TL;DR
This paper develops a method to express the Friedmann equation using directly measurable cosmological scalars derived from higher derivatives of the scale factor, enabling tests of General Relativity with various cosmological models.
Contribution
It introduces a procedure to rewrite the Friedmann equation in terms of measurable scalars for different energy-momentum tensors, providing new tests for General Relativity.
Findings
Derived constraints on cosmological scalars for dust and Chaplygin gas models.
Established a formulation of the Friedmann equation as unparametrised geodesic motion.
Connected the scalar approach with Lagrangian methods for perfect fluids.
Abstract
We clarify the procedure for expressing the Friedmann equation in terms of directly measurable cosmological scalars constructed out of higher derivatives of the scale factor. We carry out this procedure for pure dust, Chaplygin gas and generalised Chaplygin gas energy-momentum tensors. In each case it leads to a constraint on the scalars thus giving rise to a test of General Relativity. We also discuss a formulation of the Friedmann equation as unparametrised geodesic motion and its connection with the Lagrangian treatment of perfect fluids coupled to gravity.
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