Self-accelerated Universe

It is widely believed that the large redshifts for distant supernovae are explained by the vacuum energy dominance, or, in other words, by the cosmological constant in Einstein's equations, which is responsible for the anti-gravitation effect. A tacit assumption is that particles move along a geodesic for the background metric. This is in the same spirit as the consensus regarding the uniform Galilean motion of a free electron. However, there is a runaway solution to the Lorentz--Dirac equation governing the behavior of a radiating electron, in addition to the Galilean solution. Likewise, a runaway solution to the entire system of equations, both gravitation and matter equations of motion including, may provide an alternative explanation for the accelerated expansion of the Universe, without recourse to the hypothetic cosmological constant.