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.

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.

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.