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I need to convert the number of efolds to confromal time during inflation in order to do numerical integrations. Suppose expansion is De Sitter and you have to calculate the integral $$\int^0_{-\infty} d\tau F(N)$$ where F is a function of the efolds number N (from the beginning of inflation). All issues arise at the integration limits. I know that $$a = - \frac{1}{H \tau} $$ but I cannot obtain the correct relationship between N and τ.

(My guess is $$\tau = - \frac{1}{H e^N} $$ but this doesn't seem to be correct. In fact for ##N\rightarrow \infty## we get ##\tau \rightarrow 0##, but for ##N\rightarrow 0## we get ##\tau\rightarrow - \frac{1}{H}##)

Can anyone help me?

Thanks

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# I Conformal time and efolds

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