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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?

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    $\begingroup$ It is meaningless to say "before the Big Bang" because space-time came into being at the Big Bang, so there was no time before that. $\endgroup$ – user21820 Jan 15 '15 at 14:20
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    $\begingroup$ No one can say whether or not the initial state of the universe was a singularity. The current theories are good backward to a point close to, but short of, where such a singularity might have occurred. (See @jwimberley answer.) What happened earlier than that no one can say. Many authors are a bit too loose with the language on this point. Even Stephen Hawking has expressed things in a way that can be misleading. $\endgroup$ – garyp Jan 15 '15 at 14:52
  • $\begingroup$ Very relevant article that addresses this to some extent: profmattstrassler.com/2014/03/21/… $\endgroup$ – Brandon Enright Jan 15 '15 at 15:57
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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.

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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.

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