Abstract

We pave the way for future gravitational-wave detection experiments, such as the big bang observer and DECIGO, to constraint dark sectors made of $SU(N)$ Yang-Mills confined theories. We go beyond the state-of-the-art by combining first principle lattice results and effective field theory approaches to infer essential information about the nonperturbative dark deconfinement phase transition driving the generation of gravitational-waves in the early Universe, such as the order, duration and energy budget of the phase transition which are essential in establishing the strength of the resulting gravitational-wave signal.

Highlights

  • The null search results for dark matter (DM) via direct detection and colliders suggest that it is likely that DM resides in a hidden sector which couples weakly to the Standard Model (SM) [1,2,3,4,5,6,7]

  • We go beyond the stateof-the-art by combining first principle lattice results and effective field theory approaches to infer essential information about the nonperturbative dark deconfinement phase transition driving the generation of gravitational-waves in the early Universe, such as the order, duration and energy budget of the phase transition which are essential in establishing the strength of the resulting gravitational-wave signal

  • We investigate the gravitational waves (GWs) generation triggered by the dark confinement phase transition discovering, for our generic setup, that: (i) The strength parameter α, related to the energy budget of the phase transition, takes values around α ≈ 1=3, while the parameter β, that measures the inverse duration of the phase transition, assumes values of the order of 104–105 in units of the Hubble time. (ii) The GW signal emerging from sound waves dominates over the bubble collision and turbulence due to the impact of the friction term [28,29] related to the bubble-wall velocity. (iii) The strength of the induced GW signal is nearly independent of the number of colors for N ≥ 6

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Summary

INTRODUCTION

The null search results for dark matter (DM) via direct detection and colliders suggest that it is likely that DM resides in a hidden sector which couples weakly to the Standard Model (SM) [1,2,3,4,5,6,7]. These theories are physically motivated because the dynamics of the dark sector very naturally mimics the SM QCD featuring strong interactions These theories are well-behaved at short distance denoted as asymptotically freedom [8,9], meaning that the theories are, per se, ultraviolet complete before coupling to gravity, and they do not introduce new types of hierarchies beyond the SM one. We adopt state-of-the-art results of lattice simulations [19,20] combined with well-defined effective approaches [21,22,23,24] to precisely pin down the nonperturbative physics involved in the (dark) deconfinement phase transition as functions of the temperature and number of dark colors. For confinement temperatures from one to a few hundred GeV, the full range of theories will be independently tested by BBO and DECIGO They could either constrain such dark dynamics or more excitingly detect signals. We can take into account these transitions by extending the current work to properly marrying lattice data with the appropriate effective actions introduced first in [53,54]

Polyakov loop
Effective potential of the Polyakov loop model
Fitting the PLM potential to lattice data
FIRST-ORDER PHASE TRANSITION AND GRAVITATIONAL WAVES
Bubble nucleation
Inverse duration time of the phase transition
Strength parameter α
Bubble-wall velocity
Direct mass change
Δm2a a d3p ð2πÞ3
Particle splitting
A γpf2
Wall velocity
Relation to energy budget
Thin-wall approximation
Thin-wall approximation vs fitting of PLM potential
Gravitational-wave spectrum
RESULTS
CONCLUSIONS AND OUTLOOK
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