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Quadratic-potential slow-roll solution

For

V (ϕ) = m^{2} ϕ^{2}

in units where

3 H^{2} ≃ V

and for positive

ϕ

,

ϕ (t) = ϕ_{i} - \frac{2 m}{3} t,

and

a (t) = a_{i} exp (\frac{m ϕ _{i}}{3} t - \frac{m ^{2} t ^{2}}{3}) = a_{i} exp (\frac{ϕ _{i}^{2} - ϕ ( t ) ^{2}}{4}) .

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Solution