. ▁This ▁feature ▁of ▁the ▁universe ▁can ▁be ▁character ized ▁by ▁a ▁single ▁parameter ▁that ▁is ▁called ▁the ▁scale ▁factor ▁which ▁is ▁a ▁function ▁of ▁time ▁and ▁a ▁single ▁value ▁for ▁all ▁of ▁space ▁at ▁any ▁instant ▁( if ▁the ▁scale ▁factor ▁were ▁a ▁function ▁of ▁space , ▁this ▁would ▁viol ate ▁the ▁cosm ological ▁principle ). ▁By ▁convention , ▁the ▁scale ▁factor ▁is ▁set ▁to ▁be ▁unity ▁at ▁the ▁present ▁time ▁and , ▁because ▁the ▁universe ▁is ▁expand ing , ▁is ▁smaller ▁in ▁the ▁past ▁and ▁larger ▁in ▁the ▁future . ▁Ext rap ol ating ▁back ▁in ▁time ▁with ▁certain ▁cosm ological ▁models ▁will ▁yield ▁a ▁moment ▁when ▁the ▁scale ▁factor ▁was ▁zero ; ▁our ▁current ▁understanding ▁of ▁cosm ology ▁sets ▁this ▁time ▁at ▁ 1 3 . 7 9 9 ▁ ± ▁ 0 . 0 2 1 ▁billion ▁years ▁ago . ▁If ▁the ▁universe ▁continues ▁to ▁expand ▁forever , ▁the ▁scale ▁factor ▁will ▁approach ▁infinity ▁in ▁the ▁future . ▁In ▁principle , ▁there ▁is ▁no ▁reason ▁that ▁the ▁expansion ▁of ▁the ▁universe ▁must ▁be ▁monot onic ▁and ▁there ▁are ▁models ▁where ▁at ▁some ▁time ▁in ▁the ▁future ▁the ▁scale ▁factor ▁decre ases ▁with ▁an ▁att endant ▁contra ction ▁of ▁space ▁rather ▁than ▁an ▁expansion . ▁ ▁Other ▁concept ual ▁models ▁of ▁expansion ▁The ▁expansion ▁of ▁space ▁is ▁often ▁illustrated ▁with ▁concept ual ▁models ▁which ▁show ▁only ▁the ▁size ▁of ▁space ▁at ▁a ▁particular ▁time , ▁leaving ▁the ▁dimension ▁of ▁time ▁implicit . ▁ ▁In ▁the ▁" ant ▁on ▁a ▁rub