We use a Riemannian four-dimensional presentation of gravitation in which the coordinates are those of Hubble , i.e .
distances and velocity rather than the traditional space and time .
We solve the field equations and show that there are three possibilities for the Universe to expand .
The theory describes the Universe as having a three-phase evolution with a decelerating expansion , followed by a constant and an accelerating expansion , and it predicts that the Universe is now in the latter phase .
It is shown , assuming \Omega _ { m } = 0.245 , that the time at which the Universe goes over from a decelerating to an accelerating expansion , i.e. , the constant-expansion phase , occurs at 8.5 Gyr ago .
Also , at that time the cosmic radiation temperature was 146K .
Recent observations of distant supernovae imply , in defiance of expectations , that the Universe ’ s growth is accelerating , contrary to what has always been assumed , that the expansion is slowing down due to gravity .
Our theory confirms these recent experimental results by showing that the Universe now is definitely in a stage of accelerating expansion .
The theory predicts also that now there is a positive pressure , p = 0.034 g / cm ^ { 2 } , in the Universe .
Although the theory has no cosmological constant , we extract from it its equivalence and show that \Lambda = 1.934 \times 10 ^ { -35 } s ^ { -2 } .
This value of \Lambda is in excellent agreement with measurements .
It is also shown that the three-dimensional space of the Universe is Euclidean , as the Boomerang experiment shows .