David J. Weir

University of Helsinki

This talk: saoghal.net/slides/cau2023

2023 Chung-Ang University Beyond the Standard Model Workshop

Credit: Stephan Paul, arXiv:1205.2451

Credit: Stephan Paul, arXiv:1205.2451

Credit: Stephan Paul, arXiv:1205.2451

gravitational waves help?

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

Source: [PD] NASA via Wikimedia Commons

Source: arXiv:1702.00786

[qualitative curve, sketched on]

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

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

[what BSM physics might there be?]

**Particle physics model**

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

Dimensional reduction

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

Phase transition parameters

from lattice simulations

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

Real time cosmological simulations

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

**Cosmological GW background**

[what would we see as a result?]

**Particle physics model**

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

Dimensional reduction

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

Phase transition parameters

from lattice simulations

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

Real time cosmological simulations

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

**Cosmological GW background**

**Particle physics model**

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

Dimensional reduction

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

Phase transition parameters

from lattice simulations

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

Real time cosmological simulations

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

**Cosmological GW background**

- 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, can integrate out heavy new physics and study simpler model

transition duration

- Comparison at benchmark point in minimal SM
- Compare: ● 4d PT vs ● 3d PT vs ● NP (= lattice)

observable

in this corner

transition duration

- Theories that look SM-like in the IR ⇒ not observable!
- But what happens with additional light fields?

Need for accuracy: $\Sigma$SM (triplet) example arXiv:2005.11332

Perturbation theory out by 10% or more!

- 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 ✅

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

Real time cosmological simulations

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

**Cosmological GW background**

**Particle physics model** ✅

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

Dimensional reduction ✅

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

Phase transition parameters from lattice simulations ✅

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

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

- 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 $v_\mathrm{w} < c$ ...
- 'Vacuum' transitions with no couplings/friction
- 'Run away' transitions arXiv:1703.08215

- ... but if they do:
- Plasma motion lasts a Hubble time $1/H_*$
- Fluid motion becomes nonlinear on a time scale

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

Those simulations yield GW spectra like (sound waves):

[NB: curves scaled by $t$: collapse = constant emission]

$\text{SNR} = \sqrt{\mathcal{T} \int_{f_\text{min}}^{f_\text{max}} \mathrm{d} f \left[ \frac{h^2 \Omega_\text{GW}(f)}{h^2 \Omega_\text{Sens}(f)}\right]^2} $

Still need to handle astrophysical foregrounds properly!

- 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, Satumaaria Sukuvaara, Essi Vilhonen**Postdocs**:

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

Daniel Cutting, Oliver Gould, Jonathan Kozaczuk, Mark Hindmarsh, Stephan Huber, Hiren Patel, Michael Ramsey-Musolf, Kari Rummukainen, Tuomas Tenkanen

**Early universe processes**can probe BSM physics

... but we need precise predictions of key parameters $\Rightarrow$ 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?