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A brief description of the elements of noncommutative spectral geometry as an approach to unification is presented. The physical implications of the doubling of the algebra are discussed. Some high energy phenomenological as well as various cosmological consequences are presented. A constraint in one of the three free parameters, namely the one related to the coupling constants at unification, is obtained, and the possible role of scalar fields is highlighted. A novel spectral action approach based upon zeta function regularisation, in order to address some of the issues of the traditional bosonic spectral action based on a cutoff function and a cutoff scale, is discussed.
We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stuckelberg scalar) and having only three propagating degrees of freedo
One of the most important achievements of inflationary cosmology is to predict a departure from scale invariance of the power spectrum for scalar curvature cosmological fluctuations. This tilt is understood as a consequence of a quasi de Sitter class
We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetim
The mean-square width of the energy profile of bosonic string is calculated considering two boundary terms in the effective action. The perturbative expansion of the Lorentz-invariant boundary terms at the second and the fourth order in the effective
We prove the renormalizability to all orders of a refined Gribov-Zwanziger type action in linear covariant gauges in four-dimensional Euclidean space. In this model, the Gribov copies are taken into account by requiring that the Faddeev-Popov operato