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We know that this is observationally false, since in fact ##\ddot{a}>0##.

But why do they assume this?

My guess is that in the big-bang model there is a period where radiation and matter dominates over the cosmological constant and it is in this regime that ##\ddot{a}<0##.

Another guess could be that theorists of the time didn't know that ##\ddot{a}>0##. But I don't think this is a good enough answer since people keep talking about inflation so there has to be some reasoning behind the assumption that ##\ddot{a}<0## after inflation.

So, what going on here?

Thanks.