Holographic Model Research Articles

Chiral separation effect from holographic QCD

We analyze the chiral separation effect (CSE) in QCD by using the gauge/gravity duality. In QCD, this effect arises from a combination of chiral anomalies and the axial U(1) anomaly. Due to the axial gluon anomaly, the value of the CSE conductivity is not determined by the anomalies of QCD but receives radiative corrections, which leads to nontrivial dependence on temperature and density. To analyze this dependence, we use different variants of the V-QCD, a complex holographic model, carefully fitted to QCD data. We find our results for the anomalous CSE conductivity at small chemical potential and nonzero temperature to be in good qualitative agreement with recent results from lattice QCD simulations. We furthermore give predictions for the behavior of the conductivity at finite (vectorial and axial) chemical potentials.

Holographic QCD running coupling for light quarks in strong magnetic field

We study the influence of magnetic field on the running coupling constant using a bottom-up holographic model. We use the boundary condition that ensures the agreement with lattice calculations of string tension between quarks at zero chemical potential. The location of the 1st order phase transitions in (μ,T)-plane does not depend on the dilaton boundary conditions. We observe that the running coupling α decreases with increasing magnetic field for the fixed values of chemical potential and temperature. At the 1st order phase transitions, the functions α undergo jumps depending on temperature, chemical potential, and magnetic field. Published by the American Physical Society 2024

Dynamic Acoustic Holography: One-Shot High-Precision and High-Information Methodology

Acoustic holography technology is widely used in the field of ultrasound due to its capability to achieve complex acoustic fields. The traditional acoustic holography method based on single-phase holograms is limited due to its inability to complete acoustic field control with high dynamics and accuracy. Here, we propose a method for constructing an acoustic holographic model, introducing an ultrasonic array to provide dynamic amplitude control degrees of freedom, and combining the dynamically controllable ultrasonic array and high-precision acoustic hologram to achieve the highest acoustic field accuracy and dynamic range. This simulation method has been proven to be applicable to both simple linear patterns and complex surface patterns. Moreover, it is possible to reconstruct the degree of freedom of the target plane amplitude effectively and achieve a breakthrough in high information content. This high-efficiency acoustic field control capability has potential applications in ultrasound imaging, acoustic tweezers, and neuromodulation.

Constraining neutrino masses in the Barrow holographic dark energy model with Granda–Oliveros IR cutoff

The holographic dark energy (HDE) model resides in quantum gravity in connection with the entropy, which requires an appropriate IR-cutoff to support the accelerating universe. Of these, the BHDE is corresponding to the quantum-corrected Barrow entropy SB∝A1+Δ/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{B}\\propto A^{1+\\Delta /2}$$\\end{document} for which the Granda–Oliveros (GO) IR-cutoff LIR=(αH2+βH˙)-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_{IR}=(\\alpha H^2 + \\beta \\dot{H})^{-\\frac{1}{2}}$$\\end{document} avoids the causality problem of the typically used future event-horizon. As the cosmological evolution of the model has recently been studied, we include the relic-neutrinos to constraint the well-motivated model’s parameters (α,β,Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha , \\beta , \\Delta $$\\end{document}) along with the total mass of neutrinos ∑mν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sum m_{\ u }$$\\end{document} and the effective number of their species Neff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{eff}$$\\end{document} using a variety of the latest observational data. Utilizing the basic observations from 2018 Planck CMB-data, BAO-data, Pantheon sample of type Ia supernovae (SNIa), H(z) measurements of cosmic chronometers (CC) and various combinations of them, we find ∑mν<0.119\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sum m_{\ u } < 0.119$$\\end{document} eV (95 % CL) for CMB + ALL combination, aligning with ∑mν<0.12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sum m_{\ u } < 0.12$$\\end{document} eV, (95% CL) of 2018 Planck release plus BAO data. The value of Neff=2.98-0.25+0.25\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{eff}=2.98^{+0.25}_{-0.25}$$\\end{document} (68% CL) is also determined which is consistent with BAO+Planck’s Neff=2.99-0.17+0.17\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{eff}=2.99^{+0.17}_{-0.17}$$\\end{document} (68% CL). The AIC analysis shows that the model (especially its α=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =1$$\\end{document} case) is (mildly) favored over the concordance Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM for that complete combination. Furthermore, the Barrow–Granda–Oliveros parameters are found in using the above datasets, as they get α=0.98-0.06+0.06\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =0.98^{+0.06}_{-0.06}$$\\end{document}, β=0.597-0.08+0.07\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta =0.597^{+0.07}_{-0.08}$$\\end{document} and Δ=0.0054-0.0076+0.0076\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta =0.0054^{+0.0076}_{-0.0076}$$\\end{document} for CMB + ALL combination, where are in agreement with previous studies. The use of these best-fitting values in plotting the deceleration parameter q(z) shows that the universe undergoes a deceleration-acceleration transition at ztr=0.63\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z_{tr}=0.63$$\\end{document}, by entering the current phase of dark-energy domination with q0=-0.573\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q_0=-\\,0.573$$\\end{document}.

Non-interacting String and Holographic Dark Energy Cosmological Models in f(R) Theory of Gravitation

Non-interacting String and Holographic Dark Energy Cosmological Models in f(R) Theory of Gravitation

Anomalous and linear holographic hard wall models for light unflavored mesons

In this work we consider anomalous and linear holographic hard wall (HW) models for light unflavored mesons inspired by the AdS/CFT correspondence. The anomalous dimensions depend on the logarithm of the spin S of the meson state and come from a semiclassical analysis of gauge/string duality. The anomalous HW model produces very good masses and good Regge trajectories for mesons compared with PDG data. Inspired by this anomalous HW model we also propose a phenomenological modification of the dimension of the boundary operators such that the model produces asymptotic linear Regge trajectories. Both anomalous HW models considered here present mass percentage deviations of less than 3%, when compared with PDG data. Published by the American Physical Society 2024

Proceedings of a membrane update symposium: advancements, scientific insights, and future trends for dialysis membranes for enhanced clinical outcomes in end stage kidney disease patients.

From September 6 - 8 2022, the Life/2022 Membrane Symposium was held in Frankfurt, Germany, and transmitted live to a worldwide internet audience. The event was part of the Life/Nephrology Campus initiative, a continuous educational platform for the nephrology community to expand knowledge and share expertise on contemporary topics in chronic kidney disease. We describe recent questions and advances in the field, and we underline challenges in the care of dialysis patients and opportunities for integration of new findings into clinical practice to improve patient outcomes in end stage kidney disease patients. Most patients with kidney failure are on maintenance hemodialysis (MHD). The scientific program of the symposium was developed around topics about the role, functional determinants, technical aspects, limitations, and clinical implications of membranes presently in use. International experts with clinical or technical expertise as well as scientific recognition within the nephrology community were asked to prepare their presentations based on their own experiences, perceptions, opinions, and sources of information. The symposium devoted a major portion to discussing novel approaches for improving membranes and treatment quality, including updates on innovative concepts that may could potentially transform the landscape of kidney replacement therapy for chronic kidney disease patients in the future. The intent was to provide insights into current attention points for healthcare professionals new to the field of MHD, and to test a unique forum for continuing medical education integrating physician and patient experiences to promote changes in clinical practice. Furthermore, the symposium premiered a specifically developed mixed reality holographic 3D model to demonstrate recent dialyzer innovation diminishing protein fouling on membrane surfaces. As a continuous online educational platform for scientific exchange, this Life/2022 event provided online learning opportunities with on-demand content, with all symposium lectures freely available on nephrologycampus.com.

Holographic bounce cosmological models induced by viscous dark fluid from a generalized non-singular entropy function

Bounce cosmological models containing a dark viscous fluid in a spatially flat Friedmann–Robertson–Walker (FRW) universe are considered. The universe’s evolution is described in terms of generalized equation of state (EoS) parameters, in the presence of the bulk viscosity. Entropic cosmology plays a key role in the discussion, and the matter bounce behavior is described based on a nonsingular, generalized entropy function, recently proposed by S. D. Odintsov and T. Paul. Three different forms of the scale factor are investigated: an exponential, a power-law and a double-exponential function, respectively. Appropriate bounce cosmological models are formulated, via the relevant parameters of the modified EoS, and analytical expressions for the corresponding infrared cut-off are obtained, via the particle horizon. Results are displayed in holographic form, making use of generalized holographic cut-offs first introduced by S. Nojiri and S. D. Odintsov. In addition, the viability of the corresponding bounce cosmological models is investigated, taking into account the actual thermodynamic properties of our universe, by means of a no-singular, generalized entropy function. In the asymptotic case, an expression for the generalized entropy is obtained, which remarkably has the additivity property.

Nonminimal coupling holographic superconductors

We explore a holographic superconductor model in which a real scalar field is nonminimally coupled to a gauge field. We consider several types of the nonminimal coupling function h(ψ) including exponential, hyperbolic (cosh), power-law, and fractional forms. We investigate the influences of the nonminimal coupling parameter α on condensation, critical temperature, and conductivity. We can categorize our results in two groups. In the first group, conductor/superconductor phase transition is easier to occur for larger values of α, while in the second group stronger effects of the nonminimal coupling makes the formation of scalar hair harder. Although the real and imaginary parts of conductivity are impressed by different forms of h(ψ), they follow some universal behaviors such as connecting with each other through Kramers–Kronig relation in ω → 0 limit or the appearance of gap frequency at low temperatures around ωg ∼ 8 Tc, which shifts to larger values by increasing the strength of α. Among all forms of h(ψ) we observe that h(ψ) = 1 + αψ2 gives us better information in wide range of nonminimal coupling constant and temperature. Choosing the best form of h(ψ), we construct a family of solutions for holographic conductor/superconductor phase transitions to discover the effect of the hyperscaling violation when the gauge and scalar fields are nonminimally coupled. we find that the critical temperature increases for higher effects of hyperscaling violation θ and nonminimal coupling constant α. By increasing these two parameters, we obtain lower values of condensation which means that conductor/superconductor phase transition will acquire easier. Furthermore, we understand that the hyperscaling violation affects the conductivity σ of the holographic superconductors and changes the expected relation in the gap frequency. Some universal behaviors like infinite DC conductivity are observed. In addition, we consider a five-dimensional Gauss–Bonnet (GB) black hole with a flat horizon. We find out that the critical temperature decreases for larger values of GB coupling constant, λ, or smaller values of nonminimal coupling constant, α, which means that the condensation is harder to form. Moreover, we study the electrical conductivity in the holographic setup. We observe that the gap frequency shifts to larger values for stronger λ, and becomes flat by increasing α.

Classes of holographic Mott gaps

The fermion gaps are classified into order gap or Mott gap depending on the presence/absence of the order parameter. We construct the holographic model of the Mott gap using the field that is supported by the density only without introducing any order parameter. We then classify the Mott gap, depending on the shape of the gap in the density of states and whether the Fermi surface is touching the valence bond or not, into three classes: i) Symmetric gap, ii) Asymmetric gap with isolated Fermi sea. iii) Asymmetric gap with Fermi sea touching the valence band. Finally, we identify possible non-minimal gauge interactions that produce a flatband without symmetry breaking.

A holographic model of magnetohydrodynamics with fortuitous SO(3) symmetry

We study magnetohydrodynamics using holography. The gravity model is closely related to the STU supergravity in five dimensions and admits an analytical black brane solution carrying the conserved charge dual to the magnetic 1-form symmetry of the magnetohydrodynamic system. The black brane solution features a fortuitous SO(3) symmetry, providing a new symmetry principle for describing the magnetohydrodynamics. Since the bulk theory contains multiple 2-form gauge fields, the resistivity becomes matrix-valued. We find that the antisymmetric part of the resistivity matrix exhibits novel features depending on the UV cut-off of the theory. We also compute the shear and bulk viscosities and find that the bulk viscosity is proportional to the shear viscosity. Remarkably, the proportionality constant is exactly what is required for conformality, despite the zeroth-order energy-momentum tensor not being trace-free.

HERMES: Holographic Equivariant neuRal network model for Mutational Effect and Stability prediction.

Predicting the stability and fitness effects of amino-acid mutations in proteins is a cornerstone of biological discovery and engineering. Various experimental techniques have been developed to measure mutational effects, providing us with extensive datasets across a diverse range of proteins. By training on these data, machine learning approaches have advanced significantly in predicting mutational effects. Here, we introduce HERMES, a 3D rotationally equivariant structure-based neural network model for mutation effect prediction. Pre-trained to predict amino-acid propensities from their surrounding 3D structure atomic environments, HERMES can be efficiently fine-tuned to predict mutational effects, thanks to its symmetry-aware parameterization of the output space. Benchmarking against other models demonstrates that HERMES often outperforms or matches their performance in predicting mutation effects on stability, binding, and fitness, using either computationally or experimentally resolved protein structures. HERMES offers a versatile suit of tools for evaluating mutation effects and can be easily fine-tuned for specific predictive objectives using our open-source code.

Gravitational waves driven by holographic dark energy

In this paper, we have studied the effects of holographic dark energy on the evolution of gravitational waves. The background evolution of gravitational waves in a flat FRW universe is considered and studied in the presence of various holographic dark energy models. The perturbation equations governing the evolution of the gravitational waves have been constructed and solutions are obtained. These solutions are studied in detail to get a proper understanding of the characteristics of the gravitational waves in the presence of holographic dark energy. The work can be a significant tool in studying different dark energy models comparatively using the features of the gravitational wave evolution.

Holographic Lifshitz flows

Without Lorentz symmetry, generic fixed points of the renormalization group (RG) are labelled by their dynamical (or ‘Lifshitz’) exponent z. Hence, a rich variety of possible RG flows arises. The first example is already given by the standard non-relativistic limit, which can be viewed as the flow from a z = 1 UV fixed point to a z = 2 IR fixed point. In strongly coupled theories, there are good arguments suggesting that Lorentz invariance can emerge dynamically in the IR from a Lorentz violating UV. In this work, we perform a generic study of fixed points and the possible RG flows among them in a minimal bottom-up holographic model without Lorentz invariance, aiming to shed light on the possible options and the related phenomenology. We find: i) A minor generalization of previous models involving a massive vector field with allowed self-couplings leads to a much more efficient emergence of Lorentz invariance than in the previous attempts. Moreover, we find that generically the larger is the UV dynamical exponent zUV the faster is the recovery of Lorentz symmetry in the IR. ii) We construct explicitly a holographic model with a line of fixed points, realizing different Lifshitz scaling along the line. iii) We also confirm the monotonicity of a recently proposed a-function along all our Lorentz violating RG flows.

Holographic description of an anisotropic Dirac semimetal

Holographic quantum matter exploits the AdS/CFT correspondence to study systems in condensed matter physics. An example of these systems are strongly correlated semimetals, which feature a rich phase diagram structure. In this work, we present a holographic model for a Dirac semimetal in 2 + 1 dimensions that features a topological phase transition. Our construction relies on deforming a relativistic UV fixed point with some relevant operators that explicitly break rotations and some internal symmetries. The phase diagram for different values of the relevant coupling constants is obtained. The different phases are characterized by distinct dispersion relations for probe fermionic modes in the AdS geometry. We find semi-metallic phases characterized by the presence of Dirac cones and an insulating phase featuring a mass gap with a mild anisotropy. Remarkably, we find as well an anisotropic semi-Dirac phase characterized by a massless a fermionic excitation dispersing linearly in one direction while quadratically in the other.

Inverse magnetic catalysis and energy loss in a holographic QCD model

In this paper, we consider the Einstein-Maxwell-dilaton holographic model for light quarks with nonzero magnetic field and chemical potential. First, we study the phase diagrams in T−μ and T−B planes. We observe inverse magnetic catalysis which is consistent with the lattice QCD results. We discuss the influence of the magnetic field and chemical potential on the location of the critical end point (CEP). It is found that the magnetic field increases the critical μCEP of the CEP in the T−μ plane and the chemical potential increases the critical BCEP of the CEP in the T−B plane. Second, we discuss the equations of state (EOS) with nonzero magnetic field and chemical potential. We observe that the EOS near the phase transition temperature are nonmonotonic. Then we study the energy loss with a nonzero magnetic field and chemical potential. It is found that the drag force of the heavy quark and jet quenching parameter q^ show an enhancement near the phase transition temperature. The peak values of drag force and q^ are pushed toward lower temperature with increasing B or μ. This phenomenon is consistent with the phase transition temperature decrease with increasing B or μ in this holographic model. Moreover, we find that the heavy quark may lose more energy when it is perpendicular to a magnetic field, which is consistent with the results of the jet quenching parameter. Published by the American Physical Society 2024

Entanglement membrane in exactly solvable lattice models

Entanglement membrane theory is an effective coarse-grained description of entanglement dynamics and operator growth in chaotic quantum many-body systems. The fundamental quantity characterizing the membrane is the entanglement line tension. However, determining the entanglement line tension for microscopic models is in general exponentially difficult. We compute the entanglement line tension in a recently introduced class of exactly solvable yet chaotic unitary circuits, so-called generalized dual-unitary circuits, obtaining a nontrivial form that gives rise to a hierarchy of velocity scales with vE&lt;vB. For the lowest level of the hierarchy, L¯2 circuits, the entanglement line tension can be computed entirely, while for the higher levels the solvability is reduced to certain regions in spacetime. This partial solvability enables us to place bounds on the entanglement velocity. We find that L¯2 circuits saturate certain bounds on entanglement growth that are also saturated in holographic models. Furthermore, we relate the entanglement line tension to temporal entanglement and correlation functions. We also develop methods of constructing generalized dual-unitary gates, including constructions based on complex Hadamard matrices that exhibit additional solvability properties and constructions that display behavior unique to local dimension greater than or equal to three. Our results shed light on entanglement membrane theory in microscopic Floquet lattice models and enable us to perform nontrivial checks on the validity of its predictions by comparison to exact and numerical calculations. Moreover, they demonstrate that generalized dual-unitary circuits display a more generic form of information dynamics than dual-unitary circuits. Published by the American Physical Society 2024

Nucleon electric and magnetic polarizabilities in holographic QCD

We analyze the resonance contributions to the generalized Baldin sum rule, namely the sum of the generalized electric and magnetic nucleon polarizabilities αE(Q2) and βM(Q2), within the holographic QCD model by Witten, Sakai, and Sugimoto (WSS). In particular, we account for the contributions from the first low-lying nucleon resonances with spin-1/2 and spin-3/2 and both parities. After having extrapolated the WSS model parameters to fit experimental data on baryonic observables, we compare our findings with alternative predictions in literature, finding a qualitative agreement with all of them. Moreover, at least for the proton case, where data are available, our results are in qualitative accordance with resonance contributions extracted from experimental nucleon-resonance helicity amplitudes. Published by the American Physical Society 2024

Cosmic Evolution in a Bianchi type-V Universe with Barrow Holographic Dark Energy with Granda-Oliveros Length Scale as IR Cutoff

In this work, we construct a spatially homogeneous and anisotropic Bianchi type-V cosmological model with a hybrid expansion law by considering the universe to be filled with cold dark matter and non-interacting Barrow holographic dark energy with Granda-Oliveros length scale as IR cutoff. The physical and kinematical characteristics of the resulting model are discussed by studying the evolution of various parameters of cosmological importance such as the Hubble parameter, the deceleration parameter, the anisotropic parameter, the equation of state parameter, jerk parameter etc. We also examine whether the energy conditions are satisfied or violated. Our analysis reveals that the Null,Weak, and Dominant energy conditions are fullfilled, while the Strong Energy Condition is violated, which supports the accelerated expansion of the universe. Statefinder diagnostics have also been performed based on recent cosmological observations in order to compare our model with different dark energy cosmological scenario. Additionally, we establish the correspondence between the quintessence scalar field and the Barrow holographic dark energy model, supporting our description of the universe’s accelerated expansion.

Barrow holographic dark energy models in Lyra and general relativity theories

This study investigates the Barrow holographic dark energy (BHDE) matter distribution in the Bianchi I universe model in Lyra and General Relativity Theories. To this end, it obtains exact solutions by Hubble parameter, conservation equation, and BHDE energy density equation and supports them with graphics. The results show that the solutions are in harmony with the functioning of the universe and the nature of dark energy. It finally discusses the need for further research.