Title: Lectures on the Cosmological Constant Problem Author: Antonio Padilla

These lectures on the cosmological constant problem were prepared for the X Mexican School on Gravitation and Mathematical Physics. The problem itself is explained in detail, emphasising the importance of radiative instability and the need to repeatedly fine tune as we change our effective description. Weinberg's no go theorem is worked through in detail. I review a number of proposals including Linde's universe multiplication, Coleman's wormholes, the fat graviton, and SLED, to name a few. Large distance modifications of gravity are also discussed, with causality considerations pointing towards a global modification as being the most sensible option. The global nature of the cosmological constant problem is also emphasized, and as a result, the sequestering scenario is reviewed in some detail, demonstrating the cancellation of the Standard Model vacuum energy through a global modification of General Relativity.

Title: Self-tuning and the derivation of the Fab Four Authors: Christos Charmousis, Edmund J. Copeland, Antonio Padilla, Paul M. Saffin

We have recently proposed a special class of scalar tensor theories known as the Fab Four. These arose from attempts to analyse the cosmological constant problem within the context of Horndeski's most general scalar tensor theory. The Fab Four together give rise to a model of self-tuning, with the relevant solutions evading Weinberg's no-go theorem by relaxing the condition of Poincare invariance in the scalar sector. The Fab Four are made up of four geometric terms in the action with each term containing a free potential function of the scalar field. In this paper we rigorously derive this model from the general model of Horndeski, proving that the Fab Four represents the only classical scalar tensor theory of this type that has any hope of tackling the cosmological constant problem. We present the full equations of motion for this theory, and give an heuristic argument to suggest that one might be able to keep radiative corrections under control. We also give the Fab Four in terms of the potentials presented in Deffayet et al's version of Horndeski.