Slow-roll versus stochastic slow-roll inflation

We consider the classical wave equation with a thermal and Starobinsky–Vilenkin noise which in the slow-roll and long wave approximation describes the quantum fluctuations of the gravity-inflaton system in an expanding metric. We investigate the resulting consistent stochastic Einstein-Klein-Gordon system in the slow-roll regime. We show in some models that the slow-roll requirements (of the negligence of $$\partial _{t}^{2}\phi $$∂t2ϕ) can be satisfied in the probabilistic sense for the stochastic system with quantum and thermal noise for arbitrarily large time and an infinite range of fields. We calculate expectation values of some inflationary variables taking into account quantum and thermal noise. We show that the mean acceleration $$\langle \partial _{t}^{2}a\rangle $$⟨∂t2a⟩ can be negative or positive (depending on the model) when the random fields take values beyond the classical range of inflation.

Does gravity operate between galaxies? Observational evidence re-examined

The redshifts and luminosities of type 1A supernovae are conventionally fitted with the current paradigm, which holds that the galaxies are locally stationary in an expanding metric. The fit fails unless the expansion is accelerating; driven perhaps by ‘dark energy’. Is the recession of the galaxies slowed down by gravity or speeded up by some repulsive force? To shed light on this question the redshifts and apparent magnitudes of type 1A supernovae are re-analysed in a cartesian frame of reference omitting gravitational effects. The redshift is ascribed to the relativistic Doppler effect which gives the recession velocity when the light was emitted; if this has not changed, the distance reached and the luminosity follow immediately. This simple concept fits the observations surprisingly well with the Hubble constant H 0 =62.9±0.3 km s −1 Mpc −1 . It appears that the galaxies recede at unchanging velocities, so on the largest scale there is no significant intergalactic force. Reasons for the apparent absence of an intergalactic force are discussed.