Condensate decay in a radiation dominated cosmology

We study the decay of a homogeneous condensate of a massive scalar field of mass <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>m</a:mi></a:mrow></a:math> into massless fields in thermal equilibrium in a radiation dominated cosmology. The model is a for the nonequilibrium dynamics of a misaligned axion condensate decaying into radiation. After consistent field quantization in the cosmological background, we obtain the linearized causal equations of motion for a homogeneous condensate including the finite temperature self-energy corrections up to one loop. The dynamical renormalization group is implemented to obtain the time dependent relaxation rate that describes the decay dynamics of the condensate amplitude from stimulated emission and recombination of massless quanta in the medium. It is explicitly shown that a simple friction term in the equation of motion does not describe correctly the decay of the condensate. During the super-Hubble regime, relevant for ultralight dark matter, the condensate amplitude decays as <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msup><c:mrow><c:mi>e</c:mi></c:mrow><c:mrow><c:mo>−</c:mo><c:mfrac><c:mrow><c:msup><c:mrow><c:mi>g</c:mi></c:mrow><c:mrow><c:mn>2</c:mn></c:mrow></c:msup></c:mrow><c:mrow><c:mn>10</c:mn></c:mrow></c:mfrac><c:msup><c:mrow><c:mi>t</c:mi></c:mrow><c:mrow><c:mn>2</c:mn></c:mrow></c:msup><c:mi>ln</c:mi><c:mo stretchy="false">(</c:mo><c:mn>1</c:mn><c:mo>/</c:mo><c:mi>m</c:mi><c:mi>t</c:mi><c:mo stretchy="false">)</c:mo></c:mrow></c:msup></c:mrow></c:math>. In the sub-Hubble regime the amplitude decays as <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msup><g:mrow><g:mi>e</g:mi></g:mrow><g:mrow><g:mo>−</g:mo><g:mi>γ</g:mi><g:mo stretchy="false">(</g:mo><g:mi>t</g:mi><g:mo>;</g:mo><g:mi>T</g:mi><g:mo stretchy="false">(</g:mo><g:mi>t</g:mi><g:mo stretchy="false">)</g:mo><g:mo stretchy="false">)</g:mo><g:mo>/</g:mo><g:mn>2</g:mn></g:mrow></g:msup></g:mrow></g:math> with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>T</m:mi><m:mo stretchy="false">(</m:mo><m:mi>t</m:mi><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:msub><m:mi>T</m:mi><m:mn>0</m:mn></m:msub><m:mo>/</m:mo><m:mi>a</m:mi><m:mo stretchy="false">(</m:mo><m:mi>t</m:mi><m:mo stretchy="false">)</m:mo></m:math>; therefore, the finite temperature contribution to the decay rate vanishes fast during the expansion. A main conclusion is that a phenomenological friction term is inadequate to describe the decay in the super-Hubble regime, and the decay function <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>γ</s:mi><s:mo stretchy="false">(</s:mo><s:mi>t</s:mi><s:mo stretchy="false">)</s:mo></s:math> is always than that from a local friction term as a consequence of the cosmological expansion. For ultralight dark matter, the timescale, during which transient dynamics is sensitive to cosmological expansion and a local friction term is inadequate, is much longer. A friction term always the timescale of decay in the sub-Hubble case.