Mathematics of Accelerated Expansion of the Universe and Lobachevsky Space

In classical works, the Hubble constant is defined via a metric. Here we define it, as it should be, via matter, following Milne and McCrea and 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 resorting to Einstein’s lambda, dark energy, or new particles, more specifically, 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.