two signs?

Let’s have a look at the Hubble-function for a \(\Lambda\)-dominated flat FLRW-universe: \(\left(\frac{\dot{a}}{a}\right)^2 = H_0^2\Omega_\Lambda\) which would result in a solution \(a(t) = \exp(\pm H_0t)\), where usually the minus-sign is discarded: is that justified? Shouldn’t it be possible to assign a gravitational effect to a \(\Omega_\Lambda > 0\) that is unambiguous?