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

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.

On the Trans-Planckian Censorship Conjecture and the generalized non-minimal coupling

We investigate the Trans-Planckian Censorship Conjecture (TCC) and the arising bounds on the inflationary cosmology caused by that conjecture. In that investigation, we analyze TCC bounds for both Jordan and Einstein frames in the presence of a generic non-minimal coupling (to gravity) term. That term allows us to use the functional freedom it brings to the inflationary Lagrangian as an effective Planck mass. In this sense, we argue one should consider the initial field value of the effective Planck mass for the TCC. We show that as a result, one can remove the TCC upper bounds without the need to produce a new process or go beyond the standard inflation mechanism, with the generalized non-minimal coupling, and for Higgs-like symmetry-breaking potentials.

Phase space correspondence between Jordan and Einstein frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

Vacuum Brans–Dicke theory in the Jordan and Einstein frames: Can they be distinguished by lensing?

Vacuum Brans-Dicke (BD) theory continues to receive widespread attention since it is consistent with solar and cosmological experiments. The theory can be self-consistently described in two frames, the Jordan frame (JF) and the conformally rescaled Einstein frame (EF), the transformations providing an easy passage from one frame to the other at the level of actions and solutions. While coordinate transformations do not change curvature properties, conformal transformations do change them leading to corresponding changes in the numerical values of observables. A previous article by Bhadra et al.[Formula: see text] did exemplify this change between JF and EF using the diagnostic of second-order light deflection. This important work leaves room for further improvements on two points, which we do here. First, the measurement of second-order effect faced technically unsurmountable difficulties even around the Sun, hence actually abandoned. Second, the comparison of quantitative values between JF and EF should be based on a common value of [Formula: see text] connecting the two frames. Keeping these in mind, we investigate a technically easier diagnostic, viz., the weak field lensing (WFL) and compare the quantitative changes at common [Formula: see text] to show that the two frames can indeed be distinguished by lensing experiments. Specifically, the predictions of light deflection, image position, total magnification and magnification factor are computed in the EF and compared with those recently obtained (by Gao et al.[Formula: see text]) directly in the JF BD class I solution. The use of the value of BD coupling constant [Formula: see text], suggested by the Cassini spacecraft solar experiment, reveals that an exceptionally high degree of accuracy is needed to experimentally rule out one or the other frame by means of WFL measurements.

Thermodynamical correspondence of f(R) gravity in the Jordan and Einstein frames

We study the thermodynamical aspects of [Formula: see text] gravity in the Jordan and the Einstein frame, and we investigate the corresponding equivalence of the thermodynamical quantities in the two frames. We examine static spherically symmetric black hole solutions with constant Ricci scalar curvature [Formula: see text], and as we demonstrate, the thermodynamical quantities in the two frames are equivalent. However, for the case of black holes with nonconstant scalar curvature [Formula: see text], the thermodynamical equivalence of the two frames is no longer valid. In addition, we extend our study to investigate cosmological solutions with a homogeneous and isotropic background. In particular, we find that the power-law cosmology case provides an accidentally thermodynamical equivalence of the two frames. However, for nontrivial cosmology, we examine a novel exponential ultraviolet [Formula: see text] gravity. This confirms that the thermodynamical quantities in both frames are not equivalent. In conclusion, although [Formula: see text] gravity and its corresponding scalar-tensor theory are mathematically equivalent, at least for conformal invariant quantities, the two frames are not thermodynamically equivalent at a quantitative level, in terms of several physical quantities.

Inverse-chirp imprint of gravitational wave signals in scalar tensor theory

The scalar tensor theory contains a coupling function connecting the quantities in the Jordan and Einstein frames, which is constrained to guarantee a transformation rule between frames. We simulate the supernovae core collapse with different choices of coupling functions defined over the viable region of the parameter space and find that a generic inverse-chirp feature of the gravitational waves in the scalar tensor scenario.

Screenings in modified gravity: a perturbative approach

We present a formalism to study screening mechanisms in modified theories of gravity through perturbative methods in different cosmological scenarios. We consider Einstein-frame posed theories that are recast as Jordan-frame theories, where a known formalism is employed, although the resulting nonlinearities of the Klein–Gordon equation acquire an explicit coupling between matter and the scalar field, which is absent in Jordan-frame theories. The obtained growth functions are then separated into screening and non-screened contributions to facilitate their analysis. This allows us to compare several theoretical models and to recognize patterns that can be used to distinguish models and their screening mechanisms. In particular, we find anti-screening features in the symmetron model. In contrast, chameleon-type theories in both the Jordan and Einstein frames always present a screening behaviour. Up to third order in perturbation, we find no anti-screening behaviour in theories with a Vainshtein mechanism, such as the Dvali Gabadadze Porrati braneworld model and the cubic Galileon.