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Conditions for Generating Scale-Invariant Density Perturbations

Steven Gratton·Justin Khoury·Paul J. Steinhardt·Neil Turok
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Abstract

We analyze the general conditions on the equation of state $w$ required for quantum fluctuations of a scalar field to produce a scale-invariant spectrum of density perturbations, including models which (in the four dimensional effective description) bounce from a contracting to an expanding phase. We show that there are only two robust cases: $w\approx -1$ (inflation) and $w \gg 1$ (the ekpyrotic/cyclic scenario). All other cases, including the $w \approx 0$ case considered by some authors, require extreme fine-tuning of initial conditions and/or the effective potential. For the ekpyrotic/cyclic ($w \gg 1$) case, we also analyze the small deviations from scale invariance.

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Steven Gratton, Justin Khoury, Paul J. Steinhardt, Neil Turok. 2003-01-20. Conditions for Generating Scale-Invariant Density Perturbations. https://doi.org/10.1103/physrevd.69.103505

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