universe. 

Here we have investigated the effect of running couplings on the curvature invariant as the seed for initial perturbations, by deriving the improved Mukhanov–Sassaki equation. We saw that this can be solved iteratively. 

The gravitational coupling is almost constant in the radiation and matter dominated eras and thus the transfer function of perturbations to the power spectrum is not improved. We obtained the improved power spectrum and observed that it is slightly improved for large wave numbers. This means that the tail of the predicted power spectrum comes more closer to the observed data. 

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