3.1 Problems of Big Bang Cosmology 26 We make another definition, the comoving Event Horizon , as again with the third line coming from the fact that we take ˙ a ( t ) > 0. This is the maximum distance that light (information) can travel in the (infinite) future. An event that occurs at a spacetime point cannot influence an event at a future spacetime point if the latter is outside of the former’s event horizon. The Event Horizon in physical coordinates is given by In reality, Eqs. (3.5) and (3.10) are definitions that use unrealistic bound- ary conditions, as a = 0 , ∞ is unphysical. Therefore, we usually calculate particle and event horizons between two well-defined limits x$_{EH}$ ( t ) ≡ ∫ ∞ t 1 a ( t ) d t (3.6) = η ( ∞ ) − η ( t ) (3.7) x$_{EH}$ ( a ) = ∫ ∞ a 1 a $^{2}$H d a (3.8) a ( t ) x$_{EH}$ ( t ) ≡ a ( t ) ∫ ∞ t 1 a ( t ′ ) d t ′ (3.9) a ( t ) x$_{EH}$ ( a ) = a ( t ) ∫ ∞ a 1 a $^{2}$H d a (3.10) a ( t ) x$_{PH}$ ( a$_{1}$, a ) = a ( t ) ∫ a a$_{1}$ 1 a $^{2}$H d a a ( t ) x$_{EH}$ ( a, a$_{2}$ ) = a ( t ) ∫ a$_{2}$ a 1 a $^{2}$H d a (3.11)