Does black hole continuum spectrum signal f (R) gravity in higher dimensions?

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, seem 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 that bear nontrivial 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 to the well-known Reissner-Nordstrtim-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.