scholarly journals Analogies between Logistic Equation and Relativistic Cosmology

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 704
Author(s):  
Steve Dussault ◽  
Valerio Faraoni ◽  
Andrea Giusti
Keyword(s):  
Logistic Equation ◽  
Relativistic Cosmology ◽  
Friedmann Equations ◽  
Effective Lagrangian ◽  
Spatially Homogeneous

We develop several formal analogies between the logistic equation and the spatially homogeneous and isotropic relativistic cosmology described by the Einstein–Friedmann equations. These analogies produce an effective Lagrangian and Hamiltonian and new symmetries for the logistic equation.

scholarly journals Extending Friedmann Equations Using Fractional Derivatives Using a Last Step Modification Technique: The Case of a Matter Dominated Accelerated Expanding Universe

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 174
Author(s):  
Ernesto Barrientos ◽  
Sergio Mendoza ◽  
Pablo Padilla
Keyword(s):  
Fractional Derivatives ◽  
Accelerated Expansion ◽  
Relativistic Cosmology ◽  
Fractional Equations ◽  
Friedmann Equations ◽  
Dark Energy Component ◽  
Modification Technique ◽  
Acceleration Of The Universe ◽  
Expansion Of The Universe ◽  
The Universe

We present a toy model for extending the Friedmann equations of relativistic cosmology using fractional derivatives. We do this by replacing the integer derivatives, in a few well-known cosmological results with fractional derivatives leaving their order as a free parameter. All this with the intention to explain the current observed acceleration of the Universe. We apply the Last Step Modification technique of fractional calculus to construct some useful fractional equations of cosmology. The fits of the unknown fractional derivative order and the fractional cosmographic parameters to SN Ia data shows that this simple construction can explain the current accelerated expansion of the Universe without the use of a dark energy component with a MOND-like behaviour using Milgrom’s acceleration constant which sheds light into to the non-necessity of a dark matter component as well.

Problems of relativistic cosmology

1963 ◽  
Vol 80 (7) ◽  
pp. 391-438 ◽  
Author(s):  
E.M. Lifshitz ◽  
Isaak M. Khalatnikov
Keyword(s):  
Relativistic Cosmology

scholarly journals Cosmic Analogues of Classic Variational Problems

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 71 ◽  
Author(s):  
Valerio Faraoni
Keyword(s):  
Relativistic Particle ◽  
Friedmann Equation ◽  
Variational Calculus ◽  
Variational Problems ◽  
Particle Mechanics ◽  
One Dimensional ◽  
Spatially Homogeneous

Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is formally a Friedmann equation for a suitable cosmic fluid. These problems are revisited and their cosmic analogues are pointed out. Some correspond to the main solutions of cosmology, while others are analogous to exotic cosmologies with phantom fluids and finite future singularities.

scholarly journals Explicit soft supersymmetry breaking in the heterotic M-theory B − L MSSM

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anthony Ashmore ◽  
Sebastian Dumitru ◽  
Burt A. Ovrut
Keyword(s):  
Line Bundle ◽  
Supersymmetry Breaking ◽  
Moduli Space ◽  
Initial Conditions ◽  
Low Energy ◽  
Strongly Coupled ◽  
Hidden Sector ◽  
Effective Lagrangian ◽  
Soft Supersymmetry Breaking ◽  
M Theory

Abstract The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the B − L MSSM theory is reviewed, including a discussion of the “bundle” constraints that both the observable sector SU(4) vector bundle and the hidden sector bundle induced from a single line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kähler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent F-terms due to a gaugino superpotential — which spontaneously break N = 1 supersymmetry in this sector — is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli-dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kähler moduli space that satisfy all “bundle” constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.

scholarly journals Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Masaru Hongo ◽  
Suro Kim ◽  
Toshifumi Noumi ◽  
Atsuhisa Ota
Keyword(s):  
Open Systems ◽  
Effective Lagrangian ◽  
Goldstone Modes

scholarly journals Photoproduction γp→K+Λ(1520) in an effective Lagrangian approach

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Neng-Chang Wei ◽  
Yu Zhang ◽  
Fei Huang ◽  
De-Min Li
Keyword(s):  
Lagrangian Approach ◽  
Effective Lagrangian

scholarly journals NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

2000 ◽  
Vol 15 (30) ◽  
pp. 4857-4870 ◽  
Author(s):  
D. C. CABRA ◽  
E. FRADKIN ◽  
G. L. ROSSINI ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quantum Hall ◽  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Quantum Hall States ◽  
Effective Lagrangian ◽  
Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

scholarly journals The low-energy effective theory of axions and ALPs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Martin Bauer ◽  
Matthias Neubert ◽  
Sophie Renner ◽  
Marvin Schnubel ◽  
Andrea Thamm
Keyword(s):  
High Energy ◽  
New Physics ◽  
Mass Scale ◽  
Low Energy ◽  
Effective Theory ◽  
Loop Order ◽  
Flavor Changing ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Pseudoscalar Mesons

Abstract Axions and axion-like particles (ALPs) are well-motivated low-energy relics of high-energy extensions of the Standard Model, which interact with the known particles through higher-dimensional operators suppressed by the mass scale Λ of the new-physics sector. Starting from the most general dimension-5 interactions, we discuss in detail the evolution of the ALP couplings from the new-physics scale to energies at and below the scale of electroweak symmetry breaking. We derive the relevant anomalous dimensions at two-loop order in gauge couplings and one-loop order in Yukawa interactions, carefully considering the treatment of a redundant operator involving an ALP coupling to the Higgs current. We account for one-loop (and partially two-loop) matching contributions at the weak scale, including in particular flavor-changing effects. The relations between different equivalent forms of the effective Lagrangian are discussed in detail. We also construct the effective chiral Lagrangian for an ALP interacting with photons and light pseudoscalar mesons, pointing out important differences with the corresponding Lagrangian for the QCD axion.

scholarly journals Highly boosted Higgs bosons and unitarity in vector-boson fusion at future hadron colliders

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Wolfgang Kilian ◽  
Sichun Sun ◽  
Qi-Shu Yan ◽  
Xiaoran Zhao ◽  
Zhijie Zhao
Keyword(s):  
Pair Production ◽  
Vector Boson ◽  
New Physics ◽  
Higgs Bosons ◽  
Vector Boson Fusion ◽  
Final State ◽  
Proton Proton ◽  
Effective Lagrangian ◽  
Discovery Potential ◽  
New Interactions

Abstract We study the observability of new interactions which modify Higgs-pair production via vector-boson fusion processes at the LHC and at future proton-proton colliders. In an effective-Lagrangian approach, we explore in particular the effect of the operator $$ {h}^2{W}_{\mu \nu}^a{W}^{a,\mu \nu} $$ h 2 W μν a W a , μν , which describes the interaction of the Higgs boson with transverse vector-boson polarization modes. By tagging highly boosted Higgs bosons in the final state, we determine projected bounds for the coefficient of this operator at the LHC and at a future 27 TeV or 100 TeV collider. Taking into account unitarity constraints, we estimate the new-physics discovery potential of Higgs pair production in this channel.

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