One question I have: is it not possible that the big bang occurred an infinite time ago? If the expansion of the universe is accelerating with time, does it not indicate that, if we reverse the time, the deceleration is asymptotic?
In that case the big bang is compatible with a universe that has always existed and did not have a beginning
The idea is interesting and probably not unique. If you try to paint a diagram of it, how would that look? It's not time that is accelerating, so you don't just draw the time axis just longer with wider gaps between the minute marks. Which leaves me guessing and remembering my old, discrete notion that time is count of change of things, so that, for sake of argument, in one unit of time, one state change happens. In that setting, it doesn't make sense to say a change was further apart than another. Actually, information decreases, thermodynamically speaking. So, tracking back infinitely, you'd have to start with an infinite amount of entropy, proportional to energy. But the theory assumes a fixed amount of energy, as far as I know.
And it's not that the lightspeed increases with time, either. Rather, so they say, space expands - which is imaged trivially by stretching the space axis. I suppose that's normalizing for time and you could just as well fix space and compress time, invariably, to arrive at your notion, with a total lack of rigour at that.
A big bang event could explain the reason why the universe expanded in the first place, but it does not explain the accelerating expansion of the universe currently, forgive me for my ignorance if any, but in physics I was taught that any object which moves or is in constant motion was acted upon by a force, and so if the big bang created an expansion it will be a constant expansion and not an accelerating expansion as is obtained presently, as there is a requirement for a kind of force to cause an accelerating expansion which is not explained by a singular big bang but by a continuous big bang, which could as well be infinite in nature.
Again IANAP (and I'm sure any actual physicist will be horrified by my explanation), but the big bang is not an explosion that a time 0 set some mass in motion. But you are, in a way, right: the big bang is not over, is literally still happening right now. General relativity still predict that the process started a finite amount of time ago; wether the process will continue indefinitely or not is still an open question.
The expansion is an expected behaviour of space time, and is predicted by general relativity given a certain parametrization of the density of matter an energy of the universe. To explain the acceleration, though, a large energy parameter is required, which has not been yet identified with any known process, although many theories exhist; as placeholder the parameter is known as dark energy. It is of course possible, but generally considered unlikely, that general relativity is incomplete and another theory could explain the acceleration without dark energy.
The question is, does causality require time? I understand that physics can give us a definition of time as far as "happens-before" relationships go, but are "happens-before" and "happens-because-of" necessarily the same thing?
If the world has begun with a single quantum,
the notions of space and time would altogether
fail to have any meaning at the beginning;
they would only begin to have a sensible meaning
when the original quantum had been divided into
a sufficient number of quanta. If this suggestion
is correct, the beginning of the world happened
a little before the beginning of space and time.
Lemaître, G. (1931). "The Beginning of the World from the Point of View of Quantum Theory"
> If the expansion of the universe is accelerating with time
The expansion is accelerating now, but from the big bang up until a few billion years ago, it wasn't; it was decelerating. So you can't just extrapolate the current acceleration back in time.
That is a really interesting way to look at it, and yes since in reverse time, the acceleration never quite reaches zero, the universe can then be though of as an infinite occurrence that has always been expanding with no starting point.
> is it not possible that the big bang occurred an infinite time ago?
It depends on what you mean by "the big bang". The strictly correct meaning of "the big bang" is "the hot, dense, rapidly expanding state of the universe that is the earliest state for which we have good evidence". We know that state occurred a finite time ago--about 13.7 billion years.
What we don't know for sure is what came before that state, or how far into the past whatever came before it extends. The current best theory we have is that it was some kind of inflationary epoch, but different models of inflation give different answers to the question of how far back in time that epoch extended. AFAIK the possibility that inflation extended infinitely far back in time (i.e., that there was never any "initial singularity") has not been ruled out.
In that case the big bang is compatible with a universe that has always existed and did not have a beginning