My understanding of the Big Bang theory is that the age of the universe is calculated using the background radiation strength (equivalent of red shift) and calculating backwards how much time it would have taken for it to decay to current levels.

Question 1 > Is it possible that there were more than one big - bangs and the current background radiation is a composite of all of them ?

Also I understand that a blackhole is the reverse of a big bang. Does a blackhole ever return to the main universe (ceases to be a singularity) ? In case that happens - is it like new space-time being created / big-bang?

Question 2> Is it possible to have two different space times merge ? or new space time created from a singularity in an existing space-time ?

Our best understanding of things is that two distinct spacetimes can’t merge in the way you’re thinking about, at least not given our current understanding of general relativity. Given the equations that we use to describe the curvature of spacetime, you can prove mathematically that they don’t allow the topology (basically, the shape) of the Universe to change.[sup]1[/sup] Two Universes merging into one Universe counts as a topology change, so it’s disallowed.

Given the above result, I think it renders your question #1 moot. (Unless you’re talking about a Big Bang that preceded the most recent one in time — a sort of temporally cyclic universe, which is discussed in some speculative physics theories these days but isn’t on a firm scientific basis at all.)

[sup]1[/sup] Technically, topology change is allowed if something called “closed timelike curves” exist, which are basically ways to travel through space and time and get back to the same place and moment as you started out. But this wouldn’t be the case in the sort of scenario that we’re talking about here.

Thanks Mike. Isn’t Hawking radiation a sort of mini-bigbang of sorts ? Isn’t it new space time when these radiation particles come out of the singularity into the existing space time ?

Highly unlikely, the background radiation is very even. There may well have been more than one Big Bang, perhaps an immense number of them; but if so they are inaccessible to us.

Given enough time black holes will decay into radiation.

According to some cosmologists it’s possible for two universes to interpenetrate.

Two Universe merging into one basically means the spacetime has no Cauchy surfaces (for the reason of topology that you note), so it is actually the stronger condition of global hyperbolicity rather than the condition of being chronologically non-vicious (i.e. no CTCs).

That said though for any given set of initial conditions which admit a globally hyperbolic solution (note not all initial conditions will admit a globally hyperbolic solution), there are an infinite number of solutions which aren’t globally hyperbolic. So unless you know the entire history of a spacetime you can only assert it is globally hyperbolic axiomatically.

So I would actually say the idea of two big bang Universe merging into one is perfectly cromulent in regards to the equations of general relativity (of course this is without working out the details of how it merges), however we usually preclude these possibilities, mainly on the basis that the time evolution becomes completely unpredictable.

The most mainstream model which would allow for “multiple Big Bangs” is the eternal inflation model, but in that model, if there were multiple Big Bangs, they would be swept apart so quickly that there would be no chance of them ever interacting.

How can spacetimes merge when the properties necessary to allow things to merge (i.e. being in the same place at the same time) are internal features of spacetime?

There is a problem when describing the situation in that it is very easy to use potentially misleading language. The basic idea though would be that you have two separate Universes (i.e. spatially inextendible regions) with no way that anything can travel between the two, however at some point in each of their histories a wormhole opens allowing travel between the two. This is the situation which I think best fits the spirit of the OP.

Of course from a mathematical point of view the whole situation is only described by one connected 4D Lorentzian manifold (i.e. one spacetime), though the most natural way to describe the situation would be to examine the properties of several different subsets of the spacetime (e.g. Universe A before wormhole, Universe B before wormhole and total Universe after wormhole).

You could also have two different 3+1 dimensional manifolds embedded in some higher-dimensional space, and then have them collide via motion in those higher dimensions.