Freund – Nambu cosmology with the massless scalar field

Within the framework of the generalization of Freund – Nambu scalar-tensor theory of gravity, a massless scalar field is considered, the source of which is the trace of its own energy-momentum tensor. For the cosmological problem, numerical solutions of field equations were obtained, with the help of which the dependencies of the Hubble parameter and the photometric distance to the observed sources on red-shift were constructed. To the consistency of the models with observational data, contours of confidence intervals for model parameters were constructed.