I briefly highlight the salient properties of modified-inertia formulations of MOND, contrasting them with those of modified-gravity formulations, which describe practically all theories propounded to date. Future data (e.g. the establishment of the Pioneer anomaly as a new physics phenomenon) may prefer one of these broad classes of theories over the other. I also outline some possible startin...

The Dolgov-Kawasaki instability discovered in the matter sector of the modified gravity scenario incorporating a −μ/R correction to Einstein gravity is studied in general f(R) theories. A stability condition is found in the metric version of these theories to help ruling out models that are unviable from the theoretical point of view. For example, the theories f(R) = R + αμ/R, where α and n are...

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.

We investigate two Type-IIa Minimally Modified Gravity theories, namely VCDM and Cuscuton theories. confirm that all acceptable solutions are always for theory. However, the inverse does not hold. find allows existence of exact General Relativity (GR) with or without presence matter fields a cosmological constant. determine conditions such GR-VCDM in terms trace extrinsic curvature on which def...