( ( Since ( ( ( a ( given volume ) ) ( of space ) ) ( is ( ( expanding , ) ( if ( we ( assume ( that ( ( ( the ( total amount ) ) ( of ( matter ( within ( the volume ) ) ) ) ) ( is conserved ) ) ) ) ) ) ) ) ) ) ( , ( ( ( the density ) ( of matter ) ) ( ( must ( be ( decreasing ( with time ) ) ) ) . ) ) ) )
(ROOT (S (SBAR (IN Since) (S (NP (NP (DT a) (VBN given) (NN volume)) (PP (IN of) (NP (NN space)))) (VP (VBZ is) (VP (VBG expanding) (, ,) (SBAR (IN if) (S (NP (PRP we)) (VP (VBP assume) (SBAR (IN that) (S (NP (NP (DT the) (JJ total) (NN amount)) (PP (IN of) (NP (NP (NN matter)) (PP (IN within) (NP (DT the) (NN volume)))))) (VP (VBZ is) (VP (VBN conserved)))))))))))) (, ,) (NP (NP (DT the) (NN density)) (PP (IN of) (NP (NN matter)))) (VP (MD must) (VP (VB be) (VP (VBG decreasing) (PP (IN with) (NP (NN time)))))) (. .)))
Since a given volume of space is expanding, if we assume that the total amount of matter within the volume is conserved, the density of matter must be decreasing with time.
(ROOT (S (NP (DT The) (NN term) (NN volume)) (VP (VBZ means) (SBAR (S (NP (NP (DT the) (NN amount)) (PP (IN of) (NP (NN space) (NN matter)))) (VP (VBZ takes) (PRT (RP up)))))) (. .)))