Thesis 1 assumes that in an adiabatic considered Brownian Motion system the temperature would rise by a tiny heat excess. Thesis 2 postulates that the tiny heat excess in the rough range of P ≈ 10-10 Watt/kg is solely produced by the gravitational interaction of the masses, because in the adiabatic case gravity is left over as the only effective cause. Although not yet verified, the heat excess of the earth, of the big gas planets and eventually of some far away asteroids and molecular clouds may uncover some extra unexplained heat excesses. Thesis 3 assumes the Hubble number to be an indication of the heat excess, considered as a decay constant of H = Λ0 =2.27 • 10-18 s-1 (corresponding to the tailored value of 70 km/(s•Mpc) in cosmology). By multiplying with c2 any mass would exhibit a specific energy release of p/m = 0.204 Watt/kg or m ̇/m = 2.27•10-18 kg/(kg•s). This is postulated as an emission of a yet unknown quantum flow with the velocity of light c resulting in a specific scalar repulsive or recoil force |f| = m ̇/m c = 6,8•10-10 N/kg on the emitting mass. Thesis 4 identifies this as the self-gravitation of any mass and energy in the universe and it is supposed that Λ0 (former H) is the cause of gravity. A consequential stationary background scalar field |a| = Λ0•c in the universe creates gravitational redshift which is equivalent to the apparent accelerated expansion. Thesis 5 tries to reduce the scalar from the sphere to an unidirectional vector by dividing by π2 which then appears as the gravitational constant G. By the more precise value of G now Λ0 (former H) can be corrected to 2,20•10-18 s-1•corresponding to 67,89 km/(s•Mpc), the lower Planck- and WMAP-satellite value of the contemporary Hubble number discussion. Final remarks contain historical and modern ideas about the minimum mass of a hypothetical graviton. The prerequisites of an experiment are described which eventually can verify the postulated tiny heat excess.