# Lagrangian Reconstruction of Barrow Holographic Dark Energy in Interacting Tachyon Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Barrow Holographic Dark Energy

#### The Age of the Universe

## 3. Tachyon Scalar Field as Barrow Holographic Dark Energy in a Non-Flat FRW Universe

#### Observational Studies

## 4. Inflation in Barrow Holographic Dark Energy

#### Trans-Planckian Censorship Conjecture

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HDE | Holographic Dark Energy |

BHDE | Barrow Holographic Dark Energy |

## References

- Sahni, V.; Starobinsky, A.A. The Case for a positive cosmological Lambda term. Int. J. Mod. Phys. D
**2000**, 9, 373–444. [Google Scholar] [CrossRef] - Peebles, P.J.E.; Ratra, B. The Cosmological Constant and Dark Energy. Rev. Mod. Phys.
**2003**, 75, 559–606. [Google Scholar] [CrossRef] - Ratra, B.; Peebles, P.J.E. Cosmological Consequences of a Rolling Homogeneous Scalar Field. Phys. Rev. D
**1988**, 37, 3406. [Google Scholar] [CrossRef] [PubMed] - Frieman, J.A.; Hill, C.T.; Stebbins, A.; Waga, I. Cosmology with ultralight pseudo Nambu-Goldstone bosons. Phys. Rev. Lett.
**1995**, 75, 2077–2080. [Google Scholar] [CrossRef] - Turner, M.S.; White, M.J. CDM models with a smooth component. Phys. Rev. D
**1997**, 56, R4439. [Google Scholar] [CrossRef] - Caldwell, R.R.; Dave, R.; Steinhardt, P.J. Cosmological imprint of an energy component with general equation of state. Phys. Rev. Lett.
**1998**, 80, 1582–1585. [Google Scholar] [CrossRef] - Armendariz-Picon, C.; Mukhanov, V.F.; Steinhardt, P.J. A Dynamical solution to the problem of a small cosmological constant and late time cosmic acceleration. Phys. Rev. Lett.
**2000**, 85, 4438–4441. [Google Scholar] [CrossRef] - Armendariz-Picon, C.; Mukhanov, V.F.; Steinhardt, P.J. Essentials of k essence. Phys. Rev. D
**2001**, 63, 103510. [Google Scholar] [CrossRef] - Caldwell, R.R. A Phantom menace? Phys. Lett. B
**2002**, 545, 23–29. [Google Scholar] [CrossRef] - Caldwell, R.R.; Kamionkowski, M.; Weinberg, N.N. Phantom energy and cosmic doomsday. Phys. Rev. Lett.
**2003**, 91, 071301. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. Quantum de Sitter cosmology and phantom matter. Phys. Lett. B
**2003**, 562, 147–152. [Google Scholar] [CrossRef] - Feng, B.; Wang, X.L.; Zhang, X.M. Dark energy constraints from the cosmic age and supernova. Phys. Lett. B
**2005**, 607, 35–41. [Google Scholar] [CrossRef] - Guo, Z.K.; Piao, Y.S.; Zhang, X.M.; Zhang, Y.Z. Cosmological evolution of a quintom model of dark energy. Phys. Lett. B
**2005**, 608, 177–182. [Google Scholar] [CrossRef] - Elizalde, E.; Nojiri, S.; Odintsov, S.D. Late-time cosmology in (phantom) scalar-tensor theory: Dark energy and the cosmic speed-up. Phys. Rev. D
**2004**, 70, 043539. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D.; Tsujikawa, S. Properties of singularities in (phantom) dark energy universe. Phys. Rev. D
**2005**, 71, 063004. [Google Scholar] [CrossRef] - Deffayet, C.; Dvali, G.R.; Gabadadze, G. Accelerated universe from gravity leaking to extra dimensions. Phys. Rev. D
**2002**, 65, 044023. [Google Scholar] [CrossRef] - D’Agostino, R. Holographic dark energy from nonadditive entropy: Cosmological perturbations and observational constraints. Phys. Rev. D
**2019**, 99, 103524. [Google Scholar] [CrossRef] - Capozziello, S.; D’Agostino, R. A cosmographic outlook on dark energy and modified gravity. arXiv
**2022**, arXiv:2211.17194. [Google Scholar] - Capolupo, A.; Quaranta, A. Neutrino capture on tritium as a probe of flavor vacuum condensate and dark matter. Phys. Lett. B
**2023**, 839, 137776. [Google Scholar] [CrossRef] - Capolupo, A.; Quaranta, A. Boson mixing and flavor vacuum in the expanding Universe: A possible candidate for the dark energy. Phys. Lett. B
**2023**, 840, 137889. [Google Scholar] [CrossRef] - Lambiase, G.; Mishra, H.; Mohanty, S. Dark energy from Neutrinos and Standard Model Higgs potential. Astropart. Phys.
**2012**, 35, 629–633. [Google Scholar] [CrossRef] - Lambiase, G.; Mohanty, S.; Narang, A.; Parashari, P. Testing dark energy models in the light of σ
_{8}tension. Eur. Phys. J. C**2019**, 79, 141. [Google Scholar] [CrossRef] - Cohen, A.G.; Kaplan, D.B.; Nelson, A.E. Effective field theory, black holes, and the cosmological constant. Phys. Rev. Lett.
**1999**, 82, 4971–4974. [Google Scholar] [CrossRef] - Horava, P.; Minic, D. Probable values of the cosmological constant in a holographic theory. Phys. Rev. Lett.
**2000**, 85, 1610–1613. [Google Scholar] [CrossRef] [PubMed] - Thomas, S.D. Holography stabilizes the vacuum energy. Phys. Rev. Lett.
**2002**, 89, 081301. [Google Scholar] [CrossRef] [PubMed] - Li, M. A Model of holographic dark energy. Phys. Lett. B
**2004**, 603, 1. [Google Scholar] [CrossRef] - Bamba, K.; Capozziello, S.; Nojiri, S.; Odintsov, S.D. Dark energy cosmology: The equivalent description via different theoretical models and cosmography tests. Astrophys. Space Sci.
**2012**, 342, 155–228. [Google Scholar] [CrossRef] - Ghaffari, S.; Dehghani, M.H.; Sheykhi, A. Holographic dark energy in the DGP braneworld with Granda-Oliveros cutoff. Phys. Rev. D
**2014**, 89, 123009. [Google Scholar] [CrossRef] - Wang, S.; Wang, Y.; Li, M. Holographic Dark Energy. Phys. Rep.
**2017**, 696, 1–57. [Google Scholar] [CrossRef] - ’t Hooft, G. Dimensional reduction in quantum gravity. Conf. Proc. C
**1993**, 930308, 284–296. [Google Scholar] - Susskind, L. The World as a hologram. J. Math. Phys.
**1995**, 36, 6377–6396. [Google Scholar] [CrossRef] - Enqvist, K.; Hannestad, S.; Sloth, M.S. Searching for a holographic connection between dark energy and the low-l CMB multipoles. JCAP
**2005**, 02, 004. [Google Scholar] [CrossRef] - Setare, M.R. Holographic tachyon model of dark energy. Phys. Lett. B
**2007**, 653, 116–121. [Google Scholar] [CrossRef] - Hsu, S.D.H. Entropy bounds and dark energy. Phys. Lett. B
**2004**, 594, 13–16. [Google Scholar] [CrossRef] - Srivastava, S.; Sharma, U.K. Barrow holographic dark energy with Hubble horizon as IR cutoff. Int. J. Geom. Meth. Mod. Phys.
**2021**, 18, 2150014. [Google Scholar] [CrossRef] - Gong, Y.G. Holographic bound in Brans-Dicke cosmology. Phys. Rev. D
**2000**, 61, 043505. [Google Scholar] [CrossRef] - Kim, H.; Lee, H.W.; Myung, Y.S. Role of the Brans-Dicke scalar in the holographic description of dark energy. Phys. Lett. B
**2005**, 628, 11–17. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D. Unifying phantom inflation with late-time acceleration: Scalar phantom-non-phantom transition model and generalized holographic dark energy. Gen. Relativ. Gravit.
**2006**, 38, 1285–1304. [Google Scholar] [CrossRef] - Setare, M.R. The Holographic dark energy in non-flat Brans-Dicke cosmology. Phys. Lett. B
**2007**, 644, 99–103. [Google Scholar] [CrossRef] - Banerjee, N.; Pavon, D. A Quintessence scalar field in Brans-Dicke theory. Class. Quant. Grav.
**2001**, 18, 593. [Google Scholar] [CrossRef] - Xu, L.; Lu, J. Holographic Dark Energy in Brans-Dicke Theory. Eur. Phys. J. C
**2009**, 60, 135–140. [Google Scholar] [CrossRef] - Khodam-Mohammadi, A.; Karimkhani, E.; Sheykhi, A. Best values of parameters for interacting HDE with GO IR-cutoff in Brans–Dicke cosmology. Int. J. Mod. Phys. D
**2014**, 23, 1450081. [Google Scholar] [CrossRef] - Tavayef, M.; Sheykhi, A.; Bamba, K.; Moradpour, H. Tsallis Holographic Dark Energy. Phys. Lett. B
**2018**, 781, 195–200. [Google Scholar] [CrossRef] - Saridakis, E.N.; Bamba, K.; Myrzakulov, R.; Anagnostopoulos, F.K. Holographic dark energy through Tsallis entropy. JCAP
**2018**, 12, 012. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D.; Saridakis, E.N. Modified cosmology from extended entropy with varying exponent. Eur. Phys. J. C
**2019**, 79, 242. [Google Scholar] [CrossRef] - Luciano, G.G.; Gine, J. Baryogenesis in non-extensive Tsallis Cosmology. Phys. Lett. B
**2022**, 833, 137352. [Google Scholar] [CrossRef] - Saridakis, E.N. Barrow holographic dark energy. Phys. Rev. D
**2020**, 102, 123525. [Google Scholar] [CrossRef] - Moradpour, H.; Ziaie, A.H.; Kord Zangeneh, M. Generalized entropies and corresponding holographic dark energy models. Eur. Phys. J. C
**2020**, 80, 732. [Google Scholar] [CrossRef] - Drepanou, N.; Lymperis, A.; Saridakis, E.N.; Yesmakhanova, K. Kaniadakis holographic dark energy and cosmology. Eur. Phys. J. C
**2022**, 82, 449. [Google Scholar] [CrossRef] - Hernández-Almada, A.; Leon, G.; Magaña, J.; García-Aspeitia, M.A.; Motta, V.; Saridakis, E.N.; Yesmakhanova, K. Kaniadakis-holographic dark energy: Observational constraints and global dynamics. Mon. Not. R. Astron. Soc.
**2022**, 511, 4147–4158. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D.; Paul, T. Barrow entropic dark energy: A member of generalized holographic dark energy family. Phys. Lett. B
**2022**, 825, 136844. [Google Scholar] [CrossRef] - Luciano, G.G. Modified Friedmann equations from Kaniadakis entropy and cosmological implications on baryogenesis and
^{7}Li-abundance. Eur. Phys. J. C**2022**, 82, 314. [Google Scholar] [CrossRef] - Ghaffari, S.; Luciano, G.G.; Capozziello, S. Barrow holographic dark energy in the Brans–Dicke cosmology. Eur. Phys. J. Plus
**2023**, 138, 82. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D.; Faraoni, V. From nonextensive statistics and black hole entropy to the holographic dark universe. Phys. Rev. D
**2022**, 105, 044042. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D.; Paul, T. Early and late universe holographic cosmology from a new generalized entropy. Phys. Lett. B
**2022**, 831, 137189. [Google Scholar] [CrossRef] - Luciano, G.G. Cosmic evolution and thermal stability of Barrow holographic dark energy in a nonflat Friedmann-Robertson-Walker Universe. Phys. Rev. D
**2022**, 106, 083530. [Google Scholar] [CrossRef] - Luciano, G.G.; Giné, J. Generalized interacting Barrow Holographic Dark Energy: Cosmological predictions and thermodynamic considerations. arXiv
**2022**, arXiv:2210.09755. [Google Scholar] - Luciano, G.G. From the emergence of cosmic space to horizon thermodynamics in Barrow entropy-based Cosmology. Phys. Lett. B
**2023**, 838, 137721. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D.; Saridakis, E.N.; Myrzakulov, R. Correspondence of cosmology from non-extensive thermodynamics with fluids of generalized equation of state. Nucl. Phys. B
**2020**, 950, 114850. [Google Scholar] [CrossRef] - Bajardi, F.; Capozziello, S. Noether symmetries and quantum cosmology in extended teleparallel gravity. Int. J. Geom. Meth. Mod. Phys.
**2021**, 18, 2140002. [Google Scholar] [CrossRef] - Acunzo, A.; Bajardi, F.; Capozziello, S. Non-local curvature gravity cosmology via Noether symmetries. Phys. Lett. B
**2022**, 826, 136907. [Google Scholar] [CrossRef] - Liu, Y. Tachyon model of Tsallis holographic dark energy. Eur. Phys. J. Plus
**2021**, 136, 579. [Google Scholar] [CrossRef] - Gibbons, G.W. Cosmological evolution of the rolling tachyon. Phys. Lett. B
**2002**, 537, 1–4. [Google Scholar] [CrossRef] - Mazumdar, A.; Panda, S.; Perez-Lorenzana, A. Assisted inflation via tachyon condensation. Nucl. Phys. B
**2001**, 614, 101–116. [Google Scholar] [CrossRef] - Padmanabhan, T. Accelerated expansion of the universe driven by tachyonic matter. Phys. Rev. D
**2002**, 66, 021301. [Google Scholar] [CrossRef] - Ens, P.S.; Santos, A.F. f (R) gravity and Tsallis holographic dark energy. EPL
**2020**, 131, 40007. [Google Scholar] [CrossRef] - Zubair, M.; Durrani, L.R. Exploring tsallis holographic dark energy scenario in f (R, T) gravity. Chin. J. Phys.
**2021**, 69, 153–171. [Google Scholar] [CrossRef] - Sharif, M.; Saba, S. Tsallis Holographic Dark Energy in f (G, T) Gravity. Symmetry
**2019**, 11, 92. [Google Scholar] [CrossRef] - Waheed, S. Reconstruction paradigm in a class of extended teleparallel theories using Tsallis holographic dark energy. Eur. Phys. J. Plus
**2020**, 135, 11. [Google Scholar] [CrossRef] - Ghaffari, S.; Moradpour, H.; Lobo, I.P.; Morais Graça, J.P.; Bezerra, V.B. Tsallis holographic dark energy in the Brans–Dicke cosmology. Eur. Phys. J. C
**2018**, 78, 706. [Google Scholar] [CrossRef] - Aditya, Y.; Mandal, S.; Sahoo, P.K.; Reddy, D.R.K. Observational constraint on interacting Tsallis holographic dark energy in logarithmic Brans–Dicke theory. Eur. Phys. J. C
**2019**, 79, 1020. [Google Scholar] [CrossRef] - Sobhanbabu, Y.; Vijaya Santhi, M. Kantowski–Sachs Tsallis holographic dark energy model with sign-changeable interaction. Eur. Phys. J. C
**2021**, 81, 1040. [Google Scholar] [CrossRef] - Luciano, G.G. Saez-Ballester gravity in Kantowski-Sachs Universe: A new reconstruction paradigm for Barrow Holographic Dark Energy. Phys. Dark Universe
**2023**, 41, 101237. [Google Scholar] [CrossRef] - Barrow, J.D. The Area of a Rough Black Hole. Phys. Lett. B
**2020**, 808, 135643. [Google Scholar] [CrossRef] - Tsallis, C. Possible Generalization of Boltzmann-Gibbs Statistics. J. Stat. Phys.
**1988**, 52, 479–487. [Google Scholar] [CrossRef] - Tsallis, C.; Cirto, L.J.L. Black hole thermodynamical entropy. Eur. Phys. J. C
**2013**, 73, 2487. [Google Scholar] [CrossRef] - Kaniadakis, G. Statistical mechanics in the context of special relativity. Phys. Rev. E
**2002**, 66, 056125. [Google Scholar] [CrossRef] - Luciano, G.G.; Blasone, M. q-generalized Tsallis thermostatistics in Unruh effect for mixed fields. Phys. Rev. D
**2021**, 104, 045004. [Google Scholar] [CrossRef] - Luciano, G.G.; Blasone, M. Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos. Eur. Phys. J. C
**2021**, 81, 995. [Google Scholar] [CrossRef] - Barrow, J.D.; Basilakos, S.; Saridakis, E.N. Big Bang Nucleosynthesis constraints on Barrow entropy. Phys. Lett. B
**2021**, 815, 136134. [Google Scholar] [CrossRef] - Luciano, G.G.; Saridakis, E.N. Baryon asymmetry from Barrow entropy: Theoretical predictions and observational constraints. Eur. Phys. J. C
**2022**, 82, 558. [Google Scholar] [CrossRef] - Vagnozzi, S.; Roy, R.; Tsai, Y.D.; Visinelli, L. Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A
^{*}. arXiv**2022**, arXiv:2205.07787. [Google Scholar] - Di Gennaro, S.; Ong, Y.C. Sign Switching Dark Energy from a Running Barrow Entropy. Universe
**2022**, 8, 541. [Google Scholar] [CrossRef] - Guberina, B.; Horvat, R.; Nikolic, H. Nonsaturated Holographic Dark Energy. JCAP
**2007**, 01, 012. [Google Scholar] [CrossRef] - Sheykhi, A.; Hamedan, M.S. Holographic dark energy in modified Barrow cosmology. Entropy
**2023**, 25, 569. [Google Scholar] [CrossRef] - Al Mamon, A.; Mishra, A.K.; Sharma, U.K. Barrow Holographic dark energy in fractal cosmology. Int. J. Geom. Meth. Mod. Phys.
**2022**, 19, 2250231. [Google Scholar] [CrossRef] - Ghaffari, S.; Sheykhi, A.; Dehghani, M.H. Statefinder diagnosis for holographic dark energy in the DGP braneworld. Phys. Rev. D
**2015**, 91, 023007. [Google Scholar] [CrossRef] - Sheykhi, A. Holographic Scalar Fields Models of Dark Energy. Phys. Rev. D
**2011**, 84, 107302. [Google Scholar] [CrossRef] - Boulkaboul, N. Baryogenesis triggered by Barrow holographic dark energy coupling. Phys. Dark Univ.
**2023**, 40, 101205. [Google Scholar] [CrossRef] - Granda, L.N.; Oliveros, A. Infrared cut-off proposal for the Holographic density. Phys. Lett. B
**2008**, 669, 275–277. [Google Scholar] [CrossRef] - Frolov, A.V.; Kofman, L.; Starobinsky, A.A. Prospects and problems of tachyon matter cosmology. Phys. Lett. B
**2002**, 545, 8–16. [Google Scholar] [CrossRef] - Aghanim, N.; Akrami, Y.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Basak, S.; et al. Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys.
**2020**, 641, A6, Erratum in Astron. Astrophys.**2021**, 652, C4. [Google Scholar] [CrossRef] - Anagnostopoulos, F.K.; Basilakos, S.; Saridakis, E.N. Observational constraints on Barrow holographic dark energy. Eur. Phys. J. C
**2020**, 80, 826. [Google Scholar] [CrossRef] - Luciano, G.G. Constraining barrow entropy-based cosmology with power-law inflation. Eur. Phys. J. C
**2023**, 83, 329. [Google Scholar] [CrossRef] - Mohammadi, A.; Golanbari, T.; Bamba, K.; Lobo, I.P. Tsallis holographic dark energy for inflation. Phys. Rev. D
**2021**, 103, 083505. [Google Scholar] [CrossRef] - Nojiri, S.; Odintsov, S.D.; Saridakis, E.N. Holographic inflation. Phys. Lett. B
**2019**, 797, 134829. [Google Scholar] [CrossRef] - Maity, S.; Rudra, P. Inflation driven by Barrow holographic dark energy. JHAP
**2022**, 2, 1–12. [Google Scholar] [CrossRef] - Martin, J.; Brandenberger, R.H. The TransPlanckian problem of inflationary cosmology. Phys. Rev. D
**2001**, 63, 123501. [Google Scholar] [CrossRef] - Bedroya, A.; Vafa, C. Trans-Planckian Censorship and the Swampland. JHEP
**2020**, 09, 123. [Google Scholar] [CrossRef] - Banerjee, A.; Cai, H.; Heisenberg, L.; Colgáin, E.O.; Sheikh-Jabbari, M.M.; Yang, T. Hubble sinks in the low-redshift swampland. Phys. Rev. D
**2021**, 103, L081305. [Google Scholar] [CrossRef] - Lee, B.H.; Lee, W.; Colgáin, E.O.; Sheikh-Jabbari, M.M.; Thakur, S. Is local H
_{0}at odds with dark energy EFT? JCAP**2022**, 04, 004. [Google Scholar] [CrossRef] - Sheykhi, A.; Farsi, B. Growth of perturbations in Tsallis and Barrow cosmology. Eur. Phys. J. C
**2022**, 82, 1111. [Google Scholar] [CrossRef] - Luciano, G.G. Gravity and Cosmology in Kaniadakis Statistics: Current Status and Future Challenges. Entropy
**2022**, 24, 1712. [Google Scholar] [CrossRef] - Kempf, A.; Mangano, G.; Mann, R.B. Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D
**1995**, 52, 1108–1118. [Google Scholar] [CrossRef] - Scardigli, F. Generalized uncertainty principle in quantum gravity from micro-black hole Gedanken experiment. Phys. Lett. B
**1999**, 452, 39–44. [Google Scholar] [CrossRef] - Bosso, P.; Das, S. Generalized ladder operators for the perturbed harmonic oscillator. Ann. Phys.
**2018**, 396, 254–265. [Google Scholar] [CrossRef] - Luciano, G.G.; Petruzziello, L. Generalized uncertainty principle and its implications on geometric phases in quantum mechanics. Eur. Phys. J. Plus
**2021**, 136, 179. [Google Scholar] [CrossRef]

**Figure 1.**Evolution trajectories of ${\dot{T}}^{2}$ for a closed ($k=1$) universe. We set $u=0.04$ and ${b}^{2}=0.01$ as in [62].

**Figure 2.**Evolution trajectories of ${\dot{T}}^{2}$ for an open ($k=-1$) universe. We set $u=0.04$ and ${b}^{2}=0.01$ as in [62].

**Figure 3.**Evolution trajectories of ${\mathsf{\Omega}}_{D}$ versus z (we set ${\mathsf{\Omega}}_{k}=0.01$ and ${\mathsf{\Omega}}_{D}^{0}=0.73$). The dashed vertical line marks the value at present time.

**Figure 4.**Evolution trajectories of ${\omega}_{D}$ versus z (we considered the same initial conditions as in Figure 3). The dashed vertical line marks the value at present time.

**Figure 5.**Evolution trajectories of q versus z (we considered the same initial conditions as in Figure 3). The dashed vertical line marks the value at present time.

**Figure 6.**Evolution of Hubble rate versus z. The black points are the observational data in Tab. Table 1, while the red solid (blue dashed) line is the best fit according to our model ($\mathsf{\Lambda}$CDM).

**Table 1.**57 experimental points of $H\left(z\right)$ (H is expressed in $\mathrm{km}\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}\phantom{\rule{0.166667em}{0ex}}{\mathrm{Mpc}}^{-1}$ and ${\sigma}_{H}$ represents the uncertainty for each data point).

z | $\mathit{H}\left(\mathit{z}\right)$ | ${\mathit{\sigma}}_{\mathit{H}}$ | $\mathit{z}$ | $\mathit{H}\left(\mathit{z}\right)$ | ${\mathit{\sigma}}_{\mathit{H}}$ |
---|---|---|---|---|---|

0.070 | 69.0 | 19.6 | 0.4783 | 80 | 99 |

0.90 | 69 | 12 | 0.480 | 97 | 62 |

0.120 | 68.6 | 26.2 | 0.593 | 104 | 13 |

0.170 | 83 | 8 | 0.6797 | 92 | 8 |

0.1791 | 75 | 4 | 0.7812 | 105 | 12 |

0.1993 | 75 | 5 | 0.8754 | 125 | 17 |

0.200 | 72.9 | 29.6 | 0.880 | 90 | 40 |

0.270 | 77 | 14 | 0.900 | 117 | 23 |

0.280 | 88.8 | 36.6 | 1.037 | 154 | 20 |

0.3519 | 83 | 14 | 1.300 | 168 | 17 |

0.3802 | 83.0 | 13.5 | 1.363 | 160.0 | 33.6 |

0.400 | 95 | 17 | 1.430 | 177 | 18 |

0.4004 | 77.0 | 10.2 | 1.530 | 140 | 14 |

0.4247 | 87.1 | 11.2 | 1.750 | 202 | 40 |

0.4497 | 92.8 | 12.9 | 1.965 | 186.5 | 50.4 |

0.470 | 89 | 34 | |||

0.24 | 79.69 | 2.99 | 0.52 | 94.35 | 2.64 |

0.30 | 81.70 | 6.22 | 0.56 | 93.34 | 2.30 |

0.31 | 78.18 | 4.74 | 0.57 | 87.6 | 7.8 |

0.34 | 83.80 | 3.66 | 0.57 | 96.8 | 3.4 |

0.35 | 82.7 | 9.1 | 0.59 | 98.48 | 3.18 |

0.36 | 79.94 | 3.38 | 0.60 | 87.9 | 6.1 |

0.38 | 81.5 | 1.9 | 0.61 | 97.3 | 2.1 |

0.40 | 82.04 | 2.03 | 0.64 | 98.82 | 2.98 |

0.43 | 86.45 | 3.97 | 0.73 | 97.3 | 7.0 |

0.44 | 82.6 | 7.8 | 2.30 | 224.0 | 8.6 |

0.44 | 84.81 | 1.83 | 2.33 | 224 | 8 |

0.48 | 87.90 | 2.03 | 2.34 | 222.0 | 8.5 |

0.51 | 90.4 | 1.9 | 2.36 | 226.0 | 9.3 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Luciano, G.G.; Liu, Y.
Lagrangian Reconstruction of Barrow Holographic Dark Energy in Interacting Tachyon Model. *Symmetry* **2023**, *15*, 1129.
https://doi.org/10.3390/sym15051129

**AMA Style**

Luciano GG, Liu Y.
Lagrangian Reconstruction of Barrow Holographic Dark Energy in Interacting Tachyon Model. *Symmetry*. 2023; 15(5):1129.
https://doi.org/10.3390/sym15051129

**Chicago/Turabian Style**

Luciano, Giuseppe Gaetano, and Yang Liu.
2023. "Lagrangian Reconstruction of Barrow Holographic Dark Energy in Interacting Tachyon Model" *Symmetry* 15, no. 5: 1129.
https://doi.org/10.3390/sym15051129