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Production of Gravitational Waves in the Early Universe From turbulence triggered by first-order phase transitions

Yashmitha Kumaran

Abstract

This project is aimed at studying the first-order phase transitions, that is presumed to have ensued in the early universe, and its consequences on the primordial gravitational waves. The effects of bubble nucleation, growth, and coalescence are reviewed. The resulting first-order phase transition is taken as the source of the gravitational waves that were produced, in order to determine the energy density, amplitude, and frequency spectra of the relic gravitational wave background. This is accomplished by modelling the first-order phase transition as a turbulent fluid and employing relativistic hydrodynamic equations to estimate the required physical quantities. Two models are majorly studied for all the analysis done in this project. Both models compute the necessary gravitational wave spectra using the exponential Kraichnan function as the temporal decorrelation function. Also, both models contemplate the turbulence in the flow of plasma to be stationary, obeying the conditions dictated by the Kolmogorov turbulence. However, the first model uses a de-coherence function that depends on the wavenumber and time, while, the second model uses the top hat correlation, to compute the anisotropic stress. The new model introduced here adheres to the freely decaying turbulence model, but employs the time dependent de-coherence function in its computations.

Production of Gravitational Waves in the Early Universe From turbulence triggered by first-order phase transitions

Abstract

This project is aimed at studying the first-order phase transitions, that is presumed to have ensued in the early universe, and its consequences on the primordial gravitational waves. The effects of bubble nucleation, growth, and coalescence are reviewed. The resulting first-order phase transition is taken as the source of the gravitational waves that were produced, in order to determine the energy density, amplitude, and frequency spectra of the relic gravitational wave background. This is accomplished by modelling the first-order phase transition as a turbulent fluid and employing relativistic hydrodynamic equations to estimate the required physical quantities. Two models are majorly studied for all the analysis done in this project. Both models compute the necessary gravitational wave spectra using the exponential Kraichnan function as the temporal decorrelation function. Also, both models contemplate the turbulence in the flow of plasma to be stationary, obeying the conditions dictated by the Kolmogorov turbulence. However, the first model uses a de-coherence function that depends on the wavenumber and time, while, the second model uses the top hat correlation, to compute the anisotropic stress. The new model introduced here adheres to the freely decaying turbulence model, but employs the time dependent de-coherence function in its computations.
Paper Structure (46 sections, 172 equations, 16 figures)

This paper contains 46 sections, 172 equations, 16 figures.

Table of Contents

  1. Introduction
  2. Literature survey
  3. Phase transitions: mathematical representation
  4. Bubble growth and expansion
  5. Detonation
  6. Deflagration
  7. Hybrid
  8. Relativistic hydrodynamics
  9. Newtonian kinetic theory
  10. The Maxwell-Boltzmann equilibrium distribution
  11. Relativistic kinetic theory
  12. Relativistic transport fluxes
  13. General relativistic hydrodynamic equations
  14. Relativistic equilibrium distributions
  15. Some thermodynamics
  16. ...and 31 more sections

Figures (16)

  • Figure 1: Scalar field vs its Potential for different values of Temperature
  • Figure 2: Three cases of bubble expansion taken from Espinosa:2010hh with the coloured area denoting the non-zero fluid velocity, hitting the bubble wall represented by the black circles
  • Figure 3: Variation of different combinations of $\Pi$ with transverse and longitudinal components and their sum vs the non dimensionalized wavenumber, $z$
  • Figure 4: Variation of rate of spectral density (model 1) against non dimensionalized wavenumber
  • Figure 5: Variation of the gravitational wave power spectrum (model 1) against non dimensionalized wavenumber
  • ...and 11 more figures