By using the equivalence between metric and Palatini f(R) (or “modified”) gravities with ω = 0,−3/2 Brans-Dicke theories, it is shown that the EhlersGeren-Sachs theorem of general relativity is extended to modified gravity. In the case of metric f(R) gravity studied before, this agrees with previous literature.

In this paper the acoustic field propagating in the early hot (p = ǫ/3) universe of arbitrary space curvature (K = 0, ±1) is considered. The field equations are reduced to the d'Alembert equation in an auxiliary static Roberson–Walker space-time. Symbolic computation in Mathematica is applied.

For any collection of graphs G1, . . . , GN we find the minimal dimension d such that the product G1 × · · · ×GN is embeddable into R . In particular, we prove that (K5) and (K3,3) are not embeddable into R, where K5 and K3,3 are the Kuratowski graphs. This is a solution of a problem of Menger from 1929. The idea of the proof is the reduction to a problem from so-called Ramsey link theory: we s...

We construct canonical realizations of the bms3 algebra as symmetry algebras of a free KleinGordon (KG) field in 2 + 1 dimensions, for both the massive and massless case. We consider two types of realizations, one on-shell, written in terms of the Fourier modes of the scalar field, and the other one off-shell with non-local transformations written in terms of the KG field and its momenta. These...