Different parametrizations of field equations in the $f(R)$ theories of
  gravity
  In this paper we describe two different parametrizations of field equations
in the $f(R)$ theories of gravity and two resulting parametrizations of the
Friedmann Equations. In particular we show how these two parametrizations lead
to two different results for the curvature pressure and the curvature density
obtained respectively as the $i-i$ component and the $0-0$ component of the
curvature stress-energy tensor. We introduce formulas in order to pass from one
parametrization to another one for the curvature pressure and the curvature
density. Furthermore, we analyse under which conditions the two
parametrizations of the curvature stress-energy tensor lead to significantly
different results.
