Inflationary models in non-trivial field spaces encoded by their non-canonical kinetic terms have attracted attentions recently. We have then extended the so-called stochastic formalism to such a general case. This formalism investigates the fluctuation of inflatons treating them as Brownian motions. This work highlights the involved problem of this formalism, related with the mathematical uncertainty of the definition of noise integral. Comparing the correlation functions in the stochastic formalism and quantum field theory, we clarify that this uncertainty cannot be rem

Scalar-tensor theories serve models for inflation and dark energy. Many efforts have been made recently for constructing the most general scalar-tensor theories with higher-order derivatives in their Lagrangian. Since higher-derivative theories are typically associated with Ostrogradsky ghost which causes unbounded Hamiltonian, it is important to clarify how to evade it.

Within a broken local gauge vector-like $SU(3)_F$ family symmetry, we address the problem of quark masses and mixing,  and study some rare flavor violating processes induced by the new gauge bosons, which can generate transitions between different families and so introduce "Flavor Changing Neutral Currents"(FCNC) couplings at tree level. We find out that some of the most dangerous FCNC processes, like for instance; 

I will discuss prospects of formulating simple extensions of the standard model and gravity that exhibit local Weyl symmetry in the ultraviolet. The principal advantage of such constructions is that they naturally address the gauge and gravitational hierarchy problem. Furthermore,  I will argue that Cartan-Einstein gravity provides a natural framework for conformal symmetry, as this theory contains torsion vector which can be interpreted as the Weyl vector.

We show how to translate into tensorial language the Chern-Weil theorem for the Lorentz symmetry, which equates the difference of the Euler densities of two manifolds to the exterior derivative of a transgression form. For doing so we need to introduce an auxiliary, hybrid, manifold whose geometry we construct explicitely. This allows us to find the vector density, constructed out of spacetime quantities only, whose divergence is the exterior derivative of the transgression form.