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Chaotic inflation on the brane

R Maartens, D Wands, B Bassett, I Heard

TL;DR

The paper investigates slow-roll chaotic inflation on a brane embedded in five-dimensional Einstein gravity, where a density-squared term in the Friedmann equation modifies early-universe dynamics. By deriving brane-modified slow-roll parameters and the expansion history, it shows that high-energy corrections ease slow-roll and increase the number of e-folds for a given potential, while also influencing the spectrum of primordial perturbations. Using ζ as the curvature perturbation and analyzing both scalar and tensor modes, it finds that scalar perturbations are enhanced and the spectrum becomes nearly scale-invariant (n_s → 1) at high energies, with tensor modes comparatively suppressed due to brane effects. In a simple V = (1/2) m^2 φ^2 model, the brane corrections allow chaotic inflation to occur with φ_cobe below M_4 but above M_5 for sufficiently low M_5, and COBE normalization ties m to M_5 through φ_cobe, yielding testable predictions such as a modified tensor-to-scalar ratio and a shifted consistency relation. The results suggest a viable brane-world realization of chaotic inflation with distinctive perturbation signatures, while noting that bulk back-reaction was neglected and could modify the quantitative predictions.

Abstract

We consider slow-roll inflation in the context of recently proposed four-dimensional effective gravity induced on the world-volume of a three-brane in five-dimensional Einstein gravity. We find significant modifications of the simplest chaotic inflationary scenario when the five-dimensional Planck scale is below about 10^{17} GeV. We use the comoving curvature perturbation, which remains constant on super-Hubble scales, in order to calculate the spectrum of adiabatic density perturbations generated. Modifications to the Friedmann constraint equation lead to a faster Hubble expansion at high energies and a more strongly damped evolution of the scalar field. This assists slow-roll, enhances the amount of inflation obtained in any given model, and drives the perturbations towards an exactly scale-invariant Harrison-Zel'dovich spectrum. In chaotic inflation driven by a massive scalar field we show that inflation can occur at field values far below the four-dimensional Planck scale, though above the five-dimensional fundamental scale.

Chaotic inflation on the brane

TL;DR

The paper investigates slow-roll chaotic inflation on a brane embedded in five-dimensional Einstein gravity, where a density-squared term in the Friedmann equation modifies early-universe dynamics. By deriving brane-modified slow-roll parameters and the expansion history, it shows that high-energy corrections ease slow-roll and increase the number of e-folds for a given potential, while also influencing the spectrum of primordial perturbations. Using ζ as the curvature perturbation and analyzing both scalar and tensor modes, it finds that scalar perturbations are enhanced and the spectrum becomes nearly scale-invariant (n_s → 1) at high energies, with tensor modes comparatively suppressed due to brane effects. In a simple V = (1/2) m^2 φ^2 model, the brane corrections allow chaotic inflation to occur with φ_cobe below M_4 but above M_5 for sufficiently low M_5, and COBE normalization ties m to M_5 through φ_cobe, yielding testable predictions such as a modified tensor-to-scalar ratio and a shifted consistency relation. The results suggest a viable brane-world realization of chaotic inflation with distinctive perturbation signatures, while noting that bulk back-reaction was neglected and could modify the quantitative predictions.

Abstract

We consider slow-roll inflation in the context of recently proposed four-dimensional effective gravity induced on the world-volume of a three-brane in five-dimensional Einstein gravity. We find significant modifications of the simplest chaotic inflationary scenario when the five-dimensional Planck scale is below about 10^{17} GeV. We use the comoving curvature perturbation, which remains constant on super-Hubble scales, in order to calculate the spectrum of adiabatic density perturbations generated. Modifications to the Friedmann constraint equation lead to a faster Hubble expansion at high energies and a more strongly damped evolution of the scalar field. This assists slow-roll, enhances the amount of inflation obtained in any given model, and drives the perturbations towards an exactly scale-invariant Harrison-Zel'dovich spectrum. In chaotic inflation driven by a massive scalar field we show that inflation can occur at field values far below the four-dimensional Planck scale, though above the five-dimensional fundamental scale.

Paper Structure

This paper contains 5 sections, 27 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Slow-roll inflation on the brane
  3. Perturbations on the brane
  4. A simple model
  5. Conclusion

Figures (1)

  • Figure 1: The scaling of $m/M_{4}$ vs $(\lambda/M_4^4)^{1/4}$ to satisfy the COBE constraints. The straight line is the approximation used in Eq. (\ref{['approx']}), which at high energies is in excellent agreement with the exact solution, evaluated numerically in slow-roll.