Speaker
Description
A longstanding issue is the equivalence between the Jordan and the Einstein frames. It is believed, but not completely proved, that the cosmological physical observables give the same results in the two frames. Our aim is to tackle this problem from the perspective of the Hamiltonian formalism. For this reason, we will perform the Hamiltonian analysis of the Brans-Dicke theory with Gibbons-Hawking-York boundary term both in the Jordan and the Einstein frames. Contrary to many claims made in the literature in the past, it will be shown that the transformations from the Jordan to the Einstein frames are not Hamiltonian canonical transformations. We will show that if we will perform a gauge fixing of the lapse and shifts functions and implement them as secondary Dirac’s constraints in the ADM formalism, the primary first-class constraints will become second class. In this way, we can eliminate these degrees of freedom replacing the Poisson brackets with the Dirac’s brackets and solve the second-class constraints. On this reduced phase space, the Hamiltonian transformations from the Jordan to the Einstein frames are Hamiltonian canonical transformations. In our opinion, this does not mean that Jordan and Einstein frames, from Hamiltonian point of view, are physically equivalent. In fact, we have only shown that solutions of the equations of motion in the Einstein frame can generate solutions of the equations of motion in the Jordan frame. Furthermore, we will see that the Jordan Frame is Hamiltonian canonical equivalent, under some transformations called anti-Newtonian transformations, to a frame whose solutions, in the limit, behave as Carroll Gravity. This abstract is partially based on the following papers: arXiv:2003.04304 Phys. Rev. D 103 024022 (2021), arXiv:2110.12222 Phys. Rev. D 105 084008 (2022), arXiv:2112.02098 Universe 8 (2022) and others to come…
