Quantum gravity corrections to sequestering

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The sequestering proposal is a modification of gravity that provides a partial solution to the cosmological constant problem, inasmuch as it prevents the standard model contributions to vacuum energy from gravitating. Classical sequestering is locally equivalent to classical General Relativity on shell, although globally the theories differ. Nevertheless, Quantum gravity (QG) corrections are expected to break the (local) equivalence between the two. By adopting Donoghue's effective field theory (EFT) approach to QG below some cut-off (usually taken to be the Planck scale) we will study the leading order corrections coming from graviton loops in sequestering. Of course, to test the robustness of the proposal against graviton loops, our main interest lies in the corrections to the relevant operators that dominate the low energy dynamics. Consider, for example, the graviton corrections to the cosmological constant: at one loop we do not expect there to be any such corrections, so we will need to go to two loops for a non-trivial result. We then ask whether or not vacuum loops of gravitons sequester as efficiently as the matter loops. Initially we will ask this in the context of the classical model of sequestering. Naively we do not expect the graviton vacuum energy to cancel as readily as their standard model counterparts. It is important to quantify the size of this effect, and if it is a problem, to get some insight into what is required from a QG improved version of our model. We also need to consider the other leading order low energy QG corrections as these could potentially alter the desired structure of the low energy EFT. This could spoil the cancellation mechanism even in the matter sector, and although such an effect will surely be Planck suppressed, it is imperative we quantify this properly. Furthermore, QG corrections are also expected to alter the local equivalence to GR. This is because the equivalence is only true on shell, and not off shell, so one could imagine loops yielding distinct QG corrections to Newton's law.