Was there a singularity before the Big Bang or after it? I am slightly confused. Some say that the initial state of the universe was a singularity, and some say that before the Big Bang; there was a singularity. Can anybody elucidate?
 A: Different authors use different definitions of "Big Bang". One (the latter you refer to) is that the Big Bang only refers to the expansion of the universe from age $\epsilon$ to a while later, where $\epsilon$ is the earliest time for which the Big Bang theory has experimental/observational support (from nucleosynthesis, CMB, etc.). More formally, this usage restricts the "Big Bang" to refer to the period of expansion from a very small scale factor $a_{min}$ up to some larger scale factor - usually at recombination ($a_{max} = 0.001$). The actual "singularity" at $t=0$ is not the only possibility and does not have direct experimental/observational support.
A: Classical mechanics is full of singularities which disappear when the system is quantized with quantum mechanics.  Example, the singularity of the potential for the hydrogen model of the atom, whose significance  disappears with the solutions of the Schrodinger equation.
The concept of a singularity comes from the classical ( not quantized) theory of General Relativity, a solution of which defines the "kinematics" of what we call Big Bang. This solution fits , as jwimberley's answer states , the observational data, and data are the only gauges we have for deciding whether a theoretical model is valid or not. And, as he says , beyond the observational boundary the model with the singularity is not the only one.
Once a quantized model of gravity is stabilized then this question will also be addressed, although it will still be at the theoretical level. At the moment the only comprehensive models that include the standard model of particle physics and also quantize gravity are string theory models, but there is no standard string theory model for the Big Bang yet. 
