  Extra dimensions, which led to the foundation and inception of string theory,
provide an elegant approach to force-unification. With bulk curvature as high
as the Planck scale, higher curvature terms, namely f(R) gravity seems to be a
natural addendum in the bulk action. These can not only pass the classic tests
of general relativity but also serve as potential alternatives to dark matter
and dark energy. With interesting implications in inflationary cosmology,
gravitational waves and particle phenomenology it is worth exploring the impact
of extra dimensions and f(R) gravity in black hole accretion. Various classes
of black hole solutions have been derived which bear non-trivial imprints of
these ultraviolet corrections to general relativity. This in turn gets engraved
in the continuum spectrum emitted by the accretion disk around black holes.
Since the near horizon regime of supermassive black holes manifest maximum
curvature effects, we compare the theoretical estimates of disk luminosity with
quasar optical data to discern the effect of the modified background on the
spectrum. In particular, we explore a certain class of black hole solution
bearing a striking resemblance with the well-known Reissner Nordstrom de
Sitter/anti-de Sitter/flat spacetime which unlike general relativity can also
accommodate a negative charge parameter. By computing error estimators like
chi-square, Nash-Sutcliffe efficiency, index of agreement, etc. we infer that
optical observations of quasars favor a negative charge parameter which can be
a possible indicator of extra dimensions. The analysis also supports an
asymptotically de Sitter spacetime with an estimate of the magnitude of the
cosmological constant whose origin is solely attributed to f(R) gravity in
higher dimensions.
