J. Besprosvany’s research while affiliated with National Autonomous University of Mexico and other places

The standard-model can be equivalently represented with its fields in a spin-extended basis, departing from fermion degrees of freedom. The common Higgs operator connects the electroweak and Yukawa sectors, restricting the top and bottom quark masses[Phys. Rev. D 99, 073001, 2019]. Using second quantization, within the heavy-particle sector, electroweak vectors, the Higgs field, and symmetry operators are expanded in terms of bilinear combinations of top and bottom quark operators, considering discrete degrees of freedom and chirality. This is interpreted as either a basis choice or as a description of composite models. The vacuum expectation value is calculated quantum mechanically, which relates to the common mass-generating scalar operator and it reproduces the vector and quark-doublet masses. This also links the corresponding scalar-vector and Yukawa vertices, and restricts the t- and b-quark masses in a hierarchy relation.

We study the evolution and power spectrum of primordial gravitational waves in the interactive Bose–Einstein gas model for dark energy, relevant, as it addresses the coincidence problem. The model is applied in the radiation, matter and dark-energy domination stages. The model introduces a scale factor associated to the radiation-matter transition which influences the gravitational spectrum. We focus on the impact of the free parameters on both the gravitational waves amplitude and its power-spectrum slope. For sets of parameters fitting Hubble’s law, we show that the model’s parameter for today’s dark-matter energy density, the mass component, has a noticeable impact on such waves, while the others produce an indistinguishable effect. The feasibility of detecting such waves under present and future measurements is discussed.

New solutions of the Bargmann-Wigner equations are obtained: free fermion-antifermion pairs, each satisfying Dirac's equation, with parallel momenta and momenta on a plane, produce vectors satisfying Proca's equations. These equations are consistent with Dirac's and Maxwell's equations, as zero-order conditions within a Lagrangian expansion for the U(1)-symmetry quantum field theory. Such vector solutions' demand that they satisfy Maxwell's equations and quantization fix the charge. The current equates the vector field, reproducing the superconductivity London equations, thus, binding and screening conditions. The derived vertex connects to QCD superconductivity and constrains four-fermion interaction composite models.

We study the evolution and power spectrum of primordial gravitational waves in the interactive Bose-Einstein gas model for dark energy, relevant, as it addresses the coincidence problem. The model is applied in the radiation, matter and dark-energy domination stages. The model introduces a scale factor associated with the radiation-matter transition which influences the gravitational spectrum. We focus on the impact of the free parameters on both the gravitational waves amplitude and its power-spectrum slope. For sets of parameters fitting Hubble's law, we show that the model's parameter for today's dark-matter energy density has a noticeable impact on such waves, while the others produce an indistinguishable effect. The feasibility of detecting such waves under present and future measurements is discussed.

Dark energy is modelled by a Bose-Einstein gas of particles with an attractive interaction. It is coupled to cold dark matter, within a flat universe, for the late-expansion description, producing variations in particle-number densities. The model's parameters, and physical association, are: $\Omega_{G0}$, $\Omega_{m0}$, the dark-energy rest-mass energy density and the dark-matter term scaling as a mass term, respectively; $\Omega_{i0}$, the self-interaction intensity; x, the energy exchange rate. Energy conservation relates such parameters. The Hubble equation omits $\Omega_{G0}$, but also contains h, the present-day expansion rate of the flat Friedman--Lem\^aitre--Robertson--Walker metric, and $\Omega_{b0}$, the baryon energy density, used as a prior. This results in the four effective chosen parameters $\Omega_{b0}$, h, $\Omega_{m0}$, $\Omega_{i0}$, fit with the Hubble expansion rate H(z), and data from its value today, near distance, and supernovas. We derive wide $1\sigma$ and $2\sigma$ likelihood regions compatible with definite positive total CDM and IBEG mass terms. Additionally, the best-fit value of parameter x relieves the coincidence problem, and a second potential coincidence problem related to the choice of $\Omega_{G0}$.

Dark energy is modelled by a Bose-Einstein gas of particles with an attractive interaction. It is coupled to cold dark matter, within a flat universe, for the late-expansion description, producing variations in particle-number densities. The model's parameters, and physical association, are: $\Omega_{G0}$, $\Omega_{m0}$, the dark-energy rest-mass energy density and the dark-matter term scaling as a mass term, respectively; $\Omega_{i0}$, the self-interaction intensity; x, the energy exchange rate. Energy conservation relates such parameters. The Hubble equation omits $\Omega_{G0}$, but also contains h, the present-day expansion rate of the flat Friedman--Lem\^aitre--Robertson--Walker metric, and $\Omega_{b0}$, the baryon energy density, used as a prior. This results in the four effective chosen parameters $\Omega_{b0}$, h, $\Omega_{m0}$, $\Omega_{i0}$, fit with the Hubble expansion rate H(z), and data from its value today, near distance, and supernovas. We derive wide $1\sigma$ and $2\sigma$ likelihood regions compatible with definite positive total CDM and IBEG mass terms. Additionally, the best-fit value of parameter x relieves the coincidence problem, and a second potential coincidence problem related to the choice of $\Omega_{G0}$.

Standard-model fields and their associated electroweak Lagrangian are equivalently expressed in a shared spin basis. The scalar-vector terms are written with scalar-operator components acting on quark-doublet elements, and shown to be parametrization-invariant. Such terms, and the t- and b-quark Yukawa terms are linked by the identification of the common mass-generating Higgs operating upon the other fields, after acquiring a vacuum expectation value v. Thus, the customary vector masses are related to the fermions', fixing the t-quark mass $m_t$ with the relation $m^2_t+m^2_b=v^2/2$ either for maximal hierarchy, or given the b-quark mass $m_b$, implying $m_t \simeq 173.9$ GeV, for v=246 GeV. A sum rule is derived for all quark masses that generalizes this restriction. An interpretation follows that electroweak bosons and heavy quarks belong in a multiplet.

Standard-model fields and their associated electroweak Lagrangian are equivalently expressed in a shared spin basis. The scalar-vector terms are written with scalar-operator components acting on quark-doublet elements, and shown to be parametrization-invariant. Such terms, and the t- and b-quark Yukawa terms are linked by the identification of the common mass-generating Higgs operating upon the other fields, after acquiring a vacuum expectation value v. Thus, the customary vector masses are related to the fermions', fixing the t-quark mass $m_t$ with the relation $m_t^2+m_b^2=v^2/2$ , either for maximal hierarchy, or given the b-quark mass $m_b$, implying $m_t \simeq 173.9$ GeV, for v=246 GeV. An interpretation follows that electroweak bosons and heavy quarks belong in a multiplet.

An extended spin-space model in 7+1 dimensions is presented that describes the standard-model electroweak quark sector. Up to four generations of massless and massive quarks and two-Higgs doublets derive from the associated representation space, in addition to the W- and Z-vector bosons. Other mass operators are obtained that put restrictions on additional non-Higgs scalars and their vacuum expectation value. After symmetry breaking, the scalar components give rise to a hierarchy effect vertically (within doublets) associated to the Higgs fields, and horizontally (within generations) associated to the non-Higgs elements.