The cosmological equations are
(Weinberg 1972, p. 614) and
where R is the distance scale,
is the cosmological constant, and
is the universe's radius of curvature. The qualitative behavior of R(t) is determined from (1), and the three resulting solution regimes are called the de Sitter, Friedmann-Lemaître Cosmological Model, and
Defining
and integrating (1) gives
(1) and (2) can be rewritten as
and
Taking
gives
which can be rewritten as
(1)
(Weinberg 1972, p. 614) and
(2)
where R is the distance scale,
is the cosmological constant, and (3)
is the universe's radius of curvature. The qualitative behavior of R(t) is determined from (1), and the three resulting solution regimes are called the de Sitter, Friedmann-Lemaître Cosmological Model, and
Defining
(4)
and integrating (1) gives
(5)
(6)
(1) and (2) can be rewritten as
(7)
and
(8)
Taking
gives (9)
which can be rewritten as
(10)
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