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

This talk: saoghal.net/slides/bielefeld2022

Bielefeld, 15th February 2022

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

- Nonlinearities include:
- Turbulence (Kolmogorov-type and acoustic)
- 'Hot droplets'

- Consequences for
- Observables [e.g. gravitational waves]
- Processes [e.g. baryogenesis]

Tour of the 'pipeline' from particle physics model to dynamical processes in strong phase transitions

**Particle physics model**

$\Downarrow \mathcal{L}_{4\mathrm{d}}$

Dimensional reduction

$\Downarrow \mathcal{L}_{3\mathrm{d}}$

Phase transition parameters from lattice simulations

$\Downarrow \alpha, \beta, T_N, \ldots$

Real time cosmological simulations

$\Downarrow \Omega_\text{gw}(f)$

**Cosmological GW background**

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

**Particle physics model**

$\Downarrow \mathcal{L}_{4\mathrm{d}}$

Dimensional reduction

$\Downarrow \mathcal{L}_{3\mathrm{d}}$

Phase transition parameters from lattice simulations

$\Downarrow \alpha, \beta, T_N, \ldots$

Real time cosmological simulations

$\Downarrow \Omega_\text{gw}(f)$

**Cosmological GW background**

Real time cosmological simulations

$\Downarrow \Omega_\text{gw}(f)$

- Process by which the Higgs 'switched on'
- In the Standard Model it is a crossover
- Possible in extensions that it would be first
order

➥ colliding bubbles then make gravitational waves

arXiv:hep-ph/9605288 ; arXiv:hep-lat/9704013; arXiv:hep-ph/9809291

- 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

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

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

arXiv:1903.11604Benchmark: ● 4d PT vs ● 3d PT vs ● NP (lattice)

arXiv:1903.11604Perturbation theory doesn't see the phase transition!

arXiv:2005.11332- Dimensional reduction + lattice simulations a well-proven method for studying BSM theories
- Higher dimensional operators or
**light**new physics needed for a strong phase transition - Should benchmark perturbation theory with DR + lattice, particularly for strong transitions

**Particle physics model** ✅

$\Downarrow \mathcal{L}_{4\mathrm{d}}$

Dimensional reduction ✅

$\Downarrow \mathcal{L}_{3\mathrm{d}}$

Phase transition parameters from lattice simulations ✅

$\Downarrow \alpha, \beta, T_N, \ldots$

Real time cosmological simulations

$\Downarrow \Omega_\text{gw}(f)$

**Cosmological GW background**

$\Downarrow \mathcal{L}_{4\mathrm{d}}$

Dimensional reduction ✅

$\Downarrow \mathcal{L}_{3\mathrm{d}}$

Phase transition parameters from lattice simulations ✅

Real time cosmological simulations

$\Downarrow \Omega_\text{gw}(f)$

- Bubbles nucleate and grow
- Expand in a plasma - create reaction fronts
- Bubbles + fronts collide
**Sound waves**left behind in plasma- Shocks [$\rightarrow$ turbulence] $\rightarrow$ damping

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

**Assumes** GW emission stops
when nonlinearities form.

- 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**

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

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

Suppression compared to sound waves (redder = worse)

- 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

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.

**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

**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

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