<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math>-ball perturbations with more details: Linear analysis vs lattice

We analyze in detail the interactions between the nontopological soliton (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>Q</a:mi></a:math>-ball) and its perturbations. We extend the previous literature by carefully identifying the domain of applicability of linear analysis as well as discussing Friedberg, Lee, and Sirlin <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>Q</c:mi></c:math>-balls. Applications to early Universe physics are briefly commented.