Conditions for generating scale-invariant density perturbations

Steven Gratton, Justin Khoury, Paul J. Steinhardt, Neil Turok

Research output: Contribution to journalArticlepeer-review

79 Scopus citations


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 the possibility of models which (in the four dimensional effective description) bounce from a contracting to an expanding phase. We show that there are only two stable cases: [Formula Presented] and [Formula Presented] The first is utilized in inflationary models and the second in the ekpyrotic/cyclic scenario, assuming the perturbations propagate through the bounce. All other cases, including the [Formula Presented] case considered by some authors, require extreme fine-tuning of initial conditions and/or the effective potential. For the ekpyrotic/cyclic [Formula Presented] case, we also analyze the small deviations from scale invariance.

Original languageEnglish (US)
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number10
StatePublished - 2004

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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