Tests of $\Lambda$CDM and Conformal Gravity using GRB and Quasars as Standard Candles out to $z \sim 8$

We compare the cosmology of conformal gravity (CG), (Mannheim 2006), to $\Lambda$CDM. CG cosmology has repulsive matter and radiation on cosmological scales, while retaining attractive gravity at local scales. Mannheim (2003) finds that CG agrees with $\Lambda$CDM for supernova data at redshifts $z<1$. We use GRBs and quasars as standard candles to contrast these models in the redshift range $0<z<8$. We find CG deviates significantly from $\Lambda$CDM at high redshift and that $\Lambda$CDM is favoured by the data with $\Delta\chi^2=48$. Mannheim's model has a bounded dark energy contribution, but we identify a $\lambda$ fine-tuning problem and a cosmic coincidence problem.