Byblos wrote:Of course the math conceptually works. I don't even have an issue with positing an eternal steady state followed by an inflationary period. Except an eternal steady state does not, cannot on its own, arbitrarily give rise to inflation.
Probably true, depending on your definition of eternal. If time is a measure of change, then the term "eternal steady state" might have no meaning.
I don't want to get bogged down with the semantics of defining eternity and what the term "eternal steady state" means because then we venture into the metaphysical.
The fact is that the BVG theorem is independent (meaning it still holds) of the physical reality including quantum gravity (with a caveat), so long as the single condition still holds, i.e. Havg > 0. This is confirmed by Alexander Vilenkin (one third of the BVG). In an exchange with William Lane Craig Vilenkin said this:
Vilenkin wrote:The question of whether or not the universe had a beginning assumes a classical spacetime, in which the notions of time and causality can be defined. On very small time and length scales, quantum fluctuations in the structure of spacetime could be so large that these classical concepts become totally inapplicable. Then we do not really have a language to describe what is happening, because all our physics concepts are deeply rooted in the concepts of space and time. This is what I mean when I say that we do not even know what the right questions are.
The underlined being the caveat I referred to.
Of course some would argue an 'aha' moment with the reference to classical spacetime and contend (wrongly) that the theorem is only applicable to classical spacetime but not to quantum gravity, meaning that if Einstein's equations were to be altered then BVG doesn't apply.
But then he continues:
Vilenkin wrote:But if the fluctuations are not so wild as to invalidate classical spacetime, the BGV theorem is immune to any possible modifications of Einstein's equations which may be caused by quantum effects.
Craig pressed Vilenkin on this very issue and wrote him the following, asking for an explanation, which Vilenkin confirmed as an accurate description of the theorem:
Craig wrote: A ‘classical picture of spacetime’ should not be equated with general relativistic spacetime. For special relativistic spacetime, for example, also is a classical picture of spacetime. So the theorem does not presuppose general relativistic spacetime but simply a spacetime that is classical in the sense that it is linearly ordered temporally and so can be said to be expanding in the ‘later than’ direction. In any such spacetime a universe that is, on average, in a state of expansion can’t be past-eternal. But in a quantum gravity regime, if the linear ordering of time is abolished, then it is impossible to speak of expanding, and so the theorem’s one condition isn’t met. The question, then, is not one’s gravitational theory, but whether time exists in one’s model. Quantum gravity theories that do feature a linear temporal ordering fall under the theorem and so will not be past-eternal.
Note the emphasized.
Read the full blog here
which was written as a response to a debate exchange between Lawrence Krauss and Craig in which Krauss had inaccruately quoted Vilenkin.