Mathematics of accelerated expansion of the Universe and Lobachevsky space

In classical works, the Hubble constant is defined via the metric. Here we define it, as it should be, via matter, according to Milne and McCrea, extending their theory of the expanding universe to the relativistic case. This allows us to explain the accelerated expansion as a simple relativistic effect without Einstein's lambda, dark energy and new particles as an exact consequence of the classical Einstein action. The well-verified fact of accelerated expansion allows us to determine the sign of the curvature in the Friedmann model: it turns out to be negative, and we live in Lobachevsky space.