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Register a new userConformal gravity: light deflection revisited and the galactic rotation curve failure
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We show how Conformal Gravity (CG) has to satisfy a fine-tuning condition to describe the rotation curves of disk galaxies without the aid of dark matter. Interpreting CG as a gauge natural theory yields conservation laws and their associated superpotentials without ambiguities. We consider the light deflection of a point-like lens and impose that the two Schwarzschild-like metrics with and without the lens are identical at infinite distances from the lens. The energy conservation law implies that the parameter $gamma$ in the linear term of the metric has to vanish, otherwise the two metrics are physically inaccessible from each other. This linear term is responsible to mimic the role of dark matter in disk galaxies and gravitational lensing systems. Our analysis shows that removing the need of dark matter with CG thus relies on a fine-tuning condition on $gamma$. We also illustrate why the results of previous investigations of gravitational lensing in CG largely disagree. These discrepancies derive from the erroneous use of the deflection angle definition adopted in General Relativity, where the vacuum solution is asymptotically flat, unlike CG. In addition, the lens mass is identified with various combinations of the metric parameters. However, these identifications are arbitrary, because the mass is not a conformally invariant quantity, unlike the conserved charge associated to the energy conservation law. Based on this conservation law and by removing the fine-tuning condition on $gamma$, i.e. by setting $gamma=0$, the energy difference between the metric with the point-like lens and the metric without it defines a conformally invariant quantity that can in principle be used for (1) a proper derivation of light deflection in CG, and (2) the identification of the lens mass with a function of the parameters $beta$ and $k$ of the Schwarzschild-like metric.
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We discuss the effect of a conformally coupled Higgs field on conformal gravity (CG) predictions for the rotation curves of galaxies. The Mannheim-Kazanas (MK) metric is a valid vacuum solution of CGs 4-th order Poisson equation only if the Higgs field has a particular radial profile, S(r)=S_0 a/(r+a), decreasing from S_0 at r=0 with radial scale length a. Since particle rest masses scale with S(r)/S_0, their world lines do not follow time-like geodesics of the MK metric g_ab, as previously assumed, but rather those of the Higgs-frame MK metric Omega^2 g_ab, with the conformal factor Omega(r)=S(r)/S_0. We show that the required stretching of the MK metric exactly cancels the linear potential that has been invoked to fit galaxy rotation curves without dark matter. We also formulate, for spherical structures with a Higgs halo S(r), the CG equations that must be solved for viable astrophysical tests of CG using galaxy and cluster dynamics and lensing.
The conformal gravity fit to observed galactic rotation curves requires {gamma}>0. On the other hand, conventional method for light deflection by galaxies gives a negative contribution to Schwarzschild value for {gamma}>0, which is contrary to observation. Thus, it is very important that the contribution to bending should in principle be positive, no matter how small its magnitude is. Here we show that the Rindler-Ishak method gives a positive contribution to Schwarzschild deflection for {gamma}>0, as desired. We also obtain the exact local coupling term derived earlier by Sereno. These results indicate that conformal gravity can potentially test well against all astrophysical observations to date.
We calculate the deflection angle, as well as the positions and magnifications of the lensed images, in the case of covariant $f(T)$ gravity. We first extract the spherically symmetric solutions for both the pure-tetrad and the covariant formulation of the theory, since considering spherical solutions the extension to the latter is crucial, in order for the results not to suffer from frame-dependent artifacts. Applying the weak-field, perturbative approximation we extract the deviations of the solutions comparing to General Relativity. Furthermore, we calculate the deflection angle and then the differences of the positions and magnifications in the lensing framework. This effect of consistent $f(T)$ gravity on the lensing features can serve as an observable signature in the realistic cases where $f(T)$ is expected to deviate only slightly from General Relativity, since lensing scales in general are not restricted as in the case of Solar System data, and therefore deviations from General Relativity could be observed more easily.
We present a novel test of general relativity (GR): measuring the geometric component of the time delay due to gravitational lensing. GR predicts that photons and gravitational waves follow the same geodesic paths and thus experience the same geometric time delay. We show that for typical systems, the time delays are tens of seconds, and thus can dominate over astrophysical delays in the timing of photon emission. For the case of GW 170817, we use a multi-plane lensing code to evaluate the time delay due to four massive halos along the line of sight. From literature mass and distance measurements of these halos, we establish at high confidence (significantly greater than 5 sigma) that the gravitational waves of GW 170817 underwent gravitational deflection to arrive within 1.7 seconds of the photons.
LambdaCDM, for the currently preferred cosmological density Omega_0 and cosmological constant Omega_Lambda, predicts that the Universe expansion decelerates from early times to redshift z~0.9 and accelerates at later times. On the contrary, the cosmological model based on conformal gravity predicts that the cosmic expansion has always been accelerating. To distinguish between these two very different cosmologies, we resort to gamma-ray bursts (GRBs), which have been suggested to probe the Universe expansion history at z>1, where identified type Ia supernovae (SNe) are rare. We use the full Bayesian approach to infer the cosmological parameters and the additional parameters required to describe the GRB data available in the literature. For the first time, we use GRBs as cosmological probes without any prior information from other data. In addition, when we combine the GRB samples with SNe, our approach neatly avoids all the inconsistencies of most numerous previous methods that are plagued by the so-called circularity problem. In fact, when analyzed properly, current data are consistent with distance moduli of GRBs and SNe that can respectively be, in a variant of conformal gravity, ~15 and ~3 magnitudes fainter than in LambdaCDM. Our results indicate that the currently available SN and GRB samples are accommodated equally well by both LambdaCDM and conformal gravity and do not exclude a continuous accelerated expansion. We conclude that GRBs are currently far from being effective cosmological probes, as they are unable to distinguish between these two very different expansion histories.
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