What happened in the early universe? when the universe was optically opaque? in dark sectors?

The LISA mission

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

LISA: Early Universe Cosmology

Operational Requirement 7.2: Probe a broken power-law stochastic background from the early Universe as predicted, for example, by first order phase transitions ...

Source: arXiv:1206.2942

Thermal phase transitions

Key parameters for GW production

• $T_*$, temperature
  • $T_* \sim 100 \, \mathrm{GeV} \longrightarrow \mathrm{mHz}$ today
• $\alpha_{T_*}$, vacuum energy fraction
  • $\alpha_{T_*} \ll 1$: 'weak'
  • $\alpha_{T_*} \gtrsim 1$: 'strong'
• $v_\mathrm{w}$, bubble wall speed
• $\beta/H_*$, 'duration'
  • $\beta$: inverse phase transition duration
  • $H_*$: Hubble rate at transition

Ansatz from $\alpha_{T_*} \ll 1$ simulations

arXiv:1512.06239; ptplot.org

• For any theory, can get $T_*$, $\alpha_{T_*}$, $\beta/H_*$, $v_\mathrm{w}$ arXiv:1004.4187
• It's then easy to predict the signal...

(example, $T_* = 94.7~\mathrm{GeV}$, $\alpha_{T_*} = 0.066$, $v_\mathrm{w} =0.95$, $\beta/H_* = 105.9$) $\mathrm{SNR} = 95$ ☺️

New simulations: strong transitions

[With Daniel Cutting, Mark Hindmarsh: arXiv:1906.00480]

Deflagration $v_\mathrm{w} < c_\mathrm{s}$

Detonation $v_\mathrm{w} > c_\mathrm{s}$

NB: Deflagration front ends at a shock ($\approx c_\mathrm{s}$)

[Movies: Cosmic Defects Channel]

Deflagration $v_\mathrm{w} < c_\mathrm{s}$

Detonation $v_\mathrm{w} > c_\mathrm{s}$

NB: Deflagration front ends at a shock ($\approx c_\mathrm{s}$)

Strong simulation slice 1

[$\alpha_{T_*} = 0.5$, $v_\mathrm{w} = 0.44$ (deflag.)], velocity $\mathbf{v}$

Strong deflagrations: walls slow

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

Strong simulation slice 2

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

Strong deflagrations: vortical modes

GW production can be suppressed

Suppression relative to LISA CosWG ansatz

Conclusions

• Weak transitions: good estimates of power spectrum
  ☛ ptplot.org
• Strong transitions still an emerging topic:
  ☛ acoustic gravitational wave production suppressed
• Causes: vortical mode production and slower walls
• Worst for large $\alpha_{T_*}$, small $v_\mathrm{w}$
• Turbulence still a challenge, work ongoing
• In any case: LISA provides a model-independent probe of first-order phase transitions around $100~\mathrm{GeV}$