  The purpose of the present study is to show that in a particular cosmological
model, with an affine equation of state, one can obtain, besides the background
given by the scale factor, Hubble and deceleration parameters, a representation
in terms of scalar fields and, more important, explicit mathematical
expressions for the density contrast and the power spectrum. Although the model
so obtained is not realistic, it reproduces features observed in some previous
numerical studies and, therefore, it may be useful in the testing of numerical
codes and as a pedagogical tool.
