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

This talk: saoghal.net/slides/MandM

Tallinn, September 2021

Source: arXiv:1205.2451

- Three laser arms, 2.5 M km separation
- ESA-NASA mission, launch by 2034
- Mission adopted 2017 arXiv:1702.00786

Source: arXiv:1702.00786

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

**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 nucleation temperature

**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 $\Delta x \gg 1/T$
- Each step involves matching Green's functions in the effective and full theories to the 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

Benchmark: ● 4d PT vs ● 3d PT vs ● lattice

arXiv:1903.11604Need light physics or dim-6 operators

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 $\Omega_\text{col}(f)$
**Sound waves**left behind in plasma $\Omega_\text{sw}(f)$- Shocks [$\rightarrow$ turbulence] $\rightarrow$ damping $\Omega_\text{turb}(f)$

- Focusing on GWs from sound waves... arXiv:1704.05871
- ...$\Omega_\text{sw}(f)$ fairly close to broken power law arXiv:1512.06239
- ...and the linear sound shell model arXiv:1608.04735

Model ⟶ ($T_*$, $\alpha_{T_*}$, $v_\mathrm{w}$, $\beta$) ⟶ this plot

[Here: $Z_2$-symmetric xSM points from arXiv:1910.13125]

- Nonlinearities during the transition:
- Generation of vorticity
- Droplets

- Nonlinearities after the transition:
- Shocks
- turbulence

**Let's take a look at droplets**

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

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

In the spherical case, we can get a self-similar droplet. We see the same wall velocity slowdown:

Suppression compared to sound waves (redder = worse)

**Students**:

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**, a valuable field theory tool

$\Rightarrow$ test perturbative studies of phase transitions- Strong phase transitions: hot
**droplets**slow completion

$\Rightarrow$ also suppress GW production

- How accurate are bubble nucleation calculations?
- What about the onset of shocks and turbulence?
- What other physics could explain the GW suppression seen in strong transitions?