pypt:

A lightweight python library to compute cosmological phase transition information, from bubble nucleations to their gravitational wave (GW) signatures and the production of primordial black holes (PBH).

Requirements:

• numpy
• scipy
• gmpy2
• cosmoTransitions

References:

• M. Quiros, "Finite temperature field theory and phase transitions" [9901312]
• Lu, Kawana, Xie, "Old Phase Remnants in First-Order Phase Transitions" [2202.03439]
• Hooper, Krnjaic, McDermott, "Dark Radiation and Superheavy Dark Matter from Black Hole Domination" [1905.01301]

Package overview

Define your own potential function (with 1-loop improved corrections and thermal corrections) that inherits from the VFT class. The VFT class has a method get_Tc() to search for the critical phase transition temperature of your potential.

One can then pass this potential into BubbleNucleation class via

bn = BubbleNucleation(my_eff_potential)

which can then compute the nucleation temperature T* via the CosmoTransitions package.

Primordial black hole (PBH) mass spectrum and their Hawking radiation spectra can be generated via the PBH class.

Gravitational waves (GW) can be generated via the Gravitational Wave class.

ODE Solver for $\rho_V + \rho_R$ Cosmic History

From Flores, Kusenko, Sasaki (FKS) (arXiv:2402.13341)[https://arxiv.org/abs/2402.13341], a method for solving the Friedmann equations with both radiation and vacuum energy considered. This solver is contained within vac_rad_cosmic_history.py and can be called by supplying information from an effective potential, e.g.

ch = CosmicHistoryVacuumRadiation(deltaV=veff(veff.vev, T=0.0), sigma=veff.wall_tension(), vw=1.0)

result = ch.solve_system()

where the output of ch.solve_system() is a 7-dimensional solution for the parameters with the following mapping:

a, rhoR, v0, v1, v2, v3, r = y[0], y[1], y[2], y[3], y[4], y[5], y[6]

all in units of a dimensionless time parameter. An example solution is shown below for 3 different benchmark phase transitions.

One can then obtain the dimensionful Hubble parameter solution by multiplying by the equilibrium Hubble value (where the vacuum and radiation densities are equal) as

rhoV = ch.rhoV(result.t, result.y)
self.hubble2_data = 0.5 * ch.Heq2 * (rhoV + result.y[1])

Note that, as described in FKS, this solution only applies if the equilibrium point takes place after the critical temperature, $T_{eq} < T_c$. Before then we assume the universe is radiation dominated, since the scalar field would not have acquired a metastable vacuum before $T_c$.