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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.