Generation of a scale-invariant spectrum of adiabatic fluctuations in cosmological models with a contracting phase

By F. Finelli, Robert Brandenberger. 2001

364 citations recorded by the source corpus.

In pre-big-bang and in ekpyrotic cosmology, perturbations on cosmological scales today are generated from quantum vacuum fluctuations during a phase when the Universe is contracting (viewed in the Einstein frame). The backgrounds studied to date do not yield a scale-invariant spectrum of adiabatic fluctuations. Here, we present a new contracting background model (neither of pre-big-bang nor of the ekpyrotic form) involving a single scalar field coupled to gravity in which a scale-invariant spectrum of curvature fluctuations and gravitational waves results. The equation of state of this scalar field corresponds to cold matter. We demonstrate that if this contracting phase can be matched via a nonsingular bounce to an expanding Friedmann cosmology, the scale-invariance of the curvature fluctuations is maintained. We also find new background solutions for pre-big-bang and for ekpyrotic cosmology, which involve two scalar fields with exponential potentials with background values which are evolving in time. We comment on the difficulty of obtaining a scale-invariant spectrum of adiabatic fluctuations with background solutions which have been studied in the past.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0e4b8746b645c8e975f64553d09bc23e687f4f40

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Citations in the corpus

Nonsingular cosmology with a scale-invariant spectrum of cosmological perturbations from Lee-Wick theory (2008, background): “The second way is realized in the case of a matter-dominated contraction, a possibility already pointed out in [11] (see also [47]).”
Matter bounce in Horava-Lifshitz cosmology (2009, background): “As realized in [14, 15, 16], perturbations which start out as quantum vacuum fluctuations and exit the Hubble radius during a matter-dominated phase of contraction acquire a scale-invariant spectrum.”
The matter bounce scenario in loop quantum cosmology (2012, background): “As we shall see, some of the results obtained here are significantly different from those obtained in the matching procedure of [5]; these differences are due to modifications of the Friedmann and Mukhanov-Sasaki equations from quantum gravity effects.”
An infinite set of Ward identities for adiabatic modes in cosmology (2013, background): “Conversely, to observe a significant 3-point function in this limit requires violating one of the assumptions above, for instance through additional scalar fields [23–28] or an unstable background [29, 30, 33, 34].”
Non-singular cosmology in a model of non-relativistic gravity (2009, background): “One model of bouncing cosmology with a matter-dominated contraction was found to be able to provide a scale-invariant spectrum [36–40] and sizable non-Gaussianities [41, 42], which may be responsible for the current cosmological observations.”
The Matter Bounce Alternative to Inflationary Cosmology (2012, background): “[3] F.”
Trans-Planckian censorship and inflationary cosmology (2019, background): “the matter bounce [15], and the Pre-Big-Bang [16] and Ekpyrotic [17] scenarios), where the initial phase is one of contraction.”