▁important . ▁ ▁These ▁situations ▁are ▁described ▁by ▁general ▁relativ ity , ▁which ▁allows ▁the ▁separation ▁between ▁two ▁distant ▁objects ▁to ▁increase ▁faster ▁than ▁the ▁speed ▁of ▁light , ▁although ▁the ▁definition ▁of ▁" distance " ▁here ▁is ▁somewhat ▁different ▁from ▁that ▁used ▁in ▁an ▁in ert ial ▁frame . ▁ ▁The ▁definition ▁of ▁distance ▁used ▁here ▁is ▁the ▁summ ation ▁or ▁integration ▁of ▁local ▁com oving ▁distances , ▁all ▁done ▁at ▁constant ▁local ▁proper ▁time . ▁ ▁For ▁example , ▁galaxies ▁that ▁are ▁more ▁than ▁the ▁Hub ble ▁radius , ▁approximately ▁ 4 . 5   g ig ap arse cs ▁or ▁ 1 4 . 7 ▁billion ▁light - year s , ▁away ▁from ▁us ▁have ▁a ▁re cess ion ▁speed ▁that ▁is ▁faster ▁than ▁the ▁speed ▁of ▁light . ▁ ▁Vis ibility ▁of ▁these ▁objects ▁depends ▁on ▁the ▁exact ▁expansion ▁history ▁of ▁the ▁universe . ▁ ▁Light ▁that ▁is ▁em itted ▁today ▁from ▁galaxies ▁beyond ▁the ▁cosm ological ▁event ▁horizon , ▁about ▁ 5   g ig ap arse cs ▁or ▁ 1 6 ▁billion ▁light - year s , ▁will ▁never ▁reach ▁us , ▁although ▁we ▁can ▁still ▁see ▁the ▁light ▁that ▁these ▁galaxies ▁em itted ▁in ▁the ▁past . ▁ ▁Sc ale ▁factor ▁At ▁a ▁fundamental ▁level , ▁the ▁expansion ▁of ▁the ▁universe ▁is ▁a ▁property ▁of ▁spatial ▁measurement ▁on ▁the ▁largest ▁meas urable ▁scales ▁of ▁our ▁universe . ▁The ▁distances ▁between ▁cosm olog ically ▁relevant ▁points ▁increases ▁as ▁time ▁passes ▁leading ▁to ▁observable ▁effects ▁out lined ▁below