An original paper (1308.3401) studied an f(R) theory with non-minimal coupling to a massless scalar field, and used the absence of classical instabilities and superluminal propagation to constrain the gravitational sector f and the matter sector coupling. A response (1406.6422) suggested that these constraints may be too strong – arguing that (i) superluminal propagation could be interpreted as a result of considering unphysical matter content, and so it is possible to evade constraints by restricting attention to only certain matter fields, and (ii) even in the case of a massless scalar field, the derivation had neglected potentially important fluctuations. This brief note (1606.04060) attempts to justify the original claimed constraints, addressing (ii) by redoing the derivation with a different formalism, keeping track of fluctuations explicitly and showing that they have no effect (and briefly addressing (i) by arguing qualitatively that more complicated fields suffer similar pathologies to massless scalars, so more general matter fields give rise to similar constraints).

Writing down the most general Lagrangian theory one can construct using the Ricci scalar curvature, one arrives at nonminimally coupled f(R) theory. Employing classical consistency conditions, as in these papers, is an effective way to reduce the theory space (the formal constraints can immediately rule out many naively possible theories). This leaves (ideally) only a small number of theories, which can then be studied phenomenologically and compared to experiment.

This is of cosmological importance: this memory effect in FRLW can be enhanced compared to the to the effect in Minkowski. Gravitational memories may be detectable in the near future with Advanced LIGO and the upcoming eLISA mission.