avery said:
is our universe the unique possible outcome of the big bang regardless of the original state?
if not, what are the factors that may change the universe as we know it today?
Short answer is no, not unique regardless of prior state. Leonard Parker is a reputable guy who has addressed this precise problem. He has a comparatively LESS TECHNICAL presentation, as an essay for nonspecialists, written with a younger guy named Ivan Agullo.
The Gravity Research Foundation awarded it their first prize in 2011. If inflation were preceded by a period of contraction, for example, traces of the past would be expected to survive inflation---IOW could not be stretched out to featureless uniformity.
http://arxiv.org/abs/1106.4240
Stimulated creation of quanta during inflation and the observable universe
Ivan Agullo, Leonard Parker
(Submitted on 21 Jun 2011)
Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when the corresponding
stimulated creation of quanta is considered,
the characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary expansion and can be imprinted in the spectrum of primordial inhomogeneities. The non-gaussianities (particularly in the so-called squeezed configuration) in the cosmic microwave background and galaxy distribution can then tell us about the state of the universe that existed at the time when quantum field theory in curved spacetime first emerged as a plausible effective theory.
9 pages. Awarded with the First Prize in the Gravity Research Foundation Essay Competition 2011
This is important. It means one can expect that whatever states preceded the start of expansion
would have had an effect.
What was there immediately prior, e.g. during a contracting phase,
would have made a difference.
So no, there are no grounds for believing that what we have now is the sole way things could be "regardless" (as you say) of what conditions and process preceded the start of expansion.