Gravitational waves from phase transitions in the early universe
Mika Mäki, Doctoral Researcher,
Computational Field Theory group, University of Helsinki
Doctoral Education Pilot Base Camp 2
26.-28.3.2025
Early universe bubbles
- Think of a boiling water kettle
- Change in temperature ⇒ spontaneous transition from liquid to gas ⇒ bubbles
- Similarly, early in the Big Bang there have been phase transitions (changes of state for matter)
- The most notable of these is the Higgs transition around $10^{-12}$ s when elementary particles acquired their rest masses
- Standard Model: crossover (no clear boundary)
Standard Model extensions: first-order (sharp boundary)
First-order ⇒ sharp boundary ⇒ bubbles ⇒ sound waves ⇒ gravitational waves
Detection of primordial gravitational waves
- LISA: Laser Interferometer Space Antenna
- Will be launched in the 2030s
- Three satellites connected by 2.5 million kilometer long laser beams
- Measures gravitational waves at milli-Hertz frequencies
- "Listening to the sound of a cosmic kettle"
- Direct testing and comparison of particle physics theories beyond the Standard Model
Thank you!
Self-similar hydrodynamics
- Self-similar: time-independent solution
- Black circle: phase boundary, aka. bubble wall
- Colour: velocity of moving plasma
- $c_s$: speed of sound
- $v_\text{w}$: wall speed
- $c_\text{J}$: Chapman-Jouguet speed
From fluid profiles to GW spectra
🠮
Fluid shell velocity profiles
- Boundary conditions
- ODE integration
GW spectra
- Sine transform
- Conversion to observable $f$ etc.
- Experimentally testable by LISA
How to use PTtools
from pttools.analysis import plot_spectra_omgw0, plot_bubbles_v
from pttools.bubble import Bubble
from pttools.models import ConstCSModel
from pttools.omgw0 import Spectrum
alpha_n = 0.2
model = ConstCSModel(css2=1/3, csb2=1/4, alpha_n_min=alpha_n)
bubbles = [
Bubble(model, v_wall=0.3, alpha_n=alpha_n),
Bubble(model, v_wall=0.5, alpha_n=alpha_n),
Bubble(model, v_wall=0.9, alpha_n=alpha_n)
]
spectra = [Spectrum(bubble, r_star=0.1, Tn=200) for bubble in bubbles]
plot_bubbles_v(bubbles, path="bubbles.svg", v_max=0.5)
plot_spectra_omgw0(spectra, path="spectra.svg")
