International Astronomy and Astrophysics Research Journal

Results are presented from an exponential-stress model, which involves an exponential growth of dark matter and an exponential decay of ordinary matter under stress-free conditions.   They reveal a previously ignored force, which has been called the anti-gravitational force.  The anti-gravitational force (F) is a uniform force which opposes the Newtonian gravitational force that decreases outwards to zero from a singularity at the centre of the universe.  The anti-gravitational force is the sum of the outward force (M_w d²R/dt_o²) where t_o is the absolute time at the centre of the universe, due to the dark matter (M_w) left over following formation of ordinary matter (M_P), and the inward force (M_P d²R/dt_o²) due to the ordinary matter. F is shown to be related to the universal gravitational constant (G) by the formula, F = m_o.c² (1 – α²) where m_o = c²/G, c is the velocity of light, and α = M_P/M_w.

In the present mature universe, observations indicate that   α = 0.235, from which the anti-gravitational force, F = 1.14 10⁴⁴ N.  At a radius, R, the net outward force is, F (1 – (R₁ / R)²)), which is positive for R/R₁ > 1 and negative for R/R₁ < 1 where R₁ is the radius of the universe, which observations show is 0.90 10²⁶ m.

In the early universe, the exponential-stress model predicts that an inner universe is first formed, bounded by the radius at which the azimuthal velocity attains the velocity of light. Planetary observations show that this radius is 1.25 10¹⁶ m and that it is attained in the remarkably short period of 0.91 yr.  The inner universe, of which we are a part, has the paramount property that F (0) = 0, i.e. the initial net stress force is zero.  This has enabled evolution to persist in the inner universe to this day.