Galactic Rotation Curves In Conformal Scalar-Tensor Gravity

Conformal gravity is a compelling alternative to Einstein's general relativity in some cases.Although there are many precise experimental tests like gravitational waves and precession of apsides that have proved the validity of Einstein's gravity,this theory also suffers several challenges such as the singularities at small scale and large discrepancies between its predictions of galactic rotation curves and observations if only baryonic matter is considered.In this thesis,we study these issues within the frame of conformal gravityWe briefly review the idea that using conformal gauge transformations to transfer the singularity in the spacetime metric to the unobserved dilaton fields.An example of the Schwarzschild metric is discussed.And we also show how the formula for calculating the black holes' entropy should be modified in the conformal scalar-tensor gravityWe also propose to explain the characteristics of the rotation curves of observed galactic bulge and halo within conformal scalar-tensor gravity.An analytic rotation velocity formula for general spacetime metric is derived.For spherically symmetric baryonic matter distribution models of galactic bulge and halo.We show that after choosing a specific kind of scale factor,the observed shape of rotation curve can arise naturally.Besides,we found a spherically symmetric solution of conformal scalar-tensor gravity in the presence of a cosmological constant compatible with two minimal assumptions:(i)the metric is written in Schwarzschild coordinates in which the two dimensional transverse area equals 4?r2,(?)the time-like and space-like components of the metric satisfy the relation g00?-1/g11.The resulting geometry captures both the local and global structure of the universe.We find a formula which has three universal parameters for the rotation velocity with the metric we found.The first of the three parameters(?*)is related to the only ambiguity present in the metric describing the local geometry,while the second parameter(?0)appears in a similar metric,but now describing the global geometry due to all the other galaxies in the Universe.The third parameter is the cosmological constantFrom the geometry of the spacetime we have extracted the local and global con-tributions to the velocity of a probe star,the two universal parameters are fixed as?*=2.56x10-39m-1 and ?0=2.94×10-28m-1.We used the MCMC method to fit the value M/L for each galaxy by fitting the actual rotation curves of a sample of 104 galaxies.The results are shown in the Fig.s.4-2-4-8 and Table(4-1)and(4-2).The plots show an extraordinary agreement between the theoretical model and observational data.We also compared conformal gravity with metric skew tensor gravity(MSTG)and modified Newtonian dynamics(MOND)for the case of a spherically distribution of matter.It turns out that at small distances,the three theories are consistent with Newtonian gravity,but at large distance the rotation velocities behave very different:in MSTG and conformal gravity the velocity decrease but in a very different way,while the velocity is constant in MOND.Although we can fit the observed rotation curves very well with the only baryonic matter,the existence of dark matter is not excluded.When compared to models in general relativities,the needed amount of dark matter is much less.We consider the outcome of our work a good reason to further reflect the dark matter problem.