Parametric resonance in Abelian and non-Abelian gauge fields via spacetime oscillations

We study the evolution of Abelian <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo></a:math> electromagnetic as well as non-Abelian <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>2</e:mn><e:mo stretchy="false">)</e:mo></e:math> gauge fields, in the presence of spacetime oscillations. Analysis of the time evolution of Abelian gauge fields shows the presence of parametric resonance in spatial modes. A similar analysis in the case of non-Abelian gauge fields, in the linear approximation, shows the presence of the same resonant spatial modes. The resonant modes induce large fluctuations in physical observables including those that break the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>C</i:mi><i:mi>P</i:mi></i:math> symmetry. We also carry out time evolution of small random fluctuations of the gauge fields, using numerical simulations in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mn>2</k:mn><k:mo>+</k:mo><k:mn>1</k:mn></k:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mn>3</m:mn><m:mo>+</m:mo><m:mn>1</m:mn></m:math> dimensions. These simulations help to study nonlinear effects in the case of non-Abelian gauge theories. Our results show that there is an increase in energy density with the coupling, at late times. These results suggest that gravitational waves may excite non-Abelian gauge fields more efficiently than electromagnetic fields. Also, gravitational waves in the early Universe and from the merger of neutron stars, black holes, etc., may enhance <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>C</o:mi><o:mi>P</o:mi></o:math> violation and generate an imbalance in chiral charge distributions, magnetic fields, etc.