Holographic Dark Energy in Anisotropic Bianchi Cosmologies: A Quintessence Association

Abstract

This paper investigates the dynamics of Holographic Dark Energy (HDE) within the framework of an axially symmetric, homogeneous but anisotropic universe, described by a generic class of Bianchi cosmological models. We employ the Granda-Oliveros holographic cut-off, ?_?= 3(?H² + ??), and analyze the expansion history using a linearly time-dependent deceleration parameter with a negative slope. Exact solutions to the Einstein field equations are derived for three distinct cosmological scenarios. The resulting models describe an expanding, accelerating, shearing, and non-rotating universe. Analysis of the equation of state parameter ?_? reveals that the HDE component can mimic the cosmological constant (?_? ? -1), hantom energy (?_? < -1), quintessence (-1 < ?_? < -1/3), and even stiff or radiation fluids in early epochs, depending on the model parameters. A significant connection is established between the HDE formulation and a quintessence scalar field, allowing for a dynamical interpretation of dark energy. For specific parameter values, the total density parameter (?_m + ?_?) tends to unity at late times, indicating that the universe evolves towards spatial flatness and isotropy as dark energy dominates. The derived Hubble parameter H (z) shows strong concordance with observational data from Type Ia Supernovae.

Introduction

Observational evidence from Type Ia supernovae, the cosmic microwave background, and large-scale structure supports the ΛCDM model, which explains the accelerated expansion of the universe through dark energy. Although the cosmological constant is the simplest explanation, its fine-tuning problems have motivated alternative dynamical dark energy models. One such approach arises from the holographic principle, leading to Holographic Dark Energy (HDE). The Granda–Oliveros formulation of HDE provides a viable infrared cutoff that avoids causality issues and agrees well with observations.

This work studies HDE within an axially symmetric Bianchi anisotropic cosmological model, allowing investigation of early-universe anisotropy and its evolution toward isotropy. Exact solutions to Einstein’s field equations are derived by assuming a linearly time-varying deceleration parameter, which enables a transition from decelerated to accelerated expansion. Three distinct solution cases are analyzed.

Key physical and dynamical parameters—such as Hubble rates, shear, anisotropy, energy densities, and density parameters—are examined. In all cases, the models evolve toward a spatially flat and isotropic FRW universe at late times, dominated by holographic dark energy, with the total density parameter approaching unity. The equation of state of HDE exhibits both cosmological constant–like behavior and time-dependent dynamics, including possible phantom divide crossing.

A correspondence is established between the HDE model and a quintessence scalar field, providing a microphysical interpretation of dark energy in the anisotropic setting. Finally, theoretical predictions for the Hubble parameter and density parameters are shown to be consistent with Type Ia supernova and BAO observational data, demonstrating that the proposed anisotropic HDE models are both physically viable and observationally supported.

Conclusion

We have presented a detailed study of Holographic Dark Energy within a generalized anisotropic Bianchi cosmology. By assuming a linearly decreasing deceleration parameter, we obtained exact cosmological solutions that describe an accelerating universe. The analysis reveals: 1) The model successfully explains the late-time transition to acceleration and the eventual flattening and isotropization of the universe as HDE dominates. 2) The HDE component exhibits remarkable versatility, capable of mimicking the cosmological constant, phantom energy, quintessence, and even early- universe fluid phases based on the parameter nn. 3) A formal correspondence with quintessence scalar field theory is established, providing a dynamical field interpretation for the HDE. 4) The predictions for the Hubble parameter and density parameters show good agreement with current SNe Ia and BAO observational data. This work strengthens the case for HDE as a viable dynamical dark energy candidate and demonstrates how anisotropic models can naturally evolve into the isotropic universe we observe today.

References

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Copyright

Copyright © 2026 Megha Chandraprakash Gaikwad, Dr. Vishwajeet S. Goswami. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.