Hubble slow-roll parameter

A Hubble slow-roll parameter measures the fractional change of the Hubble rate or of a preceding slow-roll parameter per e-fold. Small values make the inflationary background evolve adiabatically.

The first Hubble slow-roll parameter is

ϵ = - \frac{H ˙}{H ^{2}} .

(1)

For a canonical inflaton,

ϵ = \dot{ϕ}^{2} / (2 M_{Pl}^{2} H^{2}) \geq 0

Second Hubble slow-roll parameter ( $η$ )

 0  0

Using the e-fold variable

N = lo g a

, define

η = \frac{d l o g ϵ}{d N} .

(1)

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Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 310 / 4 / b / Solution

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Hubble slow-roll parameter

First Hubble slow-roll parameter (ϵ)

Second Hubble slow-roll parameter (η)

 Ancestors (6)

 Incoming links (1)

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First Hubble slow-roll parameter ( $ϵ$ )

Second Hubble slow-roll parameter ( $η$ )

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