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Cosmology of Tsallis holographic scalar field models in Chern–Simons modified gravity and optimization of model parameters through χ2 minimization

  • Gargee Chakraborty and Surajit Chattopadhyay ORCID logo EMAIL logo
Published/Copyright: November 16, 2020
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 1

Abstract

The present study reports reconstruction schemes for tachyon, k-essence and dilaton scalar field model of Dark Energy (DE) through Tsallis holographic dark fluid under the framework of Chern–Simons modified gravity. Reproducing the conservation equation for a coupled model with interaction term Q=3Hb2ρm we have reconstructed the different scalar fields and the corresponding potentials. In the case of tachyon, ΛCDM fixed point is attained under this cosmological settings. Considering k-essence in this interacting situation, we have derived some constraints on the interaction term as well as Tsallis holographic dark energy parameter. Reconstructing dilaton scalar field, we have studied the behavior of scalar field and potential. In all those cases, the reconstructed Equation of State (EoS) parameters have been plotted and when computed for current universe z = 0 are found to be consistent with various observational data including Planck + WP + BAO. The only exception is a particular case of reconstructed k-essence model where phantom behavior is apparent, but its numerical value is deviated from the bounce set by the observations. Expressions for different constraints have been obtained and evolutionary behavior of reconstructed scalar fields and potentials for the various cases have been pictorially presented. Finally, we have developed a functional relationship between Hubble parameter and redshift and optimized the parameter values through χ2 minimization using the observed Hubble parameter values from Hai Yu et al. 2018 ApJ856 3.

Keyword: Chern–Simons modified gravity; Tsallis holographic dark energy; reconstruction; scalar field models; χ2 minimization
Corresponding author: Surajit Chattopadhyay, Department of Mathematics, Amity University Kolkata, Kolkata, India, E-mail:

Funding source: Council of Scientific and Industrial Research

Award Identifier / Grant number: 03(1420)/18/EMR-II

Acknowledgment

The authors acknowledge the insightful comments from the anonymous reviewer with sincere gratitude. Surajit Chattopadhyay acknowledges financial support from the Council of Scientific and Industrial Research (Government of India) with Grant No. 03(1420)/18/EMR-II. Both the authors acknowledge the facility and hospitality provided by the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India during a scientific visit from December, 2019 till January, 2020.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: Surajit Chattopadhyay acknowledges financial support from the Council of Scientific and Industrial Research (Government of India) with Grant No. 03(1420)/18/EMR-II.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix

The entries aij of matrix M1 are a11=11038241.53, a12=−722053586.34, a13=6727.45, a14=−432312581.53, a15=858547867.93, a16=46586767696.17, a21=−877033102.57, a22=156488356307.78, a23=−3548378.16, a24=105804396934.96, a25=−210120956810., a26=−28199731235.12, a31=10596.62, a32=−3707019.56, a33=470.24, a34=−4939175.58, a35=9808892.84, a36=−31203323.82, a41=−653295309.61, a42=114189951571.75, a43=−4922321.97, a44=−230643071204.94, a45=458043146075.83, a46=4769363678971.24, a51=1297405712.58, a52=−226774111988.94, a53=9775421.87, a54=458043189768.96, a55=−909645984956.31, a56=−9471651855143.65, a61=42575260878.14, a62=888297481066.45, a63=−49977949.92, a64=5859129272784.19, a65=−11635858800674.74, a66=238491015569206.6.

The entries bij to the matrix M2 are b11=103233.87, b12=−5706907.26, b13=551173.27, b14=−323249.89, b15=−42.18, b16=−1455461.00, b17=3320654.60, b18=−25326645.82, b19=116885.99, b21=−9463273.23, b22=−757433976.68, b23=506281448.09b24=−57247029.53, b25=4623.01, b26=−1433769720.73, b27=−989941549.74, b28=1213470794.83, b29=−34837634.59, b31=3875096.14, b32=342585986.35, b33=−74776511.35, b34=−28697766.52, b35=4336.54, b36=−44131618.66, b37=−424734819.29, b38=2275145354.22, b39=−14949488.11, b41=−1204576.97, b42=−20288143.10, b43=−22995245.35, b44=18014208.07, b45=−1849.77, b46=241935277.40, b47=228782763.67, b48=−796482589.52, b49=8052027.13, b51=4.26 , b52=520.98 , b53=5942.50, b54=−2355.26, b55=251.13, b56=−39907.08, b57=−24155.25, b58=74412.06, b59−1097.41, b61=−36149230.92, b62=−769591329.85, b63=309203826.33, b64=185297209.00, b65=−24536.85, b66=119340982.37, b67=2363423668.32, b68=−14488399773.72, b69=83186430.27, b71=−6269705.79, b72=−338944799.05, b73=−582856957.21, b74=287161544.57, b75=−21730.92, b76=4410160648.28, b77=3941026611.84, b78=−11726784629.59, b79=138694335.51, b81=−14927960.87 , b82=−282942428.80, b83=3146132224.46, b84=−1045261862.34, b85=81557.26 , b86=−21252341807.00, b87=−13745127605.69, b88=27892303350.99, b89−483730629.61, b91=−220615.89, b92=−11926943.95, b93=−20514932.60 , b94=10106704.44 , b95=−1012.11, b96=155220240.26, b97=138696772.33, b98=−412704184.44, b99=4881331.90.

The entries cij to the matrix M3 are c11=−0.14, c12=−127.61, c13=0.59, c14=−125.43, c15=−10.13, c16=0.14, c17=0.61, c21=−177.83, c22=−50226.77, c23=460.49, c24=2824.16, c25=−4352.05, c26=53.71, c27=353.85, c31=0.72, c32=367.19, c33=−2.27, c34=224.66, c35=29.98, c36=−0.39, c37=−2.02c41=−199.35, c42=−18918.55, c43=417.68, c44=58630.73, c45=−2020.32, c46=20.25, c47=253.59, c51=−13.95, c52=−4204.30, c53=36.70, c54=−148.71, c55=−360.96, c56=4.50, c57=28.62, c61=0.19, c62=53.71, c63=−0.49, c64=−3.00, c65=4.65, c66=−0.057, c67=−0.38, c71=0.80, c72=307.43, c73=−2.25, c74=104.03, c75=25.64, c76=−0.33, c77=−1.86.

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Received: 2020-08-17
Accepted: 2020-10-09
Published Online: 2020-11-16
Published in Print: 2021-01-27

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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  2. Atomic, Molecular & Chemical Physics
  3. Energy levels and transition probabilities of N+, F3+, and Ne4+ ions
  4. Dynamical Systems & Nonlinear Phenomena
  5. Genetic algorithm (GA)–based delay feedback control of chaotic behavior in the voltage mode controlled direct current (DC) drive system
  6. Time-delayed predator–prey interaction with the benefit of antipredation response in presence of refuge
  7. Gravitation & Cosmology
  8. Cosmology of Tsallis holographic scalar field models in Chern–Simons modified gravity and optimization of model parameters through χ2 minimization
  9. Solid State Physics & Materials Science
  10. Thermal conversion of CBD grown ZnS thin films to ZnO
  11. Studies on birefringence, order parameter and image analysis of liquid crystalline p-n butyloxy/butyl benzoic acid with dispersed ZnO nanoparticles
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