Related papers: The Primordial Perturbation Spectrum and Large Sca…
These lecture notes include the following topics. Chapter 1 deals with QCD and its global symmetries in the chiral limit, explicit symmetry breaking in terms of the quark masses, and the concept of Green functions and Ward identities…
The notion of the abundance of fractals is critically re-examined in light of surprising data regarding the scaling range in empirical reports on fractality.
Low lying scalar resonances emerge as a necessary part to adjust chiral perturbation theory to experimental data once unitarity constraint is taken into consideration. I review recent progress made in this direction in a model independent…
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
After discussing alternative scenarios for the origins of the electroweak symmetry breaking, I briefly review the experimental status of the Standard Model. I explore further both the hints for, and constraints on, supposing that that a…
In this paper, we discuss the dualities of the primordial perturbation spectra from various expanding/contracting phases for full space of parameter $w\equiv {p\over \rho}$ of state equation.
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the…
The basic ideas and methods of chiral perturbation theory are briefly reviewed. I discuss the recent attempts to build an effective Lagrangian in the resonance region and summarize the known large-N_C constraints on the low-energy chiral…
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…
Systematic approaches to building up gauge invariant descriptions of charged fields, such as electrons or quarks, are described. Physically relevant descriptions must then be singled out from a multiplicity of possibilities and to this end…
We study scalar field theories that break diffeomorphism invariance down to the subgroup of transverse diffeomorphisms through the matter sector in cosmological backgrounds. We focus on single- and multi-field models and develop the…
Structured perturbation results for invariant subspaces of $\Delta$-Hermitian and Hamiltonian matrices are provided. The invariant subspaces under consideration are associated with the eigenvalues perturbed from a single defective…
In general, for single field, the scale invariant spectrum of curvature perturbation can be given by either its constant mode or its increasing mode. We show that during slowly expanding or contracting, the spectrum of curvature…
Although both early and late-time modifications of the $\Lambda$CDM model have been proposed to address the Hubble tension, compelling arguments suggest that for a solution to be successful it needs to modify the expansion history of the…
We investigate the effect of potentially large distortions of the relic neutrino spectra on cosmological observables. To that end, we consider a phenomenological model of "gray" spectral distributions, described by a single parameter, which…
We consider the most general primordial cosmological perturbation in a universe filled with photons, baryons, neutrinos, and a hypothetical cold dark matter (CDM) component within the framework of linearized perturbation theory. We give a…
In inflationary cosmology, the form of the potential is still an open problem. In this work, second-order effects of the inflationary potential are evaluated and related to the known formula for the primordial perturbations at a wide range…
Some of the difficulties arising when one tries to understand confinement as well as dynamical and anomalous chiral symmetry breaking are reviewed. Criteria to be fulfilled by a successful and complete picture of these phenomena are…
The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is…
This article is devoted to the study of scalar perturbations in loop quantum cosmology. It aims at clarifying the situation with respect to the way initial conditions are set and to the specific choice of an inflaton potential. Several…