Open Access Library Journal
Vol.06 No.06(2019), Article ID:93010,5 pages
10.4236/oalib.1105498

Interacting Holographic Dark Energy in Bianchi Type-V Universe with Variable Deceleration Parameter

Vijay G. Mete1, Vaibhav D. Bokey2, Vasant S. Bawane3

1R.D.I.K. & K.D. College, Badnera, India

2Nehru Mahavidyalaya, Ner Parsopant, India

3M. F. Arts, Comm. & S. C. Science Mahavidyalaya, Warud, India

Copyright © 2019 by author(s) and Open Access Library Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY 4.0).

http://creativecommons.org/licenses/by/4.0/

Received: May 24, 2019; Accepted: June 11, 2019; Published: June 14, 2019

ABSTRACT

The present study deals with spatially homogeneous and anisotropic Bianchi Type-V universe filled with interacting dark matter and holographic dark energy. The exact solutions of Einstein’s equations are obtained by using the variable deceleration parameter in the form a ( t ) = ( sinh ( α t ) ) 1 n (Chawla et al. [1] ). The physical properties of the model are obtained and discussed in details.

Subject Areas:

Modern Physics, Theoretical Physics

Keywords:

Bianchi Type-V Universe, Holographic Dark Energy, Interacting Dark Fluids, Variable Deceleration Parameter

1. Introduction

The recent remarkable cosmological observations from high red shift Ia supernovae (SNIa) (Perlmutter et al. [2] [3] , Riess et al. [4] [5] , Astier et al. [6] , Spergel et al. [7] , Davis et al. [8] ) indicate that our universe is accelerating and confirmed later by cross-checks from cosmic microwave background radiation (Bennett et al. [9] , Spergel et al. [10] ) and large scale structure (Verde et al. [11] , Hawkins et al. [12] , Abazajian et al. [13] [14] [15] , Tegmark et al. [16] ) suggests that the universe is spatially flat and dominated by exotic component with large negative pressure. This component is usually referred to as dark energy (Weinberg et al. [17] , Carroll et al. [18] , Peebles et al. [19] , Padmanabhan et al. [20] ). Astronomical observations indicate that the universe consists of approximately 2/3 dark energy and 1/3 dark matter. The nature of dark energy and dark matter is unknown and many radically different models have been proposed. In order to explain anomalous cosmological observations in cosmic microwave background (CMB) at largest angles, Koivisto et al. [21] have suggested cosmological model with anisotropic and viscous dark energy.

Among all dark energy models, a holographic dark energy (HDE) models have received the remarkable attention (Cohen et al. [22] , Horava et al. [23] , Thomas et al. [24] , Li et al. [25] ). According to holographic principle, the number of degrees of freedom in a bounded system should be finite and related to the area of its boundary (Hooft et al. [26] ) and with the help of this principle, a field theoretical relation between a short distance (ultraviolet) cut off and a long distance (infrared) cut off was established (Cohen et al. [22] ) which ensures that the energy in a box of size L which has a cosmological length scale, does not exceed the energy of black hole of the same size. Different dark energy models are due to different types of these cut off.

Bianchi models have been studied by several authors to achieve a better understanding of the observed small amount of anisotropy in the universe. The simple Bianchi family containing flat FRW universe as a special case is the type-I space-times. The Bianchi type-V universe is a generalization of the open universe in FRW cosmology. Hence, its study as dark energy models with non-zero curvature (Coles et al. [27] ) in higher dimension is important. Holographic dark energy models have been tested and constrained by various astronomical observations (Zhang et al. [28] , Enqvist et al. [29] , Shen et al. [30] , Chang et al. [31] ). The special class models are the models in which holographic dark energy is allowed to interact with dark matter (Carvalho et al. [32] , Huang et al. [33] , Gong et al. [34] [35] , Pavon et al. [36] , Wang et al. [37] , Perivolaropoulos et al. [38] , Nojiri et al. [39] , Guberina et al. [40] [41] , Guo et al. [42] [43] [44] , Hu et al. [45] , Li et al. [46] , Setare et al. [47] [48] , Sadjadi et al. [49] , Banerjee et al. [50] , Zimdahl et al. [51] ). Sarkar et al. [52] [53] [54] have studied non interacting holographic dark energy with linearly varying deceleration parameter in Bianchi type-I and Bianchi type-V universe and also interacting holographic dark energy in Bianchi type-II.

Spatially homogeneous and anisotropic cosmological models play a significant role in the description of large behavior of the universe, and many authors have been widely studied such models in the search of a relativistic picture of the early universe. Anisotropic Bianchi type-I, Bianchi type-II and Bianchi type-V dark energy models have been extensively studied by (Adhav K. S. [55] [56] , Pradhan A. et al. [57] ). Kumar and Yadav [58] have constructed some Bianchi type-V cosmological models of accelerating universe with dark energy in general relativity by assuming constant deceleration parameter in order to solve Einstein’s field equations. The role of dark energy with variable equation of state parameter is studied in details within the evolution of Bianchi type-V universe and conjointly discovered that dark energy dominates the universe at the present epoch. Pradhan and Amirhashchi [59] have constructed an accelerating dark energy model and explored some new exact solutions of Einstein’s field equations in a spatially and anisotropic Bianchi type-V space-time with minimally interaction of perfect fluid and dark energy components. Adhav et al. [60] explored anisotropic and homogeneous Bianchi type-I universe field with interacting dark matter and holographic dark energy. Som and Sil [61] discussed the general approach of interacting holographic dark energy model.

Motivated by these investigations, we have constructed spatially homogeneous and anisotropic Bianchi type-V universe field with interacting dark matter and holographic dark energy. In this paper, we obtained the exact solutions of Einstein’s field equations by using variable deceleration parameter in the form a ( t ) = ( sinh ( α t ) ) 1 n .

2. Metric and Field Equations

The Bianchi Type-V metric can be written as

d s 2 = d t 2 a 1 2 ( t ) d x 2 a 2 2 ( t ) e 2 β x d y 2 a 3 2 ( t ) e 2 β x d z , (2.1)

where a 1 ( t ) , a 2 ( t ) and a 3 ( t ) are cosmic scale factors and β 0 is an arbitrary constant.

The Einstein’s field equations in natural limit (8πG = 1 and c = 1) are,

R i j 1 2 g i j R = ( T m i j + T Λ i j ) , (2.2)

where

T m i j = ρ m u i u j and T Λ i j = ( ρ Λ + p Λ ) u i u j + g i j p Λ (2.3)

are energy momentum tensor for dark matter (pressureless, i.e. ω m = 0 ) and holographic dark energy respectively. Here the quantity ρ m is the energy density of dark matter and ρ Λ , p Λ are energy density and pressure of holographic dark energy respectively.

In co-moving system, the Einstein field Equations (2.2) for the metric (2.1), using Equations (2.3) can be written as

a ˙ 1 a ˙ 2 a 1 a 2 + a ˙ 2 a ˙ 3 a 2 a 3 + a ˙ 3 a ˙ 1 a 3 a 1 3 β 2 a 1 2 = ρ m + ρ Λ , (2.4)

a ¨ 2 a 2 + a ¨ 3 a 3 + a ˙ 2 a ˙ 3 a 2 a 3 β 2 a 1 2 = p Λ , (2.5)

a ¨ 1 a 1 + a ¨ 3 a 3 + a ˙ 1 a ˙ 3 a 1 a 3 β 2 a 1 2 = p Λ , (2.6)

a ¨ 1 a 1 + a ¨ 2 a 2 + a ˙ 1 a ˙ 2 a 1 a 2 β 2 a 1 2 = p Λ , (2.7)

a ˙ 2 a 2 + a ˙ 3 a 3 = 2 a ˙ 1 a 1 , (2.8)

where an overhead dot (?) represents derivative with respect to time t.

On integrating the Equation (2.8), we obtain

a 1 2 = λ a 2 a 3 (2.9)

where λ is an integration constant.

On taking λ = 1 , without loss of generality, the volume scale factor V and average scale factor a is given by

V = a 3 = a 1 a 2 a 3 (2.10)

Subtracting Equation (2.5) from Equation (2.6), Equation (2.6) from Equation (2.7), Equation (2.5) from Equation (2.7) and using Equation (2.10), we get

d d t ( a ˙ 1 a 1 a ˙ 2 a 2 ) + ( a ˙ 1 a 1 a ˙ 2 a 2 ) V ˙ V = 0 (2.11a)

d d t ( a ˙ 2 a 2 a ˙ 3 a 3 ) + ( a ˙ 2 a 2 a ˙ 3 a 3 ) V ˙ V = 0 (2.11b)

d d t ( a ˙ 1 a 1 a ˙ 3 a 3 ) + ( a ˙ 1 a 1 a ˙ 3 a 3 ) V ˙ V = 0 (2.11c)

On integrating Equations (2.11a)-(2.11c) and using Equations (2.9) and (2.10), the scale factors a 1 ( t ) , a 2 ( t ) and a 3 ( t ) can be written as,

a 1 ( t ) = V 1 / 3 (2.12a)

a 2 ( t ) = D V 1 / 3 exp ( X d t V ) , (2.12b)

a 3 ( t ) = D 1 V 1 / 3 exp ( X d t V ) (2.12c)

where X and D are constants of integration.

The holographic dark energy density is given by,

ρ Λ = 3 ( α 1 H 2 + β 1 H ˙ ) (2.13)

i.e. ρ Λ = 3 ( α 1 H 2 + β 1 H ˙ ) with M p 2 = 8 π G = 1 (Granda et al. [62] ), where α 1 and β 1 are constants.

For the universe, where dark energy and dark matter are interacting with each other, the total energy density ρ = ( ρ m + ρ Λ ) satisfies the equation of continuity as,

ρ ˙ m + ρ ˙ Λ + 3 H ( ρ m + ρ Λ + p Λ ) = 0 (2.14)

It is assumed that the dark matter component is interacting with the dark energy through an interacting term Q, the continuity equation of matter and dark energy can be obtained as,

ρ ˙ m + ( V ˙ V ) ρ m = Q (2.15)

ρ ˙ Λ + ( V ˙ V ) ( 1 + ω Λ ) ρ Λ = Q (2.16)

where ω Λ = p Λ ρ Λ is the equation of state parameter for the holographic dark energy and Q > 0 measures the strength of interaction. A vanishing Q implies that the dark matter and dark energy are separately conserved. In view of continuity equations, the interaction between dark energy and dark matter must be a function of the energy density multiplied by a quantity, with units of inverse of time, which can be chosen as the Hubble parameter H. It’s a freedom to choose the form of energy density which can be any combination of dark energy and dark matter. Thus interaction between dark energy and dark matter could be expressed phenomenologically in the form as (Guo et al. [43] [44] , Amendola et al. [63] ),

Q = 3 b 2 H ρ m = b 2 V ˙ V ρ m (2.17)

where b 2 is the coupling constant.

Cai and Wang [64] have taken the same relation for interacting dark matter and phantom dark energy in order to avoid the coincidence problem.

Using Equations (2.15) and (2.17), we get the energy density of dark matter as,

ρ m = ρ 0 V ( b 2 1 ) (2.18)

where ρ 0 > 0 is a real constant of integration.

Using Equations (2.17) and (2.18), we get the interacting term Q as,

Q = 3 ρ 0 b 2 H V ( b 2 1 ) (2.19)

3. Cosmological Solution for Variable Deceleration Parameter

We consider the deceleration parameter to be a variable

q = a a ¨ a ˙ 2 = a ¨ a H 2 = b ( t ) variable. (3.1)

and following Pradhan et al. [65] and Chawla et al. [1] , we assume the law of variation of scale factor as increasing function of time

a ( t ) = [ sinh ( α t ) ] 1 n (3.2)

Using (3.2) in Equations (2.12a)-(2.12c), we obtain the expressions for scale factors as,

a 1 ( t ) = V 1 / 3 = a = ( sinh α t ) 1 / n (3.3)

a 2 ( t ) = D ( sinh α t ) 1 / n exp ( X d t ( sinh α t ) 1 / n ) (3.4)

a 3 ( t ) = D 1 ( sinh α t ) 1 / n exp ( X d x ( sinh α t ) 1 / n ) , (3.5)

where X and D are constants of integration.

Using Equations (2.10) and (3.2) in Equations (2.17) and (2.18), we obtained,

Q = 3 n ρ 0 b 2 α coth α t ( sinh ( α t ) ) 3 n ( b 2 1 ) , (3.6)

ρ m = ρ 0 ( sinh ( α t ) ) 3 n ( b 2 1 ) . (3.7)

Using Equations (3.2)-(3.5) and (3.7) in Equation (2.4) we obtained the density of holographic dark energy as,

ρ Λ = 3 α 2 n 2 coth 2 ( α t ) ( X 2 + β 2 ) [ 1 sinh ( α t ) 1 / n ] 2 ρ 0 ( sinh ( α t ) ) 3 n ( b 2 1 ) (3.8)

Using Equation (3.3)-(3.5) in Equation (2.7), we obtained the pressure as,

p Λ = α 2 n 2 [ ( 2 n 3 ) coth 2 ( α t ) 2 n ] 2 α X n coth ( α t ) ( sinh ( α t ) ) 1 n + β 2 X 2 ( sinh ( α t ) ) 2 n . (3.9)

The EOS parameter ω Λ of holographic dark energy is given by,

ω Λ = α 2 [ ( 2 n 3 ) coth 2 ( α t ) 2 n ] ( sinh ( α t ) ) 2 n 2 n α X coth ( α t ) ( sinh ( α t ) ) 1 n + n 2 ( β 2 X 2 ) 3 α 2 coth 2 ( α t ) ( sinh ( α t ) ) 2 n n 2 ρ 0 ( sinh ( α t ) ) 1 n ( 3 b 2 1 ) n 2 ( β 2 + X 2 ) (3.10)

The physical parameters such as spatial volume V, Hubble parameter H, expansion scalar θ and the time varying deceleration parameter q are obtained as,

V = a 3 = ( sinh ( α t ) ) 3 / n (3.11)

H = α n coth ( α t ) (3.12)

θ = 3 H = 3 α n coth ( α t ) (3.13)

q = n ( 1 tanh 2 ( α t ) ) 1 . (3.14)

The shear scalar σ and mean isotropy parameter Δ are given by,

σ 2 = 1 6 θ 2 = 3 α 2 2 n 2 coth 2 ( α t ) , (3.15)

Δ = 1 3 i = 1 3 ( H i H H ) 2 = 2 n 2 X 2 ( sinh ( α t ) ) 2 / n 3 α 2 coth 2 ( α t ) . (3.16)

4. Conclusions

In this paper, we have presented spatially homogeneous and anisotropic Bianchi Type-V universe field with interacting dark matter and holographic dark energy. With the consideration of variable deceleration parameter, we obtained the solutions of Einstein’s field equations.

It is found that the universe approaches to isotropy for large cosmic time as shown by different observational data and dark energy is responsible for expansion of universe. The concluding remarks of the model are as follows.

1) The sign of q represents that the universe is decelerating or accelerating i.e. a positive sign of q represents accelerating universe and negative sign of q represents decelerating universe.

In our model q > 0 for t 0 and q 1 for t i.e. the model represents the decelerating to accelerating phase and the values of deceleration parameter lie in the phase 1 q > 0 .

2) From the Equation (3.11), we can say that the spatial volume V is finite at t = 0 and expands as t increases and becomes infinite for t = .

3) From Equation (3.16), we can conclude that for the large cosmic time (i.e. t ), the anisotropy parameter Δ 0 . Therefore, for the large cosmic time, the anisotropy of the universe damped out and the universe approaches to an isotropy universe.

4) From the Equation (3.12), it is observed that the directional Hubble parameter diverges for t = 0 and converges for t = .

5) We observe that p Λ (i.e. pressure of dark energy) tends to a negative value for large cosmic time which shows that the universe is accelerating (SNeIa).

6) From the Equation (3.10), the EOS parameter ω Λ < 1 for large cosmic time. In this case, the holographic dark energy looks like phantom energy, (Abazajian et al. [15] , Ade et al. [66] , Riess et al. [4] [67] , Zimdahl [51] ). Our result is consistent with SNeIa.

7) For β = 0 in Equation (2.1), the investigated model approaches to Mete, et al. [68] .

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

Cite this paper

Mete, V.G., Bokey, V.D. and Bawane, V.S. (2019) Interacting Holographic Dark Energy in Bianchi Type-V Universe with Variable Deceleration Parameter. Open Access Library Journal, 6: e5498. https://doi.org/10.4236/oalib.1105498

References

  1. 1. Chawla, C., Mishra, R.K. and Pradhan, A. (2012) Anisotropic Bianchi-I Cosmological Models in String Cosmology with Variable Deceleration Parameter. Romanian Journal of Physics, 58, 1000. arXiv:1203.4014 [physics.gen-ph]

  2. 2. Perlmutter, S.J., et al. (1998) Discovery of a Supernova Explosion at Half the Age of the Universe. Nature, 391, 51-54. https://doi.org/10.1038/34124

  3. 3. Perlmutter, S.J., et al. (1999) Measurements of Ω and Λ from 42 High-Redshift Supernovae. The Astrophysical Journal, 517, 565-586.
    https://doi.org/10.1086/307221

  4. 4. Riess, A.G., et al. (1998) Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, 116, 1009-1038. https://doi.org/10.1086/300499

  5. 5. Riess, A.G., et al. (2004) Type Ia Supernova Discoveries at z > 1 from the Hubble Space Telescope: Evi-dence for Past Deceleration and Constraints on Dark Energy Evolution. The Astrophysical Journal, 607, 665-687. https://doi.org/10.1086/383612

  6. 6. Astier, P., et al. (2006) The Supernova Legacy Survey: Measurement of ?M, ?Λ and from First Year Data Set. As-tronomy & Astrophysics, 447, 31-48.
    https://doi.org/10.1051/0004-6361:20054185

  7. 7. Spergel, D.N., et al. (2006) Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology. The Astrophysical Journal, 170, 377. https://doi.org/10.1086/513700

  8. 8. Davis, T.M., et al. (2007) Scrutinizing Exotic Cos-mological Models Using Essence Supernova Data Combined With Other Cosmological Probes. The Astrophysical Journal, 666, 716-725. https://doi.org/10.1086/519988

  9. 9. Bennett, C.L., Halpern, M., Hinshaw, G., Jarosik, N., Kogut, A., et al. (2003) First Year Wilkinson Microwave Anisotropy Probe (WMAP) Ob-servations: Preliminary Maps and Basic Results. The Astrophysical Journal, 148, 1-43.
    https://doi.org/10.1086/377253

  10. 10. Spergel, D.N., Verde, L., Peiris, H.V., Komatsu, E., Nolta, M.R., et al. (2003) First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations Determination of Cosmological Parameters. The Astrophysical Journal, 148, 175-194.
    https://doi.org/10.1086/377226

  11. 11. Verde, L., et al. (2002) The 2dF Galaxy Redshift Survey: The Bias of Galaxies and the Density of the Universe. Monthly Notices of the Royal Astronomical Society, 335, 432-440. https://doi.org/10.1046/j.1365-8711.2002.05620.x

  12. 12. Hawkins, E., et al. (2003) The 2dF Galaxy Redshift Survey: Correlation Functions, Peculiar Velocities and the Matter Density of the Universe. Monthly Notices of the Royal Astronomical Society, 346, 78-96.
    https://doi.org/10.1046/j.1365-2966.2003.07063.x

  13. 13. Abazajian, K., et al. (2003) The First Data Release of The Sloan Digital Sky Survey. The Astronomical Journal, 126, 2081-2086. https://doi.org/10.1086/378165

  14. 14. Abazajian, K., et al. (2004) The Second Data Release of the Sloan Digital Sky Survey. The Astronomical Journal, 128, 502-512.

  15. 15. Abazajian, K., et al. (2004) The Third Data Release of The Sloan Digital Sky Survey. The Astronomical Journal, 129, 1755-1759.

  16. 16. Tegmark, M., et al. (2004) Cosmological Parameters from SDSS and WMAP. Physical Review D, 69, Article ID: 103501. https://doi.org/10.1103/PhysRevD.69.103501

  17. 17. Weinberg, S. (1989) The Cosmological Constant Problem. Review of Modern Physics, 61, 1. https://doi.org/10.1103/RevModPhys.61.1

  18. 18. Carroll, S.M. (2001) The Cosmological Constant. Living Reviews in Relativity, 4, 1.
    https://doi.org/10.12942/lrr-2001-1

  19. 19. Peebles, P.J.E. and Ratra, B. (2003) The Cosmological Constant and Dark Energy. Reviews of Modern Physics, 75, 559. https://doi.org/10.1103/RevModPhys.75.559

  20. 20. Padmanabhan, T. (2003) Cosmological Constant: The Weight of the Vacuum. Physics Reports, 380, 235-320. https://doi.org/10.1016/S0370-1573(03)00120-0

  21. 21. Koivisto, T. and Mota, D.F. (2008) Anisotropic Dark Energy: Dynamics of the Background and Perturbations. Journal of Cosmology and Astroparticle Physics, 2008, 18. https://doi.org/10.1088/1475-7516/2008/06/018

  22. 22. Cohen, A.G., Kaplan, D.B. and Nel-son, A.E. (1999) Effective Field Theory, Black Holes, and the Cosmological Constant. Physics Review Letters, 82, 4971-4974.
    https://doi.org/10.1103/PhysRevLett.82.4971

  23. 23. Horava, P. and Minic, D. (2000) Probable Values of the Cosmological Constant in a Holographic Theory. Physical Review Letters, 85, 1610.
    https://doi.org/10.1103/PhysRevLett.85.1610

  24. 24. Thomas, S. (2002) Holography Stabilizes the Vacuum Energy. Physical Review Letters, 89, Article ID: 081301. https://doi.org/10.1103/PhysRevLett.89.081301

  25. 25. Li, M. (2004) A Model of Holographic Dark Energy. Physics Letters B, 603, 1-5.
    https://doi.org/10.1016/j.physletb.2004.10.014

  26. 26. Hooft, G. (1995) Dimensional Reduction in Quantum Gravity. General Relativity and Quantum Cosmology (gr-qc), 9310026.

  27. 27. Coles, P. and Eills, G.F.R. (1994) The Case for an Open Universe. Nature, 370, 609-615. https://doi.org/10.1038/370609a0

  28. 28. Zhang, X. and Wu, F.Q. (2005) Con-straints on Holographic Dark Energy from Type Ia Supernova Observations. Physical Review D, 72, Article ID: 043524.
    https://doi.org/10.1103/PhysRevD.72.043524

  29. 29. Enqvist, K., Hannestad, S. and Sloth, M.S. (2005) Searching for a holographic connection between Dark Energy and the Low/CMB Multipoles. Journal of Cosmology and Astroparticle Physics, 2005, 4. https://doi.org/10.1088/1475-7516/2005/02/004

  30. 30. Shen, J., Wang, B., Abdalla, E. and Su, R.-K. (2005) Constraints on the Dark Energy from the Holographic Connection to the Small l CMB Suppression. Physics Letters B, 609, 200-205. https://doi.org/10.1016/j.physletb.2005.01.051

  31. 31. Chang, Z., Wu, F.-Q. and Zhang, X. (2006) Constraints on Holographic Dark Energy from X-Ray Gas Mass Fraction of Galaxy Clusters. Physics Letters B, 633, 14-18. https://doi.org/10.1016/j.physletb.2005.10.095

  32. 32. Carvalho, F.C. and Saa, A. (2004) Nonminimal Coupling, Exponential Potentials and the ω < -1 Regime of Dark Energy. Physical Review D, 70, Article ID: 087302. https://doi.org/10.1103/PhysRevD.70.087302

  33. 33. Huang, Q.-G. and Li, M. (2004) The Holographic Dark Energy in a Non-Flat Universe. Journal of Cosmology and Astro-particle Physics, 2004, 13.
    https://doi.org/10.1088/1475-7516/2004/08/013

  34. 34. Gong, Y.-G. (2004) Extended Holographic Dark Energy. Physical Review D, 70, Article ID: 064029. https://doi.org/10.1103/PhysRevD.70.064029

  35. 35. Gong, Y.-G. and Zhang, Y.-Z. (2005) Holography and Holographic Dark Energy Model. Classical and Quantum Gravity, 22, 4895-4902.
    https://doi.org/10.1088/0264-9381/22/22/014

  36. 36. Pavon, D. and Zim-dahl, W. (2005) Holographic Dark Energy and Cosmic Coincidence. Physics Letters B, 628, 206-210.
    https://doi.org/10.1016/j.physletb.2005.08.134

  37. 37. Wang, B., Gong, Y.G. and Abdalla, E. (2005) Transition of the Dark Energy Equation of State in an Interacting Holographic Dark Energy Model. Physics Letters B, 624, 141-146. https://doi.org/10.1016/j.physletb.2005.08.008

  38. 38. Perivolaropoulos, L. (2005) Crossing the Phantom Divide Barrier with Scalar Tensor Theories. Journal of Cosmology and As-troparticle Physics, 2005, 1.
    https://doi.org/10.1088/1475-7516/2005/10/001

  39. 39. Nojiri, S. and Odintsov, S.D. (2006) Unifying Phantom Inflation with Late-Time Acceleration: Scalar Phan-tom-Non-Phantom Transition Model and Generalized Holographic Dark Energy. General Relativity and Gravitation, 38, 1285-1304.
    https://doi.org/10.1007/s10714-006-0301-6

  40. 40. Guberina, B., Horvat, R. and Nikolic, H. (2005) Generalized Holographic Dark Energy and the IR Cutoff Problem. Physics Review D, 72, Article ID: 125011.
    https://doi.org/10.1103/PhysRevD.72.125011

  41. 41. Guberina, B., Horvat, R. and Ni-koli?, H. (2006) Dynamical Dark Energy with a Constant Vacuum Energy Density. Physics Letters B, 636, 80-85.
    https://doi.org/10.1016/j.physletb.2006.03.041

  42. 42. Guo, Z. K., Ohta, N. and Zhang, Y.Z. (2005) Parameterization of Quintessence and Its Potential. Physical Review D, 72, Article ID: 023504.
    https://doi.org/10.1103/PhysRevD.72.023504

  43. 43. Guo, Z.K., Ohta, N. and Tsujika-wa, S. (2007) Probing the Coupling between Dark Components of the Universe. Physics Review D, 76, Article ID: 023508.
    https://doi.org/10.1103/PhysRevD.76.023508

  44. 44. Guo, Z.K., Ohta, N. and Zhang, Y.Z. (2007) Parametrizations of the Dark Energy Density and Scalar Potentials. Modern Physics Letters A, 22, 883-890.
    https://doi.org/10.1142/S0217732307022839

  45. 45. Hu, B. and Ling, Y. (2006) Interacting Dark Energy, Holographic Principle, and Coincidence Problem. Physical Review D, 73, Article ID: 123510.
    https://doi.org/10.1103/PhysRevD.73.123510

  46. 46. Li, H., Guo, Z.K. and Zhang, Y.Z. (2006) A Tracker Solution for a Holographic Dark Energy Model. International Journal of Modern Physics D, 15, 869-877.
    https://doi.org/10.1142/S0218271806008577

  47. 47. Setare, M.R. (2006) Interacting Holographic Dark Energy Model in Non-Flat Universe. Physics Letters B, 642, 1-4. https://doi.org/10.1016/j.physletb.2006.09.027

  48. 48. Setare, M.R. (2007) The Holographic Dark Energy in Non-Flat Brans—Dicke Cosmology. Physics Letters B, 644, 99-103.
    https://doi.org/10.1016/j.physletb.2006.11.033

  49. 49. Sadjadi, H.M. (2007) The Particle versus the Future Event Horizon in an Interacting Holographic Dark Energy Model. Journal of Cosmology and Astroparticle Physics, 2007, 26. https://doi.org/10.1088/1475-7516/2007/02/026

  50. 50. Banerjee, N. and Pavon, D. (2007) Holographic Dark Energy in Brans—Dicke Theory. Physics Letters B, 647, 477-481.
    https://doi.org/10.1016/j.physletb.2007.02.035

  51. 51. Zimdahl, W. (2008) Dark Energy: A Unifying View. International Journal of Modern Physics D, 17, 651-658. https://doi.org/10.1142/S0218271808012395

  52. 52. Sarkar, S. (2014) Holographic Dark En-ergy Model with Linearly Varying Deceleration Parameter and Generalised Chaplygin Gas Dark Energy Model in Bianchi Type-I Universe. Astrophysics and Space Science, 349, 985-993.
    https://doi.org/10.1007/s10509-013-1684-y

  53. 53. Sarkar, S. (2014) Interacting Holographic Dark Energy with Variable Deceleration Parameter and Accreting Black Holes in Bianchi Type-V Universe. Astrophysics and Space Science, 352, 245-253. https://doi.org/10.1007/s10509-014-1876-0

  54. 54. Sarkar, S. (2014) Interacting Holographic Dark Energy with Variable Deceleration Parameter and Tachyon Scalar Field Dark Energy Model in LRS Bianchi Type-II Universe. Astrophysics and Space Science, 350, 821-829.
    https://doi.org/10.1007/s10509-014-1786-1

  55. 55. Adhav, K.S. (2011) State-finder Diagnostic for Variable Modified Chaplygin Gas in Bianchi Type-V Universe. As-trophysics and Space Science, 335, 611-617.
    https://doi.org/10.1007/s10509-011-0773-z

  56. 56. Adhav, K.S. (2011) Statefinder Di-agnostic for Modified Chaplygin Gas in Bianchi Type-V Universe. The European Physical Journal Plus, 126, 52.
    https://doi.org/10.1140/epjp/i2011-11052-6

  57. 57. Pradhan, A., Amirhashchi, H. and Saha, B. (2011) Bianchi Type-I Anisotropic Dark Energy Model with Constant Deceleration Parameter. International Journal of Theoretical Physics, 50, 2923-2938. https://doi.org/10.1007/s10773-011-0793-z

  58. 58. Kumar, S. and Yadav, A.K. (2011) Some Bianchi Type-V Models of Accelerating Universe with Dark Energy. Modern Physics Letters A, 26, 647-659.
    https://doi.org/10.1142/S0217732311035018

  59. 59. Pradhan, A. and Amirhashchi, H. (2011) Accelerating Dark Energy Models in Bianchi Type-V Spacetime. Modern Physics Letters A, 26, 2266-2275.
    https://doi.org/10.1142/S0217732311036620

  60. 60. Adhav, K.S., Tayade, G.B. and Bansod, A.S. (2014) Interacting Dark Matter and Holographic Dark Energy in an Anisotropic Universe. Astrophysics and Space Science, 353, 249-257. https://doi.org/10.1007/s10509-014-2015-7

  61. 61. Som, S. and Sil, A. (2014) Interacting Holographic Dark Energy Models: A General Approach. Astrophysics and Space Science, 352, 867-875.
    https://doi.org/10.1007/s10509-014-1926-7

  62. 62. Granda, L.N. and Ol-iverios, A. (2008) Infrared Cut-Off Proposal for the Holographic Density. Physics Letters B, 669, 275-277.
    https://doi.org/10.1016/j.physletb.2008.10.017

  63. 63. Amendola, L., Campos, G.C. and Rosenfeld, R. (2007) Consequences of Dark Matter-Dark Energy Inter-action on Cosmological Parameters Derived from Type Ia Supernova Data. Physical Review D, 75, Article ID: 083506.
    https://doi.org/10.1103/PhysRevD.75.083506

  64. 64. Cai, R.-G. and Wang, A. (2005) Cosmology with Interaction between Phantom Dark Energy and Dark Matter and the Coincidence Problem. Journal of Cosmology and Astroparticle Physics, 2005, 2. https://doi.org/10.1088/1475-7516/2005/03/002

  65. 65. Pradhan, A., Jaiswal, R., Jotania, K. and Khare, R.K. (2012) Dark Energy Models with Anisotropic Fluid in Bianchi Type-VI0 Space-Time with Time Dependent Deceleration Parameter. Astrophysics and Space Science, 337, 401-413.
    https://doi.org/10.1007/s10509-011-0835-2

  66. 66. Ade, P.A.R., et al. (2014) Plank 2013 Results XVI Cosmological Parameters. Astronomy and Astrophysics, 571, 1-66.

  67. 67. Riess, A.G., et al. (2007) New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing Constraints on the Early Behavior of Dark Energy. Astrophysical Journal, 659, 98-121. https://doi.org/10.1086/510378

  68. 68. Mete, V.G., et al. (2018) Interacting Dark Fluids In Bianchi Type-I Universe With Variable Deceleration Parameter. International Journal of Current Advanced Research, 7, 13609-13613.