The postulate of uniform thermal histories: a new formulation and its application to a special class of spacetimes
A new formulation of the cosmological postulate of uniform thermal histories (PUTH) is given. This formulation has the distinct feature of involving certain special vector fields which generalize the notion of Killing vector fields. It thereby quantifies the degree of departure from hypersurface homogeneity which the PUTH entails. This formulation is applied to the class of perfect fluid locally rotationally symmetric models which possess either spherical, planar, or hyperbolic symmetry. Particular emphasis is placed on the case when the fluid flow is geodesic; although this case has already been examined when the pressure and cosmological constant are both zero, many new features nevertheless come to light. Among these are obtained a coordinate-independent description which emphasizes the role of geometrically invariantly defined quantities, a new class of spacetimes which obey the PUTH yet which are not hypersurface homogeneous, an expression of the conditions for the PUTH to hold, and a somewhat unexpected characterization of a known spherically symmetric solution as the 'simplest' in the class under consideration.