On Unification of Gravity and Gauge Interactions

Considering a higher dimensional Lorentz group as the tangent symmetry, we unify gravity and gauge interactions in a natural way. The spin connection of the gauged Lorentz group is then responsible for both gravity and gauge fields, and the action for the gauged fields becomes part of the spin curvature squared. The realistic group which unifies all known particles and interactions is the $SO(1,13)$ Lorentz group whose gauge part leads to $SO(10)$ grand unified theory and contains double the number of required fermions in the fundamental spinor representation. Mirror fermions could acquire mass utilizing a mechanism employed for topological superconductors. Family unification could be achieved by considering the $SO(1,21)$ Lorentz group.Comment: 17 pages. Mirror fermions now acquire masses utilizing a mechanism employed for topological superconductor

Hidden Ghost in Massive gravity

The Hessian's determinant for a version of massive gravity given by an infinite expansion of a square root function of the induced metric, vanishes. We show that it allows us to eliminate one of four scalar fields used to generate the graviton mass. This, however, gives rise to the appearance of extra terms in the action with the squared time derivative of the metric, thus signaling that a nonlinear ghost survives.We demonstrate this phenomenon considering a simple system with constraint, which is supposed to reduces the number of physical degrees of freedom, however, we explicitly show how the constraint forces the metric to propagate an extra tachyonic state.Comment: 17 page

Mimetic Dark Matter

We reformulate Einstein's theory of gravity, isolating the conformal degree of freedom in a covariant way. This is done by introducing a physical metric defined in terms of an auxiliary metric and a scalar field appearing through its first derivatives. The resulting equations of motion split into a traceless equation obtained through variation with respect to the auxiliary metric and an additional differential equation for the trace part. As a result the conformal degree of freedom becomes dynamical even in the absence of matter. We show that this extra degree of freedom can mimic cold dark matter.Comment: 5 page

Quantum Cosmological Perturbations: Predictions and Observations

I consider the generic model independent predictions of the theory of quantum cosmological perturbations. To describe the stage of cosmic inflation, where these perturbations are amplified, the hydrodynamical approch is used. The inflationary stage is completely characterized by the deviation of the equation of state from cosmological constant which is a smooth function of the number of e-folds until the end of inflation. It is shown that in this case the spectral index should deviate from the flat one at least by 3 percent irrespective of any particular scenario. Given the value of the spectral index the lower bound on the amount of the gravitational waves produced is derived. Finally the relation between effective hydrodynamical description of inflation and inflationary scenarios is discussed

Who Ordered the Anti-de Sitter Tangent Group?

General relativity can be unambiguously formulated with Lorentz, de Sitter and anti-de Sitter tangent groups, which determine the fermionic representations. We show that besides of the Lorentz group only anti-de Sitter tangent group is consistent with all physical requirements.Comment: 6 page