We classify all known perfect fluid cosmological solutions of the Einstein equations according to whether they are tilted or non-tilted. A non-tilted universe will have observers who see a homogeneous, isotropic universe with matter at rest with respect to them. A tilted universe will have observers who see matter moving relative to them. These classifications are useful when considering fluid models of the universe in that the Hubble parameter and expansion are observer dependent and can be different in a tilted versus a non-tilted universe. This gives more insight when fitting these models with observations of our real universe. We make these tilt classifications by establishing whether the 4-velocity of each model's fluid is aligned with the normal of the hyper-surfaces of homogeneity spanned by the Killing vectors for the space-time, which we obtain for each solution. These computations are performed using the Differential Geometry software package being developed at Utah State University. We incorporate the Killing vector fields and the tilt classification into a library of solutions to Einstein's Field Equations as part of the package, providing users with access to the solutions and their physical and geometric properties.
Ward, Bryant, "Tilt Classifications in Perfect Fluid Cosmology" (2017). Physics Capstone Project. Paper 54.