# Hubble time dilation

The Hubble time dilation is a hypothetical effect of accumulation of time dilation (in curved space) with distance from observer, so for small distances it looks roughly propotional to the distance. The exact effect is

dτ / dt = exp( − r / Rs),

where τ is proper time at event in deep space (time of deep space), t is coordinate time of the event (time of observer), r is distance to the event in deep space from observer, and Rs is radius of curvature of space (about 13 billion light years, called by cosmologists Einstein's radius of universe, or RE). The above equation implies that the observed cosmological redshift is caused by the difference between τ and t and the Hubble constant of our universe equals

Ho = c / Rs,

where c is speed of light in vacuum and Rs is as before the radius of curvature of space. When this Hubble constant, being in reality an exponential function

H(r) = Z / r = [exp(r / Rs) − 1] / r,

where Z is observed redshift of deep space galaxy, r is distance to this deep space galaxy, is split into Taylor series around r = ct = 0 it simmulates an accelerating expansion of space as observed in 1998 with accuracy to one standard deviation (maximum available accuracy of observation confirming an astronomical oservation as consistent with theory) as

$dH/dt=-H_o^2/2$,

where dH / dt is change of Hubble constant with distance in time units t, and Ho is Hubble constant itself.

This result has been then taken for the action of "dark energy" since news about gravitation demystified were not published since February 1985 when the fact that our universe is stationary has been discovered through never done before, simple, Newtonian calculation of redshift in stationary universe of density approximately

$6\times 10^{-27}kg/m^3$

as explained in gravitation demystified article.