Scale Invariance via a Phase of Slow Expansion

We consider a cosmological scenario in which a scale-invariant spectrum of curvature perturbations is generated by a rapidly evolving equation of state on a slowly expanding background. This scenario generalizes the ‘‘adiabatic ekpyrotic’’ mechanism proposed recently by Khoury and Steinhardt [Phys. Rev. Lett. 104, 091301 (2010)]. Whereas the original proposal assumed a slowly contracting background, the present work shows that the mechanism works equally well on an expanding background. This greatly expands the realm of broader cosmological scenarios in which this mechanism can be embedded. We present a phase space analysis and show that both the expanding and contracting versions of the scenario are dynamical attractors, with the expanding branch having a broader basin of attraction. In both cases, a finite range of scale-invariant modes can be generated within the regime of validity of perturbation theory. Disciplines Physical Sciences and Mathematics | Physics Comments Suggested Citation: Joyce, A. and Khoury, J. (2011). Scale invariance via a phase of slow expansion. Physical Review D 84, 023508. © 2011 American Physical Society http://dx.doi.org10.1103/PhysRevD.84.023508 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/196 Scale invariance via a phase of slow expansion Austin Joyce and Justin Khoury Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA (Received 6 May 2011; published 11 July 2011) We consider a cosmological scenario in which a scale-invariant spectrum of curvature perturbations is generated by a rapidly evolving equation of state on a slowly expanding background. This scenario generalizes the ‘‘adiabatic ekpyrotic’’ mechanism proposed recently by Khoury and Steinhardt [Phys. Rev. Lett. 104, 091301 (2010)]. Whereas the original proposal assumed a slowly contracting background, the present work shows that the mechanism works equally well on an expanding background. This greatly expands the realm of broader cosmological scenarios in which this mechanism can be embedded. We present a phase space analysis and show that both the expanding and contracting versions of the scenario are dynamical attractors, with the expanding branch having a broader basin of attraction. In both cases, a finite range of scale-invariant modes can be generated within the regime of validity of perturbation theory. DOI: 10.1103/PhysRevD.84.023508 PACS numbers: 98.80.Cq