In several papers the 5-dimensional Projective Unified Field Theory (PUFT) of the author (Schmutzer 1998, Schmutzer 1999, Schmutzer 2000a) was applied to a homogeneous, isotropic and closed cosmological model without pressure (cosmology of the attraction era). Here we derive a cosmological equation of state for the pressure. This step enables us to treat cosmology for the complete time scale from the big start (Urstart) to the present time (repulsion era and attraction era). Here following subjects are treated, where our specific terminology of PUFT is taken over from our previous publications quoted above: cosmological equation of state for the pressure, numerical integration of the system of the resulting cosmological differential equations and evaluation of the results. Specific outcomes (temporal course and present values) are given for the following cosmological quantities: radius and age of the world, cosmological frequency shift (Hubble factor), deceleration parameter, effective gravitational “constant”, mass density, temperature, pressure, entropy, behavior of the photon gas and of the mechanical particle gas etc.