Metric gravity theories and cosmology. I. Physical interpretation and viability

TL;DR

This paper critically examines metric gravity theories in cosmology, highlighting the challenges in reconstructing Lagrangians from data and emphasizing the importance of establishing physical viability before application.

Contribution

It clarifies the limitations of current gravity theories in cosmology and stresses the need for physical interpretation and viability assessment prior to observational confrontation.

Findings

Reconstruction of Lagrangians from cosmological data is impossible due to the simplicity of Robertson-Walker spacetime.

Multiple frames of dynamical variables hinder direct comparison with astronomical data.

Establishing physical content and viability of gravity theories is essential before their application to cosmology.

Abstract

We critically review some concepts underlying current applications of gravity theories with Lagrangians depending on the full Riemann tensor to cosmology. We argue that it is impossible to reconstruct the underlying Lagrangian from the observational data: the Robertson-Walker spacetime is so simple and "flexible" that any cosmic evolution may be fitted by infinite number of Lagrangians. Confrontation of a solution with the astronomical data is obstructed by the existence of many frames of dynamical variables and the fact that initial data for the gravitational triplet depend on which frame is minimally coupled to ordinary matter. Prior to any application it is necessary to establish physical contents and viability of a given gravity theory.