Galactic rotation curves have proven to be the testing ground for dark matter bounds in spiral galaxies of all morphologies. Dwarf galaxies serve as an increasingly interesting case of rotation curve dynamics due to their typically rising rotation curve as opposed to the flattening curve of large spirals. Dwarf galaxies usually vary in galactic structure and mostly terminate at small radial distances. This, coupled with the fact that Cold Dark Matter theories struggle with the universality of galactic rotation curves, allow for exclusive features of alternative gravitational models to be analyzed. Recently, THINGS (The HI Nearby Galactic Survey) has been extended to include a sample of 25 dwarf galaxies now known as the LITTLE THINGS Survey. Here, we show an application of alternative gravitational models to the LITTLE THINGS survey, specifically focusing on conformal gravity and Modified Newtonian Dynamics. In this work, we provide an analysis and discussion of the rotation curve predictions of each theory to the sample. Further, we show how these two alternative gravitational models account for the recently observed universal trends in centripetal accelerations in spiral galaxies. This work highlights the similarities and differences of the predictions of the two theories in dwarf galaxies. The sample is not large or diverse enough to strongly favor a single theory, but we posit that both conformal gravity and MOND can provide an accurate description of the galactic dynamics in the LITTLE THINGS sample without the need for dark matter.

Abstract. In recent years, due to the lack of direct observed evidence of cold dark matter, coupled with the shrinking parameter space to search for new dark matter particles, there has been increased interest in Alternative Gravitational theories. This paper, addresses three recent advances in conformal gravity, a fourth order renormalizable metric theory of gravitation originally formulated by Weyl, and later advanced by Mannheim and Kazanas. The first section of the paper applies conformal gravity to the rotation curves of the LITTLE THINGS survey, extending the total number of rotation curves successfully fit by conformal gravity to well over 200 individual data sets without the need for additional dark matter. Further, in this rotation curve study, we show how MOND and conformal gravity compare for each galaxy in the sample. Second, we look at the original Zwicky problem of applying the virial theorem to the Coma cluster in order to get an estimate for the cluster mass. However, instead of using the standard Newtonian potential, here we use the weak field approximation of conformal gravity. We show that in the conformal case we can get a much smaller mass estimate and thus there is no apparent need to include dark matter. We then show that this calculation is in agreement with the observational data from other well studied clusters. Last, we explore the calculation of the deflection of starlight through conformal gravity, as a first step towards applying conformal gravity to gravitaitonal lensing.