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A simple example of "non-minimal" Pre-Big Bang scenario

PIetro Conzinu, Maurizio Gasperini, Eliseo Pavone

TL;DR

The paper investigates whether a non-minimal pre-big bang scenario, featuring a high-curvature string phase populated by non-vacuum fluid sources, can yield a relic stochastic gravitational-wave background compatible with PTA observations. It derives the axion perturbation equation including $\alpha^{\prime}$ corrections and the tensor perturbation equation with viscosity in the String frame, and analyzes how the pump-field parameters $\beta_h$ and $\beta_\sigma$ (and their broken-duality counterparts) shape the spectra. The authors present explicit background solutions for radiation-like, unstable-string, and string-hole fluids that satisfy PTA constraints, including viscous, non-dual cases that can produce blue-tilted high-frequency spectra and break $S$-duality with $\epsilon = -H_V/\dot{\beta}$. They show that such non-minimal models can yield observable gravitational-wave signals in the PTA band and potentially extend into LISA, ET, and DECIGO sensitivities, offering a physically motivated route to connect high-energy string-phase dynamics with current and future GW data. The work highlights a concrete mechanism—viscosity-induced breaking of $S$-duality—that broadens the viable parameter space and provides testable predictions for upcoming gravitational-wave experiments.

Abstract

We give an example of non-minimal pre-big bang scenario able to produce the PTA signal considering a modified evolution of the high-curvature string phase, including the contribution of high-energy string sources. We use a fluid-dinamical model of sources and show that their effective viscosity breaks the $S$-duality symmetry of the tensor-axion perturbation spectra, as in general expected for the non-minimal scenario.

A simple example of "non-minimal" Pre-Big Bang scenario

TL;DR

The paper investigates whether a non-minimal pre-big bang scenario, featuring a high-curvature string phase populated by non-vacuum fluid sources, can yield a relic stochastic gravitational-wave background compatible with PTA observations. It derives the axion perturbation equation including corrections and the tensor perturbation equation with viscosity in the String frame, and analyzes how the pump-field parameters and (and their broken-duality counterparts) shape the spectra. The authors present explicit background solutions for radiation-like, unstable-string, and string-hole fluids that satisfy PTA constraints, including viscous, non-dual cases that can produce blue-tilted high-frequency spectra and break -duality with . They show that such non-minimal models can yield observable gravitational-wave signals in the PTA band and potentially extend into LISA, ET, and DECIGO sensitivities, offering a physically motivated route to connect high-energy string-phase dynamics with current and future GW data. The work highlights a concrete mechanism—viscosity-induced breaking of -duality—that broadens the viable parameter space and provides testable predictions for upcoming gravitational-wave experiments.

Abstract

We give an example of non-minimal pre-big bang scenario able to produce the PTA signal considering a modified evolution of the high-curvature string phase, including the contribution of high-energy string sources. We use a fluid-dinamical model of sources and show that their effective viscosity breaks the -duality symmetry of the tensor-axion perturbation spectra, as in general expected for the non-minimal scenario.

Paper Structure

This paper contains 12 sections, 54 equations, 2 figures.

Table of Contents

  1. Introduction
  2. A non-vacuum string phase: background and perturbation equations
  3. Background dynamics of the string phase
  4. Axion perturbations with $\alpha^{\prime}$ corrections
  5. Tensor perturbations including viscosity
  6. Examples of physical models compatible with the PTA signal
  7. Anisotropic fluid sources without viscosity: $S$-dual GW spectrum
  8. Viscosity and broken $S$-duality
  9. Conclusion
  10. Field equations for the non-minimal, non-vacuum string phase
  11. Axion perturbations in the string phase background
  12. The non-minimal relic GW spectrum and the associated constraints

Figures (2)

  • Figure 1: Examples of GW spectra produced by non-minimal but still $S$-dual models, with a string phase described by the background solutions of Sect. \ref{['sec31']}. All plotted spectra satisfy the constraints of Appendix \ref{['secC']}, but with different values of $\beta_h$ and $\sigma_i/M_{\rm P}$. In particular: the red spectrum corresponds to $\beta_h=-0.05$ and $\sigma_i/M_{\rm P}=1$; the blue spectrum corresponds to $\beta_h=-0.058$ and $\log (\sigma_i/M_{\rm P})=-1/2$; the orange spectrum corresponds to $\beta_h=-0.073$ and $\log(\sigma_i/M_{\rm P})=-1/2$. Also shown is a typical $S$-dual spectrum with $\beta_h=-0.064$ and $\log(\sigma_i/M_{\rm P})=-1/2$ (the magenta plotted curve), providing an explicit example of how this class of models, beside explaining the already detected signal, could also produce signals in the sensitivity range of future detectors such as LISA, ET and DECIGO.
  • Figure 2: The allowed region (the pink shaded area) spanned by the GW spectra produced by a string phase described by the solution (\ref{['314']}). The two limiting GW spectra, represented by the red and blue curves, are both violating the standard $S-$duality symmetry with the same symmetry breaking parameter, $\epsilon=0.16$. However, the red curve corresponds to $\log(\sigma_i/M_{\rm P})=-0.81$, the blue one corresponds to $\log(\sigma_i/M_{\rm P})=-0.49$.