A note on quantum fields in conformally flat spacetimes

We develop a technique relating scalar fields with different masses in different conformally flat spacetimes. We apply this technique to the case of FRW spacetimes, with [Formula: see text], and discuss several examples. We also study various energy conditions and discuss how they constrain the spacetimes related by this technique. We calculate the two-point scalar correlator in the radiation-dominated universe with a hyperbolic spatial section from the one in the Milne universe using the above mapping. Finally, we consider trace anomaly and renormalized stress tensor for conformally flat spacetimes, especially Milne and radiation-dominated universe (with [Formula: see text]) using the transformation.

Nonlocal gravity: Conformally flat spacetimes

The field equations of the recent nonlocal generalization of Einstein’s theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity (NLG) in 2D spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein’s field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of NLG.