Can there be bounce in Weakly Broken Galileon (WBG) theories?

      Inflation is considered to be a crucial part of the universe cosmological history, however the so called ``standard model of the universe`` still faces the problem of the initial singularity. Such a singularity is unavoidable if inflation is realized using a scalar field while the background spacetime is described by the standard Einstein action. As a consequence, there has been a lot of effort in resolving this problem through quantum gravity effects or effective field theory techniques. A potential solution (alternative) to the cosmological singularity problem (Big Bang Cosmology) may be provided by non-singular bouncing/cyclic cosmologies. Such scenarios have been constructed through various approaches to modified gravity, effective field theory techniques, etc. One very general class of gravitational modification are galileon theories (the Lagrangian is imposed to satisfy the Galilean symmetry) which are a re-discovery of Horndeski general scalar-tensor theory. Recently, a model of Weakly Broken Galileon (WBG) symmetry appeared in the literature. In this construction the notion of WBG invariance was introduced, which characterizes the unique class of gravitational couplings that maximally preserve the defining symmetry. In my talk I shall discuss the bounce and cyclicity realization in the framework of WBG theories. I shall talk about 1) the bouncing and cyclic solutions at the background level, reconstructing the potential and the galileon functions that can give rise to a given scale factor, 2) analytical expressions for the bounce requirements. I shall also present a detailed investigation of the perturbations, which after crossing the bouncing point give rise to various observables, such as the scalar and tensor spectral indices and the tensor-to- scalar ratio. Lastly, I shall give an insight on the stability of our model, hence show for a specific choice of the galileon functions, WBG theories evade gradient instabilities, which is equivalent to bypassing Kobayashi’s no-go theorem.