Einstein tells us and it has been observed the rate at which time moves is slower is all environments where the gravitation density is greater than where it is being observed from. (please see graphic)   This means, the further we look back in time, where the gravitational density of the universe was greater the slower time would move and for events to occur from the of the present than they actually did.  In other words this would suggest that it evolved faster in the past and therefore is younger that the present value if considers the Relativistic slowing of time when determining the expansion rate of the universe. However, we also know the gravitational density of the universe has a nonlinear slowing effect on its expansion because its attractive properties decrease as the volume of the universes increase due to its expansion.   In other words, the gravitational density has an opposite effect on its expansion. Therefore, to determine the actual the rate of expansion of the universe at each point in its history one must not only take into account the time dilation due to its gravitational density but also the slowing effect that density has on its expansion at each of those point.  In other words, one makes it APPEAR to move slower while the other faster.

Yet, because of the non-linear effects between the time dilation created by its gravitational density and the effects that density has on the universe rate of expansion there will be a point in its history were one will APPEAR to overtake the other.

The fact that it has been observed that about 4 billion years ago the universe’s expansion change from decelerating to an accelerated phase give us a way to verify the above conclusion

In other words if one calculates the expansion rate of the universe by taking into account the APPARENT speeding up of its evolution resulting from the increase rate at time passes due to the decreasing gravitational density of an expanding universe and finds that it counteracts slowing effect cause by that density about 4 billion years ago it would go a long way to verify the above mechanism.

Some may say that gravitational time dilation would not effect the timing of the expansion because it is  also expanding.   However, Einstein define the time dilation only in terms of the effects a differential gravitational potential has on it therefore an expanding universe will have not effect it.  Some may also say that because the universe is expanding the gravitational density is expanding and weakening at the same rate therefore when we look back the effects it will have on the timing of its expansion will cancel.   However, Einstein tells us the timing of events that cause the universe to expand in the past is locked along with the gravitation density of the universe at the time the expansion took place  Therefore, we must measure the the timing of the events that define the them from the perspective of the gravitational density when those events took place.

Other may say the time dilation effect as discussed in this post is introduced in this calculation, the age of the universe might come down heavily.  This would be true if time was the only factor that must be considered when defining the rate of the universe expansion. For example the gravitational density of the universe would not only effect the passage of time but also it would cause a slowing of expansion due to its attractive forces  Therefore, to define its actual expansion rate one must take into account both slowing effect of gravities attractive forces and the effects it has on time.  The apparent change over to an accelerating universe occurs because of the non-linear relationship that gravity has on time and the expansion rate.  It is possible if one takes both the magnitude of gravity attractive force has on the universe expansion rate and time dilation on its expansion we may discover that it is older than the currently accepted value  of 13 billion years.

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