Tests of CPT invariance in gravitational waves with LIGO-Virgo catalog GWTC-1
Sai Wang, Zhichao Zhao
Abstract
Abstract A discovery of gravitational waves from binary black holes raises a possibility that measurements of them can provide strict tests of CPT invariance in gravitational waves. When CPT violation exists, if any, gravitational waves with different circular polarizations could gain a slight difference in propagating speeds. Hence, the birefringence of gravitational waves is induced and there should be a rotation of plus and cross modes. For CPT-violating dispersion relation $${\omega ^{2}=k^{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>ω</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math> $${\pm 2\zeta k^{3}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>±</mml:mo><mml:mn>2</mml:mn><mml:mi>ζ</mml:mi><mml:msup><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:math> , where a sign $${\pm }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>±</mml:mo></mml:math> denotes different circular polarizations, we find no substantial deviations from CPT invariance in gravitational waves by analyzing a compilation of ten signals of binary black holes in the LIGO-Virgo catalog GWTC-1. We obtain a strict constraint on the CPT-violating parameter, i.e., $$\zeta =0.14^{+0.22}_{-0.31}\times 10^{-15}\,\text {m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ζ</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:msubsup><mml:mn>14</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.31</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.22</mml:mn></mml:mrow></mml:msubsup><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>15</mml:mn></mml:mrow></mml:msup><mml:mspace/><mml:mtext>m</mml:mtext></mml:mrow></mml:math> , which is around two orders of magnitude better than the existing one. Therefore, this study stands for the up-to-date strictest tests of CPT invariance in gravitational waves.