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In the Friedmann equations, an infinite initial density is avoided only whenthe universe is spatially flat. With such equations being then valid when thescale factor $a=0$, the universe must also be in the state of vacuum when $a$is infinitesimal. Matter creation thus largely comes from nonlinearity of theFriedmann equations at a finite $a$. For the correspondence between such aninitial vacuum and the Friedmann universe, therefore, a vacuum density issuggested to be gravitationally significant only when it could also have amatter phase. The effective cosmological term is then due to such a vacuumdensity.

Initial Friedmann universe, its spatial flatness, matter creation, and the cosmological term