Post-newtonian tests of gravitational quantum field theory with spin and scaling gauge symmetry

Abstract A self-consistent gravitational quantum field theory, with gravitational force treated on the same footing as the other three fundamental interactions, was established recently. The gravidynamics predicted by such a theory could lead to important implications, and the comparisons with experimental results may provide us opportunities to test such new approach of gravity based on the framework of the quantum field theory of gauge interactions. In this work, we start with the effective field equation of the gravitational quantum field theory, and then solve the perturbative gravigauge field order by order up to the 1st post-Newtonian level under the assumption of a simplified energy–momentum tensor of perfect fluids. Having the constraints on the related post-Newtonian parameters from the most up-to-date observational data, the new bound on the combined coupling in the gravitational quantum field theory $$|\gamma _G(\alpha _G-\alpha _W/2)|\le (2.4\pm 30)\times 10^{-6} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>G</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>G</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>W</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mo>≤</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2.4</mml:mn> <mml:mo>±</mml:mo> <mml:mn>30</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> is obtained. Under such bound, we found that the new gravitational quantum field theory successfully passed and found no conflict with the contemporary keynote Solar system experiments of gravity.