Searching for dark torsion signatures at LIGO in Nieh–Yan teleparallel chiral gravitational waves and Chern–Simons invariants

Abstract Romano has recently found that frequency modulation of gravitational waves (GWs) could be used as a dark matter probe. Many candidates for dark matter (DM) of various sources have been proposed in the literature. In this work, we use a teleparallel modified GW model to obtain DM dark torsion from LIGO data, where frequency modulation and frequency bands from various sources of GWs are investigated with regard to their suitability for DM dark torsion detection. In particular, nonhomogeneous and nonuniform chiral chemical potential generates GWs and dark torsion from primordial magnetic fields. It is shown that pulsar sources for GWs bathing the surface of the Earth on a contortion background of $$10^{-15}\,\textrm{s}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <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:msup> <mml:mtext>s</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> possess amplitudes well within the parameters of LIGO capabilities of amplitudes on the order of $$10^{-22}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>22</mml:mn> </mml:mrow> </mml:msup> </mml:math> . GWs are also investigated in the context of having been produced by a primordial magnetic field and inhomogeneity on the chiral chemical potential. The torsion signatures at LIGO correspond to the amplitude dependence of massive torsion by GWs.