Could the matter that is sucked into the black hole be crushed into an infinitely dense ball, similar to the one which started our universe. I have other ideas about this thought, but wanted to see what other people have to say about it.

Black holes aren't infinitely dense. Their volume has been infinitely compressed, which just means that mathematically we don't know what's going on in there when so much mass is so dense. That's the way I understand it.

Black hole does not have infinite mass.

Black hole does not have infinite volume.

 

After sucking more and more particles with time,

either mass and volume of BH is growing.

This idea has been looked at, for example:

https://www.insidescience.org/news/every-black-hole-contains-new-universe

http://www.forbes.com/sites/startswithabang/2016/10/20/could-our-universe-have-arisen-from-a-black-hole/

 

I don't think anyone has ruled it out, but it hasn't been confirmed either. We need a theory of quantum gravity to have a better understanding of (a) black holes and (b) the early universe.

Do you really understand the theory of black holes before making any speculations?

 

Consider this:

 

A black hole prevents light (photons) from escaping its surface. If this is true of photons then it must be true of gravitons.

 

If gravitons cannot escape the surface of a black hole, then a black hole cannot exert any gravitational force! Cannot attract any other object!

 

A black hole doesn't exist -- Even though many supermassive objects do exist in the universe.

There is no evidence that gravitons exist. And, apart from that, a black hole would not need to emit gravitons any more than a magnet emits photons. Gravity would be mediated by virtual gravitons (in the same way that magnetism is mediated by virtual photons). These are not really particles and so the problem doesn't arise.

 

As gravity is (currently) described in terms of space-time curvature, the existence or behaviour of gravitons is moot.

In point of detail under GR gravity doesn't escape a Bh. Spacetime curvature itself is gravity and has no need to escape