Weak field and slow motion limits in energy–momentum powered gravity.

We explore the weak field and slow motion limits, Newtonian and Post-Newtonian limits, of the energy–momentum powered gravity (EMPG), viz., the energy–momentum squared gravity (EMSG) of the form f (T μ ν T μ ν) = α (T μ ν T μ ν) η with α and η being constants. We have shown that EMPG with η ≥ 0 and general relativity (GR) are not distinguishable by local tests, say, the Solar System tests; as they lead to the same gravitational potential form, PPN parameters, and geodesics for the test particles. However, within the EMPG framework, M ast , the mass of an astrophysical object inferred from astronomical observations such as planetary orbits and deflection of light, corresponds to the effective mass M eff (α , η , M) = M + M empg (α , η , M) , M being the actual physical mass and M empg being the modification due to EMPG. Accordingly, while in GR we simply have the relation M ast = M , in EMPG we have M ast = M + M empg . Within the framework of EMPG, if there is information about the values of { α , η } pair or M from other independent phenomena (from cosmological observations, structure of the astrophysical object, etc.), then in principle it is possible to infer not only M ast alone from astronomical observations, but M and M empg separately. For a proper analysis within EMPG framework, it is necessary to describe the slow motion condition (also related to the Newtonian limit approximation) by | p eff / ρ eff | ≪ 1 (where p eff = p + p empg and ρ eff = ρ + ρ empg ), whereas this condition leads to | p / ρ | ≪ 1 in GR. [ABSTRACT FROM AUTHOR]