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Cosmic inflation

Slow-roll approximation

Comoving curvature perturbation

{title2=$\Delta_{\mathcal R}^2$}

At leading order in canonical single-field slow roll and evaluated at horizon exit $k=aH$,
$$
\Delta_{\mathcal R}^2(k)=\frac1{2\epsilon M_{\rm Pl}^2}
\left(\frac{H}{2\pi}\right)^2.
$$


Slow-roll curvature power spectrum

Scalar spectral index in Hubble slow-roll parameters

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 310 / 4 / b / Solution

Slow-roll curvature power spectrum ( $Δ_{R}^{2}$ )

Scalar spectral index in Hubble slow-roll parameters ( $n_{s} - 1 = - 2 ϵ - η$ )

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Slow-roll curvature power spectrum (ΔR2​)

Scalar spectral index in Hubble slow-roll parameters (ns​−1=−2ϵ−η)