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Quartic-potential slow-roll solution

For

V (ϕ) = λ ϕ^{4} /4

with

H^{2} ≃ 8 π G V / (3 c^{2})

and positive

ϕ

,

ϕ (t) = ϕ_{0} exp [- c \frac{λ}{6 π G} (t - t_{0})],

and

a (ϕ) = a_{0} exp [\frac{π G}{c ^{2}} (ϕ_{0}^{2} - ϕ^{2})] .

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Solution