As far as I know, the laws of physics are time-reversal invariant, which means there is no preferred direction of time. The arrow of time emerges with entropy which is a property of macrostates, not microstates. So, on a microscopic description of physical reality, why do we say the Big Bang happened first, or that it was the beginning of the Universe, if there is no preferred direction of time? Why can't we equally say the Big Bang happened last?
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In CPT-symmetric universe model, universe does not violate CPT symmetry. Instead, at the BigBang pair of universes are born. In one of them time goes forward, while in another - backwards. So, indeed for one of the universes BigBang would be a first event in time arrow, while for another - last event, because it rolls back in time. However, we can't tell these universes apart,- both of them see another counterpart as running backwards in time.
While currently there is no solid evidence of our "sister universe" running backwards in time, some interesting hints may exist. For example, in this Antarctic ANITA experiment, tau neutrinos were detected coming out from Earth. While there exists multiple explanations of this event, one of them (the exotic one) may be that $\nu_\tau$ travels back in time, so in effect we are capturing them from this alternate universe.
Agnius Vasiliauskas
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