Gravitational waves as a probe of early universe phase transitions

David J. Weir [they/he] - Helsinki - davidjamesweir

This talk: saoghal.net/slides/EuCAPT

EuCAPT colloquium, January 2022

While you were waiting

You were watching a movie of vorticity $\nabla \times \mathbf{v}$ in a simulation of 2D acoustic turbulence by Jani Dahl

arXiv:2112.12013

Outline

1. Context: early universe, LISA, pipeline
Pause for questions
2. Microphysics: beyond the Standard Model
Pause
3. Macrophysics: out of equilibrium
4. Wrapping up: key points and questions to ask

What happened in the early universe? when the universe was optically opaque? in dark sectors?

LISA is coming!

• Three laser arms, 2.5 M km separation
• ESA-NASA mission, launch 2030s
• Mission exited 'phase A' in December 2021

arXiv:1702.00786

LISA: "Astrophysics" signals

LISA: Stochastic background?

[qualitative curve, sketched on]

This talk is about:

How a background might be made by a phase transition

Questions so far

You could ask...

Why focus on LISA (for potentially detecting a cosmological stochastic background)?

Image by ed_needs_a_bicycle on Flickr [CC-BY-NC-SA]

How does a stochastic cosmological background come about, then?

• What happens during first order phase transitions?
• What are the consequences for gravitational waves?

One approach

Particle physics model
$\Downarrow \mathcal{L}_{4\mathrm{d}}$
Dimensional reduction
$\Downarrow \mathcal{L}_{3\mathrm{d}}$
Lattice Monte Carlo simulations
$\Downarrow \alpha, \beta, T_N, v_\mathrm{w}, \ldots$
Real time cosmological simulations
$\Downarrow \Omega_\text{gw}(f)$
Cosmological GW background

Model-independent parameters bridge the gap

Including:

• $\alpha$, the phase transition strength
• $\beta$, the inverse phase transition duration
• $T_N$, the temperature at which bubbles nucleate
• $v_\mathrm{w}$, the speed at which bubbles expand

A "pipeline"

Microphysics

Particle physics model
$\Downarrow \mathcal{L}_{4\mathrm{d}}$
Dimensional reduction
$\Downarrow \mathcal{L}_{3\mathrm{d}}$
Lattice Monte Carlo simulations

My focus: extensions of the Standard Model

SM electroweak phase transition

• Process by which the Higgs 'switched on'
• In the Standard Model it is a crossover
• Possible in extensions that it would be first order
  ➥ subsequent processes make gravitational waves

SM electroweak phase diagram

How? Dimensional reduction

• At high $T$, system looks 3D at distances $\Delta x \gg 1/T$

• Match Green's functions at each step to desired order
• Handles the infrared problem, light fields can be studied on lattice arXiv:hep-ph/9508379

Using the dimensional reduction

• Simulate DR'ed 3D theory on lattice arXiv:hep-let/9510020
• With DR, integrate out heavy new physics and recycle

How to get strong transitions?

Theories that look SM-like in the IR ⇒ not observable!

When new physics is heavy

Benchmark: ● 4d PT vs ● 3d PT vs ● NP (lattice)

DR: $\Sigma$SM (triplet) example

Perturbation theory doesn't see the phase transition!

Key points so far

• Dimensional reduction + lattice simulations a well-proven method for studying BSM theories
• Higher dimensional operators or light new physics needed for observable gravitational waves
• Should benchmark perturbation theory with DR + lattice, particularly for strong transitions

Questions so far

You could ask...

But how do you calculate the wall velocity?

Macrophysics

Out of equilibrium physics

1. Bubbles nucleate and grow
2. Expand in a plasma - create reaction fronts
3. Bubbles + fronts collide
4. Sound waves left behind in plasma
5. Shocks [$\rightarrow$ turbulence] $\rightarrow$ damping

Explore $\Omega_\text{gw}(f)$ with PTPlot.org

Model ⟶ ($\alpha$, $\beta$, $T_N$, $v_\mathrm{w}$ ) ⟶ this plot

arXiv:1910.13125

Explore $\Omega_\text{gw}(f)$ with PTPlot.org

Assumes GW emission stops when nonlinearities form.

arXiv:1910.13125

Nonlinearities?

• Nonlinearities during the transition:
  • Generation of vorticity
  • Droplets
• Nonlinearities after the transition:
  • Shocks
  • Turbulence (and acoustic turbulence)

Let's take a look at droplets and acoustic turbulence

Strong deflagrations ⇒ droplets

[$\alpha_{T_*} = 0.34$, $v_\mathrm{w} = 0.24$ (deflag.)], velocity $\mathbf{v}$

Droplets form ➤ walls slow down

At large $\alpha_{T_*}$ reheated droplets form in front of the walls

Sound waves ➤ acoustic turbulence

• Thermal phase transitions produce sound waves
• Over time, sound waves steepen into shocks
• Overlapping field of shocks = 'acoustic turbulence'
• Distinct from, but related to Kolmogorov turbulence

arXiv:2112.12013

2d acoustic turbulence

Acoustic turbulence: GWs

Spectral shape $S$ as function of $k$ and integral scale $L_0$:

Different from sound waves and Kolmogorov turbulence!
⇒ all must be taken into consideration.

Thanks

• Students:
  Jani Dahl, Anna Kormu, Lauri Niemi, Satumaaria Sukuvaara, Essi Vilhonen
• Postdocs:
  Daniel Cutting, Oliver Gould
• Collaborators:
  Jonathan Kozaczuk, Mark Hindmarsh, Stephan Huber, Hiren Patel, Michael Ramsey-Musolf, Kari Rummukainen, Tuomas Tenkanen

What I want you to remember

• Dimensional reduction is a valuable field theory tool
  $\Rightarrow$ lattice Monte Carlo simulations of phase transitions
• Nonlinearities matter when studying phase transitions
  $\Rightarrow$ large-scale real-time cosmological simulations

More questions you can ask me

• How accurate are bubble nucleation calculations?
• What are the consequences of droplet formation?
• What about other types of turbulence?