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Register a new userA hybrid simulation of gravitational wave production in first-order phase transitions
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The LISA telescope will provide the first opportunity to probe the scenario of a first-order phase transition happening close to the electroweak scale. By now, it is evident that the main contribution to the GW spectrum comes from the sound waves propagating through the plasma. Current estimates of the GW spectrum are based on numerical simulations of a scalar field interacting with the plasma or on analytical approximations -- the so-called sound shell model. In this work we present a novel setup to calculate the GW spectra from sound waves. We use a hybrid method that uses a 1d simulation (with spherical symmetry) to evolve the velocity and enthalpy profiles of a single bubble after collision and embed it in a 3d realization of multiple bubble collisions, assuming linear superposition of the velocity and enthalpy. The main advantage of our method compared to 3d hydrodynamic simulations is that it does not require to resolve the scale of bubble wall thickness. This makes our simulations more economical and the only two relevant physical length scales that enter are the bubble size and the shell thickness (that are in turn enclosed by the box size and the grid spacing). The reduced costs allow for extensive parameter studies and we provide a parametrization of the final GW spectrum as a function of the wall velocity and the fluid kinetic energy.
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We study the effect of density perturbations on the process of first-order phase transitions and gravitational wave production in the early Universe. We are mainly interested in how the distribution of nucleated bubbles is affected by fluctuations in the local temperature. We find that large-scale density fluctuations ($H_* < k_* < beta$) result in a larger effective bubble size at the time of collision, enhancing the produced amplitude of gravitational waves. The amplitude of the density fluctuations necessary for this enhancement is ${cal P}_zeta (k_*) gtrsim (beta / H_*)^{-2}$, and therefore the gravitational wave signal from first-order phase transitions with relatively large $beta / H_*$ can be significantly enhanced by this mechanism even for fluctuations with moderate amplitudes.
We study gravitational wave (GW) production in strongly supercooled cosmological phase transitions, taking particular care of models featuring a complex scalar field with a U$(1)$ symmetric potential. We perform lattice simulations of two-bubble collisions to properly model the scalar field gradients, and compute the GW spectrum sourced by them using the thin-wall approximation in many-bubble simulations. We find that in the U$(1)$ symmetric case the low-frequency spectrum is $proptoomega$ whereas for a real scalar field it is $proptoomega^3$. In both cases the spectrum decays as $omega^{-2}$ at high frequencies.
Primordial black holes (PBHs) produced in the early Universe have attracted wide interest for their ability to constitute dark matter and explain the compact binary coalescence. We propose a new mechanism of PBH production during first-order phase transitions (PTs) and find that PBHs are naturally produced during PTs model-independently. Because of the randomness of the quantum tunneling, there always exists some probability that the vacuum decay is postponed in a whole Hubble volume. Since the vacuum energy density remains constant while radiation is quickly redshifted in the expanding Universe, the postponed vacuum decay then results in overdense regions, which finally collapse into PBHs as indicated by numerical simulations. Utilizing this result one can obtain mutual predictions and constraints between PBHs and GWs from PTs. The predicted mass function of PBHs is nearly monochromatic. We investigate two typical cases and find that 1) PBHs from a PT constitute all dark matter and GWs peak at $1$Hz, 2) PBHs from a PT can explain the coalescence events observed by LIGO-Virgo collaboration, and meanwhile GWs can explain the common-spectrum process detected by NANOGrav collaboration.
We study the generation of intergalactic magnetic fields in two models for first-order phase transitions in the early Universe that have been studied previously in connection with the generation of gravitational waves (GWs): the Standard Model supplemented by an $|H|^6$ operator (SM+$H^6$) and a classically scale-invariant model with an extra gauged U(1) $B - L$ symmetry (SM$_{B-L}$). We consider contributions to magnetic fields generated by bubble collisions and by turbulence in the primordial plasma, and we consider the hypotheses that helicity is seeded in the gauge field or kinetically. We study the conditions under which the intergalactic magnetic fields generated may be larger than the lower bounds from blazar observations, and correlate them with the observability of GWs and possible collider signatures. In the SM+$H^6$ model bubble collisions alone cannot yield large enough magnetic fields, whereas turbulence may do so. In the SM$_{B-L}$ model bubble collisions and turbulence may both yield magnetic fields above the blazar bound unless the B$-$L gauge boson is very heavy. In both models there may be observable GW and collider signatures if sufficiently large magnetic fields are generated.
We discuss the possibility of forming primordial black holes during a first-order phase transition in the early Universe. As is well known, such a phase transition proceeds through the formation of true-vacuum bubbles in a Universe that is still in a false vacuum. When there is a particle species whose mass increases significantly during the phase transition, transmission of the corresponding particles through the advancing bubble walls is suppressed. Consequently, an overdensity can build up in front of the walls and become sufficiently large to trigger primordial black hole formation. We track this process quantitatively by solving a Boltzmann equation, and we determine the resulting black hole density and mass distribution as a function of model parameters.
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