In the current era of "precision cosmology", measuring the expansion rate of the Universe (Hubble constant, or H0) more accurately and precisely helps to better constrain the properties of dark energy. Cepheid-based distances are a critical step in the Extragalactic Distance Scale and have been recently used to measure H0 with a total uncertainty of only 3.4%. I will present my work on Cepheid variables in three different galaxies as part of this effort. NGC 4258 is a galaxy with a very precise and accurate distance (3% uncertainty) based on radio interferometric observations of water masers orbiting its central massive black hole. Therefore, it can be used to obtain a robust absolute calibration of the Cepheid Period-Luminosity relation. I analyzed observations of NGC 4258 obtained at Gemini North over four years and increased the number of long-period Cepheids (P>45 days) known in this galaxy. NGC 5584 was the host of type Ia SN 2007af. I applied a difference imaging technique to Hubble Space Telescope (HST) observations of this galaxy and discovered several hundred Cepheids. I compared my results with previous work based on traditional PSF photometry. The distance estimates of the two samples matched within the errors of the measurements, and so the difference imaging technique was a success. Additionally, I validated the first "white-light" variability search with the HST F350LP filter for discovering Cepheids. NGC 4921 is located in the heart of the Coma cluster at a distance of about 100 Mpc. I conducted a search for Cepheid variables using HST, extending the reach of Hubble by a factor of 3 relative to previous Cepheid work. Since Coma is in the Hubble flow, this approach eliminates the need for a secondary distance indicator and enables a direct determination of H0 based exclusively on a Cepheid distance. I present preliminary results from this challenging project.
