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The gravitational wave landscape of cosmic string networks with varying tension

Luca Brunelli, Filippo Revello, Gonzalo Villa

TL;DR

This work analyzes gravitational waves from scaling cosmic string networks in cosmologies where the string tension varies with time due to moduli dynamics. By deriving Swampland-inspired bounds on the permissible rate of tension variation and applying them to explicit Type IIB constructions with wrapped D3 and NS5 branes, the authors classify the GW spectral shapes into three regimes and compute the corresponding spectral indices as functions of the background equation of state and the tension-variation parameter $q$. In particular, they find that tension decreasing in the early universe can boost high-frequency GW amplitudes and that certain wrapped-brane scenarios yield tension evolutions $\mu(t) \sim t^{\pm 1}$ or $\mu(t) \sim t^{\pm 1/2}$, with one case $\mu(t) \sim t^{-1}$ producing a spectral index independent of the background. The Swampland bounds further constrain the allowable indices, offering a connection between high-energy consistency conditions and observable GW signals, with implications for pre-BBN cosmology and moduli stabilisation in string theory.

Abstract

We fully classify the phenomenology of gravitational wave emission from scaling cosmic string networks with varying tension and compute the spectral indices of the resulting stochastic backgrounds. In string compactifications, periods of varying tension occur when moduli acquire a time-dependence. We present concrete examples in type IIB string theory as D3- and NS5- branes wrapping internal cycles, which become dynamical due to the effect of moduli potentials. Moreover, we use Swampland constraints to derive general bounds on the allowed time-variation of the effective string tension in FLRW backgrounds and on the resulting spectral indices.

The gravitational wave landscape of cosmic string networks with varying tension

TL;DR

This work analyzes gravitational waves from scaling cosmic string networks in cosmologies where the string tension varies with time due to moduli dynamics. By deriving Swampland-inspired bounds on the permissible rate of tension variation and applying them to explicit Type IIB constructions with wrapped D3 and NS5 branes, the authors classify the GW spectral shapes into three regimes and compute the corresponding spectral indices as functions of the background equation of state and the tension-variation parameter . In particular, they find that tension decreasing in the early universe can boost high-frequency GW amplitudes and that certain wrapped-brane scenarios yield tension evolutions or , with one case producing a spectral index independent of the background. The Swampland bounds further constrain the allowable indices, offering a connection between high-energy consistency conditions and observable GW signals, with implications for pre-BBN cosmology and moduli stabilisation in string theory.

Abstract

We fully classify the phenomenology of gravitational wave emission from scaling cosmic string networks with varying tension and compute the spectral indices of the resulting stochastic backgrounds. In string compactifications, periods of varying tension occur when moduli acquire a time-dependence. We present concrete examples in type IIB string theory as D3- and NS5- branes wrapping internal cycles, which become dynamical due to the effect of moduli potentials. Moreover, we use Swampland constraints to derive general bounds on the allowed time-variation of the effective string tension in FLRW backgrounds and on the resulting spectral indices.
Paper Structure (16 sections, 47 equations, 1 figure)

This paper contains 16 sections, 47 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Time-dependent string tension
  3. A Swampland Argument
  4. Decompactification & tensionless limits
  5. Scaling solutions
  6. Novel scenarios in Type IIB
  7. Manifolds with Factored Volume
  8. Contributions to the Scalar Potential
  9. The fibre
  10. The torus
  11. Gravitational Wave Spectrum
  12. Qualitative aspects
  13. The different scenarios
  14. Bounds on the spectral index
  15. Conclusions
  16. ...and 1 more sections

Figures (1)

  • Figure 1: Parameter space ($n,q$), where $G\mu \sim t^{-q}$ and $H=2/(nt)$. The main text computes spectral indices of the GW background from scaling networks of cosmic strings in these backgrounds. The orange (undashed) region is scenario 1, with spectral index computed in Eq. \ref{['eq:OGW']}. The blue (undashed) region is scenario 2, with spectral index computed in Eq. \ref{['eq:1GW']}. Dashed regions are either excluded by the Swampland bound in Eq. \ref{['eq:b3']} (right) or have a spectral index of $-1/3$, dominated by higher modes (scenario 3).