Misalignment dynamics of scalar condensates with Yukawa coupling: Particle and entropy production

Misalignment dynamics, the nonequilibrium evolution of a scalar (or pseudoscalar) condensate in a potential landscape, broadly describes a solution to the strong <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>C</a:mi> <a:mi>P</a:mi> </a:mrow> </a:math> problem, a mechanism for cold dark matter production and (pre)reheating postinflation. Often, when radiative corrections are included phenomenologically by replacing the potential by the effective potential which is a , its usefulness is restricted to (near) equilibrium situations. We study the misalignment dynamics of a scalar condensate Yukawa coupled to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>N</c:mi> <c:mi>f</c:mi> </c:msub> </c:math> fermions in a manifestly energy conserving, fully renormalized Hamiltonian framework. A large <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>N</e:mi> <e:mi>f</e:mi> </e:msub> </e:math> limit allows us to focus on the fermion degrees of freedom, which yield a negative contribution to the effective potential, a radiatively induced instability and ultraviolet divergent field renormalization. We introduce an adiabatic basis and an adiabatic expansion that embodies the derivative expansion in the effective action, the zeroth order is identified with the effective potential, higher orders account for the derivative expansion including field renormalization, and describe profuse particle production. Energy conserving dynamics leads to the conjecture of emergent asymptotic highly excited stationary states with a distribution function <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>n</g:mi> <g:mi>k</g:mi> </g:msub> <g:mo stretchy="false">(</g:mo> <g:mi>∞</g:mi> <g:mo stretchy="false">)</g:mo> <g:mo>∝</g:mo> <g:mn>1</g:mn> <g:mo>/</g:mo> <g:msup> <g:mi>k</g:mi> <g:mn>6</g:mn> </g:msup> </g:math> and an extensive entropy which is identified with an entanglement entropy. Subtle aspects of renormalization associated with the initial value problem are analyzed and resolved. Possible new manifestations of asymptotic spontaneous symmetry breaking (SSB) as a consequence of the dynamics, even in the absence of tree-level SSB, and cosmological inferences are discussed.