The Mattig Expression for a d-dimensional Gauss Bonnet FRWL Cosmology
  Here we study the form of the Mattig equation applied in a cosmological
setting for spacetime metric gravity models described by the Gauss-Bonnet
action. We start with expressing the Mattig relation for cosmological
magnitudes in terms of standard metric functions and redshift values. Then we
present the Gauss-Bonnet field equations and the associated limits for special
solutions in an arbitrary number of dimensions. These solutions are used to
rewrite the Mattig relation with correction terms from the Gauss-Bonnet
contributions for the case where the Gauss-Bonnet scale factor can be directly
used to find the distance modulus and for the case where the Gauss-Bonnet field
equations can be expressed as a small high z perturbation on the standard
Einstein field equations. As a result we can express the perturbative distance
modulus, which includes the apparent magnitude, as an additive correction to
the standard distance modulus. This results in a small shift in the apparent
magnitude of a high z object which gives a contribution depending on the
Gauss-Bonnet coupling, spacetime dimension and the cosmological constant.
