<P> The criterion for determining whether a particle horizon for the Universe exists is as follows . Define a comoving distance d p (\ displaystyle d_ (p)) by </P> <Dl> <Dd> d p = ∫ 0 t 0 c a (t) d t . (\ displaystyle d_ (p) = \ int _ (0) ^ (t_ (0)) (\ frac (c) (a (t))) dt \ .) </Dd> </Dl> <Dd> d p = ∫ 0 t 0 c a (t) d t . (\ displaystyle d_ (p) = \ int _ (0) ^ (t_ (0)) (\ frac (c) (a (t))) dt \ .) </Dd> <P> In this equation, a is the scale factor, c is the speed of light, and t is the age of the Universe . If d p → ∞ (\ displaystyle d_ (p) \ rightarrow \ infty) (i.e., points arbitrarily as far away as can be observed), then no event horizon exists . If d p ≠ ∞ (\ displaystyle d_ (p) \ neq \ infty), a horizon is present . </P>

What is the escape speed at the event horizon of a black hole