David J. Weir [they/he]

University of Helsinki

This talk: saoghal.net/slides/coswg2023

10th LISA Cosmology Working Group Workshop

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

By considering how GWs get redshifted on the way to us, and assuming they get produced at cosmological scales:

Event | Time (s) | Temp (GeV) | $\mathbf{g}_*$ | Frequency (Hz) |
---|---|---|---|---|

QCD phase transition | $10^{-3}$ | $0.1$ | $\sim 10$ | $10^{-8}$ |

EW phase transition | $10^{-11}$ | $100$ | $\sim 100$ | $10^{-5}$ LISA! |

??? | $10^{-25}$ | $10^9$ | $\gtrsim 100$ | $100$ |

End of inflation | $\gtrsim 10^{-36}$ | $\lesssim 10^{16}$ | $\gtrsim 100$ | $\gtrsim 10^8$ |

[order-of-magnitude calculation!]

arXiv:2008.09136

**First-order phase transitions** are a

- Out of sight of particle physics experiments, or
- At higher energy scales than colliders can reach

- 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

[what BSM physics might there be?]

**Particle physics model**

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

Magical field theory stuff OG's talk!

(perturbative or lattice)

$\Downarrow$

Phase transition parameters

$\Downarrow \alpha, \beta, T_N, v_\mathrm{w}, \ldots$

Real time cosmological simulations

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

**Cosmological GW background**

[what would we see as a result?]

[what BSM physics might there be?]

**Particle physics model**

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

Magical field theory stuff OG's talk!

(perturbative or lattice)

$\Downarrow$

Phase transition parameters

$\Downarrow \alpha, \beta, T_N, v_\mathrm{w}, \ldots$

Real time cosmological simulations

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

**Cosmological GW background**

[what would we see as a result?]

[what BSM physics might there be?]

**Particle physics model**

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

Magical field theory stuff OG's talk!

(perturbative or lattice)

$\Downarrow$

Phase transition parameters

$\Downarrow \alpha, \beta, T_N, v_\mathrm{w}, \ldots$

Real time cosmological simulations

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

**Cosmological GW background**

[what would we see as a result?]

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

- Bubbles nucleate (temperature $T_\mathrm{N}$, on timescale $\beta^{-1}$)
- Bubble walls expand in a plasma (at velocity $v_\mathrm{w}$)
- Reaction fronts form around walls (with strength $\alpha$)
- Bubbles + fronts collide GWs
**Sound waves**left behind in plasma GWs- Shocks [$\rightarrow$ turbulence] $\rightarrow$ damping GWs

- Not all phase transitions have $v_\mathrm{w} \ll c$ ...
- 'Vacuum' transitions with no couplings/friction
- 'Run away' transitions arXiv:1703.08215

- ... but if they do:
- Shear stress sourced most efficiently in first $1/H_*$
- Fluid motion becomes nonlinear on a time scale

$$\tau_\text{sh} = \frac{R_*}{\overline{U}} = \frac{\text{Bubble radius (i.e. typical length scale)}}{\text{Typical fluid velocity}}$$

- Nonlinearities during the transition:
- Generation of vorticity
- Formation of droplets

- Nonlinearities after the transition:
- Shocks
- Turbulence (Kolmogorov
and acoustic)

**Let's take a look at droplets and 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

case

scenario ➘

Wall velocity

Peak fluid 3-velocity

- Long-lived regions with moderate wall velocities
- Could this help with baryogenesis? For strong transitions, walls often move too quickly.
- Proposals for dark strongly interacting matter 'nuggets' where the phases coexist e.g. arXiv:1810.04360 arXiv:1912.02830
- Other applications?
- Further 3D simulations will be needed

- 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.

Validated theoretical modelling of GWs from Kolmogorov turbulence with large-scale simulations

**Students**:

Jani Dahl, Ethan Edwards, Jenni Häkkinen, Anna Kormu, Tiina Minkkinen, Satumaaria Sukuvaara, Essi Vilhonen**Postdocs**:

Deanna C. Hooper, Lauri Niemi**Collaborators**:

*including*Pierre Auclair, Chiara Caprini, Daniel Cutting, Oliver Gould, Mark Hindmarsh, Kari Rummukainen, Dani Steer, Tuomas Tenkanen

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

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