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Nongaussian and nonscale-invariant perturbations from tachyonic preheating in hybrid inflation

Neil Barnaby, James M. Cline

TL;DR

The paper analyzes tachyonic preheating in hybrid inflation as a potent source of second-order curvature perturbations, deriving how the tachyon contributes to ζ^(2) and can induce observable non-Gaussianity. It develops a Green-function framework in the long-wavelength limit, demonstrates the cancellation of nonlocal terms at leading order, and provides explicit expressions for the time-integrated tachyon perturbations that feed the bispectrum and power spectrum. By translating these results into f_NL and f_L constraints, the authors map exclusions in the hybrid-inflation parameter space and show that spectral distortions often dominate over non-Gaussianity in constraining the model. Applying the analysis to brane-antibrane inflation, they obtain stringent bounds on the string coupling g_s (notably g_s < 10^−4.5 in the KKLMMT setup), highlighting strong phenomenological implications for string-inspired inflation models.

Abstract

We show that in hybrid inflation it is possible to generate large second-order perturbations in the cosmic microwave background due to the instability of the tachyonic field during preheating. We carefully calculate this effect from the tachyon contribution to the gauge-invariant curvature perturbation, clarifying some confusion in the literature concerning nonlocal terms in the tachyon curvature perturbation; we show explicitly that such terms are absent. We quantitatively compute the nongaussianity generated by the tachyon field during the preheating phase and translate the experimental constraints on the nonlinearity parameter f_{NL} into constraints on the parameters of the model. We also show that nonscale-invariant second-order perturbations from the tachyon field can become larger than the inflaton-generated first-order perturbations, leading to stronger constraints than those coming from nongaussianity. The width of the excluded region in terms of the logarithm of the dimensionless coupling g, grows linearly with the log of the ratio of the Planck mass to the tachyon VEV, \log(M_p/v); hence very large regions are ruled out if the inflationary scale v is small. We apply these results to string-theoretic brane-antibrane inflation, and find a stringent upper bound on the string coupling, g_s < 10^{-4.5}.

Nongaussian and nonscale-invariant perturbations from tachyonic preheating in hybrid inflation

TL;DR

The paper analyzes tachyonic preheating in hybrid inflation as a potent source of second-order curvature perturbations, deriving how the tachyon contributes to ζ^(2) and can induce observable non-Gaussianity. It develops a Green-function framework in the long-wavelength limit, demonstrates the cancellation of nonlocal terms at leading order, and provides explicit expressions for the time-integrated tachyon perturbations that feed the bispectrum and power spectrum. By translating these results into f_NL and f_L constraints, the authors map exclusions in the hybrid-inflation parameter space and show that spectral distortions often dominate over non-Gaussianity in constraining the model. Applying the analysis to brane-antibrane inflation, they obtain stringent bounds on the string coupling g_s (notably g_s < 10^−4.5 in the KKLMMT setup), highlighting strong phenomenological implications for string-inspired inflation models.

Abstract

We show that in hybrid inflation it is possible to generate large second-order perturbations in the cosmic microwave background due to the instability of the tachyonic field during preheating. We carefully calculate this effect from the tachyon contribution to the gauge-invariant curvature perturbation, clarifying some confusion in the literature concerning nonlocal terms in the tachyon curvature perturbation; we show explicitly that such terms are absent. We quantitatively compute the nongaussianity generated by the tachyon field during the preheating phase and translate the experimental constraints on the nonlinearity parameter f_{NL} into constraints on the parameters of the model. We also show that nonscale-invariant second-order perturbations from the tachyon field can become larger than the inflaton-generated first-order perturbations, leading to stronger constraints than those coming from nongaussianity. The width of the excluded region in terms of the logarithm of the dimensionless coupling g, grows linearly with the log of the ratio of the Planck mass to the tachyon VEV, \log(M_p/v); hence very large regions are ruled out if the inflationary scale v is small. We apply these results to string-theoretic brane-antibrane inflation, and find a stringent upper bound on the string coupling, g_s < 10^{-4.5}.

Paper Structure

This paper contains 19 sections, 200 equations, 15 figures.

Table of Contents

  1. Introduction
  2. Metric and Matter Perturbations
  3. Hybrid Inflation
  4. Background Dynamics
  5. Inflationary Dynamics of First Order Fluctuations
  6. Conditions for a slowly varying tachyon mass
  7. Tachyonic Instability
  8. Second Order Fluctuations in the Long Wavelength Approximation
  9. The Master Equation
  10. The Green Function
  11. The Gauge Invariant Curvature Perturbation
  12. The Tachyon Curvature Perturbation
  13. Time-integrated tachyon perturbation
  14. Bispectrum and spectrum of second order metric perturbation
  15. Constraint from tachyon contribution to spectrum
  16. ...and 4 more sections

Figures (15)

  • Figure 1: Exact solution and our approximation for the function $N_k$ in eq. (\ref{['Nk']}).
  • Figure 2: Ratio of the exact mode functions to the approximation (\ref{['mode']}), at large times.
  • Figure 3: Contours of $\ln M_p^2/\lambda v^2$ in the plane of $N_*$ and $\ln c$.
  • Figure 4: $({\rm sign}(f)\ln(1+|f|)$ versus $N$, showing behavior of the the function $f$ defined in (\ref{['feqn']}), for $\ln c = 1$, $N_*=22.5$
  • Figure 5: Log of the integrand of the $p$ integral in eq. (\ref{['Beq']}), for a case where the maximum occurs near $\ln(p/\sqrt{c} H)= N_i$ .
  • ...and 10 more figures