The Infinitude of Time
It's widely accepted that time is infinite in the future direction. Is it also infinite in the past direction? Some thoughts:
Some cosmological models have a beginning of time. But there are others that have infinite past time. I'm not a cosmologist, so I can't say much more. I'll just comment on the philosophical arguments.
Some philosophers claim there must be a beginning of time, because otherwise there would be an "actual infinity", or an infinite series would be "completed". I think this argument is refuted by Zeno's Paradox. To move from point A to point B, an object must first reach the halfway point. But before that, it must reach the 1/4 mark. Before that, the 1/8 mark, etc. This is an infinite series of preconditions that is actually completed every time an object moves.
Also, some theists say that God "created time". But even God could not do this. The creation of X requires a time when X does not exist, followed by a time when X exists. But there couldn't have been a time when time did not exist. Similarly, with or without God, there could not have been an event of time coming into existence, since that requires a time when there was no time.
The idea of a beginning of time is like the idea of an edge of space. It's not logically contradictory (there's a consistent mathematical structure for it), but when you try to imagine it, it seems impossible. When you try to imagine the edge of space, you find yourself imagining looking past the edge, into the place where there is no space -- but there couldn't be such a place. Likewise, when you try to imagine the beginning of time, you imagine time coming into existence -- first there wasn't any time, then there was -- but there couldn't be such an event.
All this makes me suspect that time goes back forever in the past direction.