  Cosmology is a field of physics in which the use of General Relativity theory
is indispensable. However, a cosmology based on Newtonian gravity theory for
gravity is possible in certain circumstances. The applicability of Newtonian
theory can be substantially extended if it is modified in such way that
pressure has a more active role as source of the gravitational field. This was
done in the neo-Newtonian cosmology. The limitation on the construction of a
Newtonian cosmology, and the need for a relativistic theory in cosmology are
reviewed. The neo-Newtonian proposal is presented, and its consequences for
cosmology are discussed.
