New duality relating density perturbations in expanding and contracting Friedmann cosmologies

Boyle, Latham A.; Steinhardt, Paul J.; Turok, Neil

doi:10.1103/physrevd.70.023504

Cited by 63 publications

(60 citation statements)

References 45 publications

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“…The scaling symmetry is also general enough to provide reasonable representatives of a large class of models in which the equation of state parameter w varies slowly during the time that primordial perturbations are laid down. Within the context of these scaling solutions it has been possible to completely characterize the conditions under which a scale-invariant spectrum of density perturbation is created, after the spirit of previous studies in the one-field case [64,5,65].…”

Section: Discussionmentioning

confidence: 99%

“…This simple dependence makes it quite straightforward to study the phenomenology of the two field model, as well as to include a variety of other models studied by previous researchers within the framework described here. In these senses we have characterized the natural two-field two-derivative generalizations of the single-field scaling solutions which have been studied in both expanding and collapsing universes [64,5,65].…”

Section: Introductionmentioning

confidence: 99%

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Scale invariance in expanding and contracting universes from two-field models

Tolley

Wesley

2007

J. Cosmol. Astropart. Phys.

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We study cosmological perturbations produced by the most general twoderivative actions involving two scalar fields, coupled to Einstein gravity, with an arbitrary field space metric, that admit scaling solutions. For expanding universes, we find that scaleinvariant adiabatic perturbation spectra can be produced for any equation of state parameter w that satisfies −1 ≤ w < −1/3, and that all the scaling solutions are attractors. For contracting universes, we show that scale-invariant adiabatic perturbations can be produced continuously as modes leave the horizon for any w > −1/3. The corresponding background solutions are unstable, which we argue is a universal feature of contracting models that yield scale-invariant spectra. At no point do we assume slow-roll. The presence of a nontrivial metric on field space is a crucial ingredient in our results.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scale invariance in expanding and contracting universes from two-field models

Tolley

Wesley

2007

J. Cosmol. Astropart. Phys.

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“…(38) in Ref. [62]), where w exit (k) is the equationof-state parameter, evaluated at the moment when k exits the Hubble horizon. Note that Eq.…”

Section: Two Simple Consequencesmentioning

confidence: 99%

Relating gravitational wave constraints from primordial nucleosynthesis, pulsar timing, laser interferometers, and the CMB: Implications for the early universe

Boyle¹,

2008

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We derive a general master equation relating the gravitational-wave observables r and Ω gw 0 (f ); or the observables Ω gw 0 (f 1 ) and Ω gw 0 (f 2 ). Here r is the so-called "tensor-to-scalar ratio," which is constrained by cosmic-microwave-background (CMB) experiments; and Ω gw 0 (f ) is the energy spectrum of primordial gravitational-waves, which is constrained e.g. by pulsar-timing (PT) measurements, laser-interferometer (LI) experiments, and the standard Big Bang Nucleosynthesis (BBN) bound. Differentiating the master equation yields a new expression for the tilt d ln Ω gw 0 (f )/d ln f of the present-day gravitational-wave spectrum. The relationship between r and Ω gw 0 (f ) depends sensitively on the uncertain physics of the early universe, and we show that this uncertainty may be encapsulated (in a model-independent way) by two quantities:ŵ(f ) andn t (f ), wheren t (f ) is a certain logarithmic average over n t (k) (the primordial tensor spectral index); andŵ(f ) is a certain logarithmic average overw(a) (the effective equation-of-state parameter in the early universe, after horizon re-entry). Here the effective equation-of-state parameterw(a) is a combination of the ordinary equation-of-state parameter w(a) and the bulk viscosity ζ(a). Thus, by comparing observational constraints on r and Ω gw 0 (f ), one obtains (remarkably tight) constraints in the {ŵ(f ),n t (f )} plane. In particular, this is the best way to constrain (or detect) the presence of a "stiff" energy component (with w > 1/3) in the early universe, prior to BBN. (The discovery of such a component would be no more surprising than the discovery of a tiny cosmological constant at late times!) Finally, although most of our analysis does not assume inflation, we point out that if CMB experiments detect a non-zero value for r, then we will immediately obtain (as a free by-product) a new upper boundŵ < ∼ 0.55 on the logarithmically averaged effective equation-of-state parameter during the "primordial dark age" between the end of inflation and the start of BBN.

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“…The idea of cosmological duals is not new [4,11,28], but we focus here on ζ instead of the Newtonian potential [11,28] and specialize to attractor solutions by demanding that ζ → constant.…”

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confidence: 99%

Towards a cosmological dual to inflation

Khoury

Miller

2011

Phys. Rev. D

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We derive all single-field cosmologies with unit sound speed that generate scale invariant curvature perturbations on a dynamical attractor background. We identify three distinct phases: slow-roll inflation; a slowly contracting adiabatic ekpyrotic phase, described by a rapidly-varying equation of state; and a novel adiabatic ekpyrotic phase on a slowly expanding background. All of these yield identical power spectra. The degeneracy is broken at the 3-point level: unlike the nearly gaussian spectrum of slow-roll inflation, adiabatic ekpyrosis predicts large non-gaussianities on small scales.The observational evidence for primordial density perturbations with nearly scale invariant and gaussian statistics is compatible with the simplest inflationary scenarios. But is inflation unique? Are there dual cosmologies with indistinguishable predictions? Such questions are critical to our understanding of the very early universe.Inflation not only generates scale invariant and gaussian density perturbations, it does so on an attractor background. On super-horizon scales, the curvature perturbation on comoving hypersurfaces [1, 2], denoted by ζ, measures differences in the expansion history of distant Hubble patches [2]. In single-field inflation, ζ approaches a constant at long wavelengths. In the strict k → 0 limit, ζ → δa/a, so the perturbation simply renormalizes the scale factor of the background solution; such a perturbation can be removed by an appropriate rescaling of global coordinates. For finite k, the perturbation cannot be completely removed, but different Hubble patches experience the same cosmological evolution, up to a shift of local time coordinates and a rescaling of local spatial coordinates. See [3] for a detailed discussion.Achieving both scale invariance and dynamical attraction in alternative scenarios has proven challenging. The ζ equation of a contracting, matter-dominated universe is identical to that of inflation [4], but ζ grows outside the horizon, indicating an unstable background. The contracting phase in the original ekpyrotic scenario [5-10], with V (φ) = −V 0 e −φ/M , is an attractor [11,12], but the resulting spectrum is strongly blue [11][12][13]. A scale invariant spectrum can be obtained through entropy perturbations [14,15], as in the New Ekpyrotic scenario [14], but this requires two scalar fields.The adiabatic ekpyrotic mechanism [16][17][18][19][20] proposed recently offers a counterexample: a single-field model for which the background is a dynamical attractor and generates a scale invariant ζ. The mechanism

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New duality relating density perturbations in expanding and contracting Friedmann cosmologies

Cited by 63 publications

References 45 publications

Scale invariance in expanding and contracting universes from two-field models

Scale invariance in expanding and contracting universes from two-field models

Relating gravitational wave constraints from primordial nucleosynthesis, pulsar timing, laser interferometers, and the CMB: Implications for the early universe

Towards a cosmological dual to inflation

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