The momentum constraint equation in Parameterised Post-Newtonian Cosmology

TL;DR

This paper develops a theory-independent momentum constraint equation within the Parameterised Post-Newtonian Cosmology framework, enabling tests of gravity across various cosmological scales and theories.

Contribution

It introduces a compact, adaptable momentum constraint equation applicable to multiple gravity theories and cosmological phenomena, extending PPN formalism to cosmology.

Findings

Equations work well for quintessence, scalar-tensor, and vector-tensor models.

Applicable to both non-linear structures and super-horizon perturbations.

Facilitates theory-independent gravity constraints in cosmology.

Abstract

We derive a theory-independent version of the momentum constraint equation for use in cosmology, as a part of the Parameterised Post-Newtonian Cosmology (PPNC) framework. Our equations are constructed by adapting the corresponding quantities from formalisms devised for testing and constraining gravity in isolated astrophysical systems, thereby extending the domain of applicability of these approaches up to cosmological scales. Our parameterised equations include both scalar and divergenceless-vector gravitational potentials, and can be applied to both conservative and non-conservative theories of gravity. They can also be used to describe the gravitational fields of both non-linear structures and super-horizon perturbations. We apply the parameterised equations we propose to quintessence models of dark energy, as well as to scalar-tensor and vector-tensor theories of gravity. We find them to work well in each case. Our equations are highly compact, and are intended to be useful for constraining gravity in a theory-independent fashion in cosmology.