Gravitational waves
... and particle physics

arXiv:2505.17824, etc.

David J. Weir [they/he] - University of Helsinki

This talk: saoghal.net/slides/ppd2026

Particle Physics Day 2026, 11 November 2026

What happened in the early universe? before recombination? in dark sectors?

Credit: Stephan Paul, arXiv:1205.2451

Credit: Stephan Paul, arXiv:1205.2451

Credit: Stephan Paul, arXiv:1205.2451

Credit: Stephan Paul, arXiv:1205.2451

LISA is coming!

• Three laser arms, 2.5 M km separation
• ESA-NASA mission, launch 2030s
• Finnish involvement: data processing (DDPC) node
• Next mock dataset 'Mojito' made in Finland (CDC-FI)

helsinki.fi/infrastructures/cosmology-data-centre-finland

LISA: "Astrophysics" signals

LISA: Stochastic background?

[qualitative curve, sketched on]

PTA evidence for a SGWB

Source: arXiv:2306.16213

Gravitationa waves ...

[from phase transitions]

First order phase transition

• High temperatures: potential has one global minimum
• Below $T_\mathrm{c}$, second minimum becomes global minimum
• Nucleation temp. $T_\mathrm{n}$: ~ 1 bubble per causal volume
• 'Percolation' temp. $T_\mathrm{p}$: broken phase clusters join up

Summary: what happens?

1. Nucleation (temperatures $T_\mathrm{n}$→$T_\mathrm{p}$, duration $\beta^{-1}$)
2. Bubble walls expand in a plasma (at velocity $v_\mathrm{w}$)
   
3. Reaction fronts form around walls (with strength $\alpha$)

Detonations vs deflagrations

• If the scalar field wall moves supersonically and the fluid enters the wall at rest, we have a detonation
• If the scalar field wall moves subsonically and the fluid enters the wall at its maximum velocity, we have a deflagration
• Can also get a hybrid where the wall moves supersonically but some fluid bunches up in front of it, like a deflagration

Detonations, hybrids, deflagrations

Source: Espinosa, Konstandin, No and Servant

OK, expanding bubbles associated with reaction fronts. Then what?

4. Bubbles (size $R_*$) + fronts collide GWs
5. Sound waves left behind, plasma 4-velocity $U$ GWs
6. System becomes 'turbulent'; KE starts to decay GWs
7. GW production saturates; Hubble damping

What is a strong phase transition?

• Plasma velocities become relativistic
  ⇒ flows quickly become nonlinear
• Nonlinearities include:
  • shocks ➠ acoustic turbulence $t_{\mathrm{sh}} \sim R_* / U_{\parallel}$
  • vortices ➠ [vortical] turbulence $t_{\mathrm{ed}} \sim R_* / U_{\perp}$
  (in reality hard to separate into two types)
• Transport of energy to small scales ⇒ KE decay
• Typically strong means $\alpha$ 'large'
  (maybe better to focus on what the flows look like)

Strong simulation example

Created by José Correia for arXiv:2505.17824.

Sound shell model 1

• $\alpha_n \ll 1$, $v_\mathrm{w} \ll 1$: sound waves are main GW source
  • Neglect nonlinear interactions between bubbles etc.
  • Also ignore later nonlinear motion in the fluid
    (i.e. shocks and turbulence)
• Begin by obtaining the fluid velocity profile around the bubble wall, as a function of $\xi = r/t$,

Sound shell model 2

• Velocity power spectrum $P_v(f)$ from superposing random spherical shells with scaled profile $v(\xi)$
• Convolve $P_v(f)$ with itself and integrate over time to get GW power spectrum

PTtools for fluid profiles/SSM

By Mika Mäki

• pip-installable python package; Numba + JAX support
• Everything (with sensible defaults) in 5+5 lines:

									from pttools.ssm import NucType
									from pttools.bubble import Bubble
									from pttools.models import BagModel
									from pttools.omgw0 import Spectrum
									import matplotlib.pyplot as plt
									
									model = BagModel(alpha_n_min=0.01)
									bubble = Bubble(model, v_wall=0.5, alpha_n=0.2)
									spectrum = Spectrum(bubble, nuc_type=NucType.EXPONENTIAL, r_star=0.1)
									spectrum_fig = spectrum.plot_multi()
									plt.savefig('spectrum_fig.pdf')
								

(makes a set of four plots like on the previous slide)

github.com/CFT-HY/pttools

Survey of ansätze 1

• Single broken power law from 'CosWG20' arXiv:1910.13125: $$ \begin{multline} \Omega_\text{gw}(f) = \Omega_\text{gw, comm} \\ \times 0.687 \cdot \underbrace{\mathrm{min}(H_*\tau_\text{sh},1) (H_*R_*)}_{\text{life time} \times \text{coherence time}} C(f/f_\text{peak}) \end{multline} $$
  where $\Omega_\text{gw, comm} = 3 \textcolor{red}{F_\text{gw,0}} \textcolor{blue}{K^2} \textcolor{purple}{\tilde{\Omega}_\text{gw}}$ combines:
  dilution $\textcolor{red}{F_\text{gw,0}}$, PT efficiency $\textcolor{blue}{K^2}$, GW efficiency $\textcolor{purple}{\tilde{\Omega}_\text{gw}}$
• Spectral shape $ C(s) = s^3 \left(\frac{7}{4 + 3 s^2}\right)^{\frac{7}{2}} $ i.e. $f^3 \to f^{-1}$
• 'Inspired by' simulations arXiv:1704.05871

Survey of ansätze 2

• Double broken power law from 'GH21' arXiv:2106.05984: $$ C(s) = s^9 \left( \frac{1+ r_b^4}{r_b^4 + s^4}\right)^{\frac{9-b}{4}}\left( \frac{b + 4}{b + 4 -m + ms^2}\right)^{\frac{b+4}{2}} $$
• $f^9 \to f^b \to f^{-4}$ with peaks at $s=1$ and $s=r_b$
• $m$ chosen such that $C(1) = 1$ for $r_b < 1$
• $r_b$ and $b$ chosen by fitting to SSM results
• Different DBPL in arXiv:2403.03723 ('CosWG24')

How strong a phase transition do you need to see something at LISA?

(Assuming double broken power law ansatz) arXiv:2106.05984

But: is a double broken power law valid when $\alpha$ is big?

Ansätze vs. simulation results 1

Courtesy Mika Mäki

Ansätze vs. simulation results 2

Courtesy Mika Mäki

... and particle physics

The PTA signal is not fully explained

arXiv:2306.09411

PTAs vs MeV-scale phase transitions

• Left: with BBN, supernovae, beam dump limits, etc.
• Right: sampling over PTA likelihood.

arXiv:2602.09092

LISA probes TeV-scale BSM physics

e.g. $Z_2$ singlet extension from arXiv:1910.13125

Combined collider/GW constraints are a wicked problem

• Theoretical uncertainties abound:
  • In the BSM phenomenology
  • In the prediction of the GW power spectrum
  • In the modelling of other (degenerate) GW sources
• And the expertise is distributed across disciplines...