  We perform a systematic search for rotationally invariant cosmological
solutions to matrix models, or more specifically the bosonic sector of
Lorentzian IKKT-type matrix models, in dimensions $d$ less than ten,
specifically $d=3$ and $d=5$. After taking a continuum (or commutative) limit
they yield $d-1$ dimensional space-time surfaces, with an attached Poisson
structure, which can be associated with closed, open or static cosmologies. For
$d=3$, we obtain recursion relations from which it is possible to generate
rotationally invariant matrix solutions which yield open universes in the
continuum limit. Specific examples of matrix solutions have also been found
which are associated with closed and static two-dimensional space-times in the
continuum limit. The solutions provide for a matrix resolution of cosmological
singularities. The commutative limit reveals other desirable features, such as
a solution describing a smooth transition from an initial inflation to a
noninflationary era. Many of the $d=3$ solutions have analogues in higher
dimensions. The case of $d=5$, in particular, has the potential for yielding
realistic four-dimensional cosmologies in the continuum limit. We find
four-dimensional de Sitter $dS^4$ or anti-de Sitter $AdS^4$ solutions when a
totally antisymmetric term is included in the matrix action. A nontrivial
Poisson structure is attached to these manifolds which represents the lowest
order effect of noncommutativity. For the case of $AdS^4$, we find one
particlular limit where the lowest order noncommutativity vanishes at the
boundary, but not in the interior.
