  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.
