Cosmological and astrophysical tests of modified gravity

Three alternative theories to General Relativity will be studied. The aim is to test these theories by applying them to astronomical objects or the cosmological background. The first one is unimodular relativity. The cosmological perturbation theory of this model is studied and the predictions on temperature fluctuations of the CMB are found. The second one is dRGT massive gravity. In this theory a charged black hole solution is found and compared to those in GR, followed by constraints on the parameter space. The third one is a general massive gravity theory which shares the same background equation with the massless case except the evolution equation for the tensor perturbations. The signature of the graviton mass on the CMB polarization spectrum will be studied. A moderate graviton mass (comparable to the Hubble rate during recombination) leads to interesting modifications on the B mode polarization power spectrum. A large graviton mass is found to suppress the spectrum, therefore a tight constraint on the graviton mass can be found.