On the well formulation of the Initial Value Problem of metric--affine $f(R)$-gravity

TL;DR

This paper demonstrates that the initial value problem in metric-affine f(R)-gravity is well-formulated across various scenarios, countering recent criticisms and establishing its theoretical consistency.

Contribution

It proves the well-posedness of the initial value problem in metric-affine f(R)-gravity, including matter fields, using Gaussian normal coordinates.

Findings

The initial value problem is always well-formulated in vacuum and matter scenarios.

Results counter recent criticisms questioning f(R)-gravity's viability.

The analysis uses Gaussian normal coordinates for demonstration.

Abstract

We study the well formulation of the initial value problem of f(R)-gravity in the metric-affine formalism. The problem is discussed in vacuo and in presence of perfect-fluid matter, Klein-Gordon and Yang-Mills fields. Adopting Gaussian normal coordinates, it can be shown that the problem is always well-formulated. Our results refute some criticisms to the viability of f(R)-gravity recently appeared in literature.