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So while learning about modelling inflation using a single scalar field slow roll, most authors seem to use the Friedmann equation with the spatial curvature taken to be 0. Now one of the precursors that led to inflation was that inflation could solve the flatness problem. So at the beginning of inflation the dimensionless quantity defined as $\frac{|k|}{H^2 a^2}$ can be of order unity and then at the end of inflation decrease drastically. However, wherever I read the entire inflationary phase using the slow roll model is done as I said using $k=0$ in the Friedmann equations. Now my first thought is that may be it is reasonable because the curvature contribution will quickly decrease as $a$ expands, but given that inflation itself happens for a short duration is this justifiable. The other possible explanation is that it is just for analytic convenience. I would really appreciate any leads on this issue.

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