Cosmological phase transitions at three loops: The final verdict on perturbation theory
Andreas Ekstedt, Philipp Schicho, Tuomas V. I. Tenkanen
Abstract
We complete the perturbative program for equilibrium thermodynamics of cosmological first-order phase transitions of gauge-Higgs theories that map into the (three-dimensional) superrenormalizable <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>SU</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>2</a:mn> <a:mo stretchy="false">)</a:mo> <a:mo>+</a:mo> <a:mi>doublet</a:mi> </a:mrow> </a:math> effective theory at high temperatures. To this end, we determine their finite-temperature effective potential at next-to-next-to-next-to-next-to-leading order ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi mathvariant="normal">N</e:mi> <e:mn>4</e:mn> </e:msup> <e:mi>LO</e:mi> </e:math> ). The computation of the three-loop effective potential required to reach this order is also presented for U(1) gauge theories and is readily extendable to generic models in dimensionally reduced effective theories. Our <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi mathvariant="normal">N</h:mi> <h:mn>4</h:mn> </h:msup> <h:mi>LO</h:mi> </h:math> result is the last perturbative order before confinement renders electroweak gauge-Higgs theories nonperturbative at four loops. By contrasting our analysis with nonperturbative lattice results, we find a remarkable agreement. As a direct application for predictions of gravitational waves produced by a first-order transition, our computation provides the final fully perturbative results for the phase transition strength and speed of sound. Published by the American Physical Society 2024