An alternative cosmological model is summarized. Light speed, c, slowly decreases as the cosmic time, t, increases and matches the expansion speed of the Universe itself, since c is the maximum speed at which any two particles can run away, i.e. the top escape velocity. This Universe has a radius, R, predicted by Schwarzschild equation at any time, which second derivative vs. t follows the simple equation:
(1) R’’ = -GM/R2
where G is the gravitational constant, M is the mass of the observable Universe. Combining Schwarzschild equation with (1) and integrating we can obtain:
(2) R =3ct/2
With this self-consistent set of equations, it can be deduced that the Hubble parameter is:
(3) H =2/3t
And, since the radiation temperature T is a measure of photon’s energy, which is proportional to c2, we can obtain:
(4) T/To=Ro/R
where subscript o indicate today’s values. Equations 3 and 4 agree with Einstein-De Sitter model.
In our model, the redshift of distant galaxies has a gravitational contribution reflected in the decrease of light energy, E, since photons suffer the pull of the Universal mass as they travel from the past, more dense, Universe to the present state, in the same way other particles do.
(5) zG = (E-Eo)/Eo = (c2 – co2 )/ 2co2 = Ro-R/2R
As we can see this contribution has one half of the value of the nowadays-accepted expression for z, so that the total redshift would be the sum of both:
(6) z = (Ro/R)-1 + Ro-R/2R = 3r/2(Ro-r)
where r (=Ro-R) is the distance to the observed galaxy. From this equation and direct observational data good lineal fits are obtained, then Ro and M (assumed to be constant) can be estimated, and the time evolution of c, R, T and mass density can be predicted. Some preliminary results are:
ü Ro (m) = 2,0 * 1026
ü to (years) = 1,4 * 1010
ü (dc/dt)o (m/s2) = -2,2* 10-10 (a decay of 1 m/s would be observed in ca.140 years).
Today’s mass density would be 4*10-27 kg/m3 , about 40% of ‘conventional’ critical density. At any time the actual density should be equal to the critical density, i.e., the agreement of the critical density in the Einstein-De Sitter universe with the empirical determinations is not casual. The metric of this Universe is flat and the expansion would continue forever since its rate has exactly the value needed to equilibrate the gravitational pull at any moment. The entire Universe must be causally interconnected so that its maximum expansion rate must be c, since c is also the rate of gravity interactions. This was a problem in the frame of inflation theory, which assumes that, during an early period, the Universe was expanding faster than light. Now this inflation reveals to be not superluminical, although faster than today’s speed of light. Finally the model predicts -without need of introducing an ‘ad hoc’ repulsive dark energy- that supernovae with z near 1 are farther away than previously expected, so that they will appear fainter, as recently observed. Within this model an object showing z=1 is at a distance of 8 * 1025 m; while in conventional models it would be at 6,7 * 1025 m. This difference would lead to about 30% less apparent luminosity.