  For several crucial microseconds of its early history, the Universe consisted
of a Quark-Gluon Plasma. As it cooled during this era, it traced out a
trajectory in the quark matter phase diagram. The form taken by this trajectory
is not known with certainty, but is of great importance: it determines, for
example, whether the cosmic plasma passed through a first-order phase change
during the transition to the hadron era, as has recently been suggested by
advocates of the "Little Inflation" model. Just before this transition, the
plasma was strongly coupled and therefore can be studied by holographic
techniques. We show that holography imposes a strong constraint (taking the
form of a bound on the baryonic chemical potential relative to the temperature)
on the domain through which the cosmic plasma could pass as it cooled, with
important consequences for Little Inflation. In fact, we find that holography
applied to Little Inflation implies that the cosmic plasma must have passed
quite close to the quark matter critical point, and might therefore have been
affected by the associated fluctuation phenomena.
