The Einstein Telescope standard siren simulations for f(Q) cosmologies

Abstract To investigate the model and extra frictional effects in standard siren simulation of f ( Q ) cosmologies, we simulated three types of standard siren data based on different fiducial models ( $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM and f ( Q ) models). Both effects are important in standard siren simulation. Explicitly, the $$f(Q)_P$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>P</mml:mi> </mml:msub> </mml:mrow> </mml:math> and $$f(Q)_E$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>E</mml:mi> </mml:msub> </mml:mrow> </mml:math> models need more observational data (e.g. growth factor) to further study. The $$f(Q)_{PE}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>PE</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> model could be ruled out by the EM data. And both the $$f(Q)_{HT}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>HT</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> models will be excluded by the future standard siren data.