[Yahya A.Sharif]

The initial singularity of the universe contained infinite gravity density, the universe and space-time were created by the big bang, all gravity contained by this singularity " gravity of all matter of the universe "expanded to infinity.

Your view of the big bang is out dated, all mass did not appear from a singularity. It appeared from inflating areas of space where mass did not exist. Have a look at inflationary theory Guth > Linde etc

This theory explains what happens after the big bang and after the initial singularity, even though matter didn't exist , high density energy exited.
https://en.wikipedia.org/wiki/Inflation_(cosmology)

[pensador]

This theory explains what happens after the big bang and after the initial singularity, even though matter didn't exist , high density energy exited.
https://en.wikipedia.org/wiki/Inflation_(cosmology)

That link is misleading.
Try this one https://profmattstrassler.com/2014/03/17/my-new-articles-on-big-bang-inflation-etc/

Other models exist, which are also only theoretical. That indicate that as the expansion of space accelerates, and matter becomes separated another inflationary phase will be reached and another big bang will happen. forget the singularity, its a result of a outdated mathematical model. 

De sitter universe is interesting too, inflation will take place in the absence of mass and cause a big bang, if I understood it right. 

Edit a better link on inflation https://profmattstrassler.com/articles-and-posts/relativity-space-astronomy-and-cosmology/history-of-the-universe/inflation/

[esquire]

when i view images of the cmbr, i see possible evidence of a cyclical expansion. the temperature gradiant appears to swirl in a fairly consistant manner and direction.  now, consider this cyclical expansion an oscillation of an expanding universe, a universe that is expanding and then rescinding, as described by the cyclic model. if the universe experiences periods of oscillation, then the oscillations must be examined for causation, with gravity being undoubtedly a component. so if, gravity plays a part in the contractions of the universe. how does this comport with its infinite or finite reach?

in the cyclic model each oscillation is followed by an expansion. the size of the expansions and contractions remain uniformed to the previous expansion. so that when a contraction takes place an increase in matter ensues, followed by an increase in gravity. when an expansion cycle takes place, the universe expands proportionally in response to the increase in gravity via a repeller/attractor model for dark matter. in this case dark matter constites the hidden atractor that forments the expansion cycle. 

if the above is represenative, gravity is reduced to a secondary status during the expansion phase, which in essence limits it's effect. can anything that is limited, truly be infinite? logic dictates, it cannot.

[yor_on (OP)]

Yahya, what Alan gave you defining infinity I would call a equation, or formula, and its purpose was exactly the same as what you argue, that's it's not measurable.