Jordan and Einstein Frames Hamiltonian Analysis for FLRW Brans-Dicke Theory

Universe

Gabriele Gionti S. J.¹  Matteo Galaverni¹ 

[1] Specola Vaticana (Vatican Observatory), V-00120 Vatican City, Vatican City State;

关键词: Jordan–Einstein frame;    Hamiltonian formalism;    Brans–Dicke theory;    Dirac’s constraint theory;    canonical transformations;    quantum gravity;   

DOI  :  10.3390/universe8010014

来源: DOAJ

【 摘 要 】

We analyze the Hamiltonian equivalence between Jordan and Einstein frames considering a mini-superspace model of the flat Friedmann–Lemaître–Robertson–Walker (FLRW) Universe in the Brans–Dicke theory. Hamiltonian equations of motion are derived in the Jordan, Einstein, and anti-gravity (or anti-Newtonian) frames. We show that, when applying the Weyl (conformal) transformations to the equations of motion in the Einstein frame, we did not obtain the equations of motion in the Jordan frame. Vice-versa, we re-obtain the equations of motion in the Jordan frame by applying the anti-gravity inverse transformation to the equations of motion in the anti-gravity frame.

【 授权许可】

Unknown