"In the case where the universe does not recollapse, the proper distance to the is...d_{MAX}(t) = a(t) \int_{0}^{r_{MAX}(t)} \frac{dr}{\sqrt{1-Kr^2}} = a(t)\int_{0}^{\infty} \frac{dt'}{a(t')}... In the absence of a cosmological constant, a(t) grows like t^{\frac{2}{3}}, and the integral diverges, so there is no event horizon. But with a cosmological constant, a(t) will eventually grow as exp(Ht) with H = H_0 \Omega^{1/2}_\Lambda constant and... an event horizon... approaches... d_{MAX}(\infty) = 1/H. As time passes all sources of light outside our gravitationally bound will move beyond this... and become unobservable. The same is true for the quintessence theory... In that case a(t) eventually grows as exp(const \times\, t^{2/{(2+\frac{\alpha}{2})}}), so for any \alpha \ge 0 the integral... [d_{MAX}(t)] converges."