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The objective of this thesis is to present a viable extension of general relativity free from cosmological singularities. A viable cosmology, in this sense, is one that is free from ghosts, tachyons or exotic matter, while staying true to…
A minimal model based on the Co-varying Physical Couplings (CPC) framework for gravity is proposed. The CPC framework is based on the assumptions of a metric-compatible four-dimensional Riemannian manifold where a covariantly conserved…
The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex…
We consider modified gravity cosmological models that can be transformed into two-field chiral cosmological models by the conformal metric transformation. For the $R^2$ gravity model with an additional scalar field and the corresponding…
One hundred years ago this year attempts began to generalise general relativity with the ambition of incorporating electromagnetism alongside gravitation in a unified field theory. These developments led to gauge theories and models with…
We consider a $2d$ sigma model with a $2+N$ - dimensional Minkowski signature target space metric having a covariantly constant null Killing vector. We study solutions of the conformal invariance conditions in $2+N$ dimensions and find that…
Since viable $f(R)$ gravity models must reconcile early-universe inflation with late-time acceleration, we specifically study the dynamical behavior of such a theory during the matter-dominated to dark-energy-dominated transition epoch. By…
Recently, based on the theory of teleparallel gravity, a simple and ghost free parity violating gravity model was proposed in [M. Li, H. Rao, and D. Zhao, J. Cosmol. Astropart. Phys. 11 (2020) 023], where the Weitzenb\"{o}ck connection was…
Weyl's conformal theory of gravity is an extension of Einstein's theory of general relativity which associates metrics with 1-forms . In the case of locally integrable (closed non-exact) 1-forms the spacetime manifolds are no more simply…
We introduce the linear connection in the noncommutative geometry model of the product of continuous manifold and the discrete space of two points. We discuss its metric properties, define the metric connection and calculate the curvature.…
Ces notes de cours visent a decrire de maniere pedagogique certaines extensions populaires du modele standard des interactions fortes et electrofaibless. Les sujets abordes comprennent le secteur de Higgs, le modele symetrique gauche-droit,…
A Higgsless model for strong, electro-weak and gravitational interactions is proposed. This model is based on the local symmetry group SU(3)xSU(2)xU(1)xC where C is the local conformal symmetry group. The natural minimal conformally…
Without going to the details, I give a short, qualitative and historical description of the development of the Standard Model, from quantum electrodynamics, further through quantum chromodynamics, then to weak interactions with parity- and…
This is the last of three papers on Conformal General Relativity (CGR), which ascribes inflation to a spontaneous breakdown of conformal symmetry, followed by a sudden energy transfer from geometry to matter identified as big bang. This…
In this contribution to the volume "From My Vast Repertoire -- The Legacy of Guido Altarelli" I discuss selected topics of Standard Model (SM) physics at the LHC and their connection to the work of Guido Altarelli. An overarching connection…
By referring to theorems of Donaldson and Hitchin, we exhibit a rigorous AdS/CFT-type correspondence between classical 2+1 dimensional vacuum general relativity theory on S x R and SO(3) Hitchin theory (regarded as a classical conformal…
In this thesis, we investigate the method of conformal renormalization applied to theories with degrees of freedom beyond the metric ones. Specifically, we examine this method in the presence of a scalar field. To do this, as part of a…
Many theories of gravity admit formulations in different, conformally related manifolds, known as the Jordan and Einstein conformal frames. Among them are various scalar-tensor theories of gravity and high-order theories with the Lagrangian…
We investigate f(R)-gravity models performing the ADM-slicing of standard General Relativity. We extract the static, spherically-symmetric vacuum solutions in the general case, which correspond to either Schwarzschild de-Sitter or…
We consider conformal gravity as a gauge natural theory. We study its conservation laws and superpotentials. We also consider the Mannheim and Kazanas spherically symmetric vacuum solution and discuss conserved quantities associated to…