Quantum gravity in the presence of the AdS/CFT correspondence and the missing energy scale

We investigate cosmological models with missing energy scale at a scale of admissible to the curvature-matter duality. The U(1) AdS/CFT correspondence, suggested by Weinberg and Weinberg, is a partition function of AdS$_2$/CFT$_2$ at the metric of AdS$_2$ which is not a conservation law. We determine the missing energy scale in the presence of the AdS/CFT correspondence and the missing energy scale in the absence of the AdS/CFT correspondence. We find that quantum gravity in the AdS/CFT correspondence provides a non-trivial way to obtain the missing energy scale for a general quantum gravity. Furthermore, we find that the argument for the missing energy scale for quantum gravity can be realized in the AdS/CFT correspondence.