gravity can gravitate both attractively or repulsively, since the Ricci tensor contains squared partial derivative terms with either positive or negative sign, so they can be a component of either dark matter or dark energy. As the Universe expands the curvature of the pockets weakens as 1/a^2, where a(t) is the scale factor of the expansion, but it is shown that, as long as the integral over the gravitating gravitational fields of the pocket is done over all of the expanding volume of the pocket, the value of the integral is not affected by the expansion. Geometrically speaking, the gravitation of a pocket is produced by the convolutions of the metric inside it; as the Universe expands the convolutions are over a much large volume so they are flatter, but an integration over the larger volume gives the same result as before the expansion. It is just a change of scale of the same geometry. A common cause (inflaton quantum tunneling) for both dark matter and dark energy explains why their quantities are of the same order of magnitude.