Primordial black holes in a dimensionally oxidizing Universe

Abstract

The spontaneous creation of primordial black holes in a violently expanding Universe is a well studied phenomenon. Based on quantum gravity arguments, it has been conjectured that the early Universe might have undergone a lower dimensional phase before relaxing to the current (3 + 1) dimensional state. In this article we combine the above phenomena: we calculate the pair creation rates of black holes nucleated in an expanding Universe, by assuming a dimensional evolution, we term "oxidation", from (1 + 1) to (2 + 1) and finally to (3 + 1) dimensions. Our investigation is based on the no boundary proposal that allows for the construction of the required gravitational instantons. If, on the one hand, the existence of a dilaton non-minimally coupled to the metric is necessary for black holes to exist in the (1 + 1) phase, it becomes, on the other hand, trivial in (2 + 1) dimensions. Nevertheless, the dilaton might survive the oxidation and be incorporated in a modified theory of gravity in (3 + 1) dimensions: by assuming that our Universe, in its current state, originates from a lower-dimensional oxidation, one might be led to consider the pair creation rate in a sub-class of the Horndeski action. Our findings for this case show that, for specific values of the Galileon coupling to the metric, the rate can be unsuppressed. This would imply the possibility of compelling parameter bounds for non-Einstein theories of gravity by using the spontaneous black hole creation.

Modified Gravity and Cosmology: An Update by the CANTATA Network

“…Extra dimensions -One of the most tempting routes of modification of General Relativity has been the possibility that our spacetime has more than four dimensions, with the extra ones inaccessible to low-energy exploration methods. The necessary compactification procedure typically results in specific modifications of the gravitational Lagrangian [19], which can be found among the many covered in the huge assortment of possibilities [20].…”