Higher orders for cosmological phase transitions: a global study in a Yukawa model
Oliver Gould, Cheng Xie
Abstract
A bstract We perform a state-of-the-art global study of the cosmological thermal histories of a simple Yukawa model, and find higher perturbative orders to be important for determining both the presence and strength of strong first-order phase transitions. Using high-temperature effective field theory, we calculate the free energy density of the model up to $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( y 5 T 4 ), where y is the Yukawa coupling and T is the temperature. The locations of phase transitions are found using the results of lattice Monte-Carlo simulations, and the strength of first-order transitions are evaluated within perturbation theory, to 3-loop order. This is the first global study of any model at this order. Compared to a vanilla 1-loop analysis, accurate to $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( y 2 T 4 ), reaching such accuracy enables on average a five-fold reduction in the relative uncertainty in the predicted critical temperature T c , and an additional ∼ 50% strong first-order transitions with latent heat $$ L/{T}_c^4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>L</mml:mi> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> <mml:mn>4</mml:mn> </mml:msubsup> </mml:math> > 0 . 1 to be identified in our scan.