To explain a little further about the difference between the hot Big Bang of Singularity theorem and the hot Big Bang of Inflation theorem, it might be worth looking at where the former fails.
We know that the discovery of a cosmological constant with a positive value in 1998 violated the terms and conditions under which Singularity theorem applies. We also know that General Relativity breaks down at infinities, meaning that it cannot actually tell us anything about the very thing it predicts - a singularity.
But there is a third problem with Hawking and Penrose’s theorem that arises from the way they reversed the flow of time to get the initial singularity to ‘push’ the universe open and to cause it to expand. Their theorem comes in two parts, the first dealing with the gravitational singularities of black holes and the second dealing with the cosmological singularity that was the origin of the entire universe.
Their calculations showed that the core of a massive star MUST collapse to form a gravitational singularity when that star explodes and dies. Such a collapse is spherical because the star itself is spherical. The sphere of the core implodes, collapsing into itself in a spherical fashion, growing smaller and smaller until it becomes a point of infinite density and infinite spatial curvature.
But if you reverse that spherical collapse and apply the equations in reverse to how the initial singularity MUST expand, then it must likewise do so in a spherical fashion, becoming larger and larger until it becomes the entire universe. Which means that the universe it creates is a sphere. Which is a problem, because a spherical universe violates the underlying principles of General Relativity and also violates the Cosmological Principle.
Cosmological principle - Wikipedia
In General Relativity the status of all observers and every location are considered to be equal and equivalent. There is no absolute frame of reference by which locality or movement can be measured. That is why in GR, everything is relative, not absolute. My location cannot be ascertained by measuring anything except another observer’s. Yours cannot be ascertained by measuring anything except another observer’s. Therefore the positions of all observers are relative to each others. Nothing is absolute.
But in the spherically expanding universe that emerges from the initial singularity there is an absolute frame of reference. Any sphere will have a centre, a radius and a boundary. So one observer could be closer to the centre than another. Which means that their status is not equal, equivalent and relative.
This violates the basic principles of General Relativity.
And so Hawking and Penrose’s time-reversed expanding universe, which was generated by using the equations of General Relativity ended up violating the very thing that created it.
However, Inflation theorem suffers from none of the above problems. There are no infinities in it to generate a singularity which will cause a breakdown in GR. There is no centre and no edge to the universe in Inflation theorem, which means that all observers everywhere share the same equal and equivalent status. Finally, a positive cosmological constant is not a problem that spells the failure and refutation of the theorem, as it did for Singularity theorem.
I will explain all about these things in the coming days in the Inflation thread.
Thank you,
Walter.