Cosmological density perturbations with modified gravity

Methods that have been used to compute density perturbations in the context of inflationary cosmology are briefly reviewed. It is then shown that the guage-invariant quantity considered by Unruh (1988) is also invariant with respect to the conformal transformation which provides an easy way to analyze nonminimally coupled modes. The analysis confirms the nonminimal coupling density perturbations formula of Fakir and Unruh (1990).