[Paper Review] Detecting the relic gravitational wave from the electroweak phase transition at SKA

Yohei Kikuta, Kazunori Kohri+1 more|arXiv (Cornell University)|May 16, 2014

Cosmology and Gravitation Theories6 references3 citations

TL;DR

This paper investigates the detectability of stochastic gravitational wave backgrounds from the electroweak phase transition using the Square Kilometre Array (SKA) pulsar timing experiments. It demonstrates that SKA can probe small $ ilde{\beta}$ regions—characteristic of models like the MSSM—offering a powerful, complementary probe to LHC experiments for testing Higgs sector physics beyond the Standard Model.

ABSTRACT

We discuss possibilities to observe stochastic gravitational wave backgrounds produced by the electroweak phase transition in the early universe. Once the first-order phase transition occurs, which is still predicted in a lot of theories beyond the standard model, collisions of nucleated vacuum bubbles and induced turbulent motions can become significant sources of the gravitational waves. Detections of such gravitational wave backgrounds are expected to reveal the Higgs sector physics. In particular, through pulsar timing experiments planned in Square Kilometre Array (SKA) under construction, we will be able to detect the gravitational wave in near future and distinguish particle physics models by comparing the theoretical predictions to the observations.

Motivation & Objective

• To assess the detectability of stochastic gravitational wave backgrounds produced during a first-order electroweak phase transition.
• To evaluate the sensitivity of the Square Kilometre Array (SKA) to these gravitational wave signals in the low-frequency band ($10^{-9}$ Hz to $10^{-4}$ Hz).
• To examine the impact of finite vacuum energy in the false vacuum on the cosmological evolution and gravitational wave production.
• To compare theoretical predictions with observational constraints from SKA, eLISA, and DECIGO, focusing on distinguishing particle physics models.

Proposed method

• Uses the envelope approximation to model gravitational wave production from colliding bubble walls during a first-order phase transition.
• Applies analytical formulas for the gravitational wave energy density spectrum sourced by bubble collisions and turbulence.
• Introduces the parameters $\alpha$ (ratio of vacuum energy to radiation energy density) and $\tilde{\beta}$ (inverse phase transition duration) as key observables.
• Incorporates the effect of finite vacuum energy in the false vacuum on the expansion history and phase transition dynamics.
• Performs sensitivity comparisons across experiments (SKA, eLISA, Ultimate DECIGO) using signal-to-noise ratio and foreground noise (WD-WD binaries).
• Uses model-independent analysis and MSSM-motivated effective potentials to compute physical parameters like $\alpha$ and $\tilde{\beta}$.

Experimental results

Research questions

• RQ1 Can the Square Kilometre Array (SKA) detect gravitational wave backgrounds from the electroweak phase transition?
• RQ2 How do the parameters $\alpha$ and $\tilde{\beta}$ influence the detectability of gravitational waves from first-order phase transitions?
• RQ3 What is the impact of finite vacuum energy in the false vacuum on the cosmological expansion and gravitational wave production?
• RQ4 How do the detection prospects for SKA compare with those of eLISA and DECIGO in the low-frequency band?
• RQ5 Which particle physics models—particularly those with small $\tilde{\beta}$—are most accessible to SKA pulsar timing experiments?

Key findings

• SKA has the potential to detect gravitational wave backgrounds from the electroweak phase transition in the frequency range $10^{-9}$ Hz to $10^{-4}$ Hz.
• The SKA is especially sensitive to small $\tilde{\beta}$ values, which are naturally predicted in models like the MSSM, enabling the discrimination of such theories.
• The detectability of gravitational wave signals depends critically on the parameters $\alpha$ and $\tilde{\beta}$, with the highest sensitivity in the $\alpha \sim 0.1$ to $1$ and $\tilde{\beta} \sim 10$ to $100$ range.
• The region excluded by Planck constraints on the Higgs boson mass and vacuum stability is consistent with the detectable parameter space for SKA.
• Foreground noise from white dwarf binaries (WD-WD) limits the observable region at the lowest frequencies, but the SKA's sensitivity still allows access to key theoretical models.
• The paper confirms that gravitational wave observations from the electroweak phase transition can serve as a complementary probe to LHC experiments for exploring physics beyond the Standard Model.