The Mathematical Validity of the f(R) Theory of Modified Gravity

This monograph solves the Cauchy problem for the $f(R)$ theory of modified gravity, which generalizes Einstein's theory. In the Einstein-Hilbert functional, the spacetime scalar curvature $R$ is replaced by a nonlinear function $f(R)$. The field equations are of order four in the derivatives of the metric. In this pioneering work, the authors provide a rigorous validation of this theory by analyzing the singular convergence of $f(R)$ toward $R$.