I will discuss a new class of solutions to the Cosmological Constant and Higgs fine-tuning problems that do not require the presence of new physics at the Large Hadron Collider. Instead, they involve a new proposal for the history of the universe wherein these parameters achieve their observed values as a result of cosmic evolution. In addition, I will exploit a loop-hole in the singularity theorems of General Relativity to allow for a calculable, non-singular 'bounce', essential for a solution to the cosmological constant problem.

##### Jean-Luc Lehners, Max Planck Institute for Gravitational Physics (Potsdam-Golm)

##### Spinor driven cosmic bounces

When coupling fermions to gravity, torsion is naturally induced. I will review the possibility that fermion bilinears can act as a source for torsion, altering the dynamics of the early universe such that the big bang gets replaced with a classical non-singular bounce. The cosmological fluctuations in these models admit many interesting features: they do not admit a scalar-vector-tensor decomposition, and consequently some types of scalar fluctuations can act as a source for gravitational waves already at linear order. Moreover, the perturbations are directionally dependent, an effect which might lead to distinguished observational signatures.

##### Harvey S. Reall, Cambridge University, UK

##### On the well-posedness of Lovelock and Horndeski theories of gravity

Lovelock theories are the most general theories of a metric tensor with second order equations of motion. Horndeski theories are the most general four-dimensional theories of a metric tensor and a scalar field with second order equations of motion. Many hundreds of papers have been written about these theories. But it is unknown whether they satisfy a basic consistency requirement, namely well-posedness of the initial value problem. I will discuss this problem and explain why the method used to establish well-posedness of the Einstein equation fails for Lovelock theories and the most general Horndeski theories.