ISSN ONLINE(2319-8753)PRINT(2347-6710)

All submissions of the EM system will be redirected to Online Manuscript Submission System. Authors are requested to submit articles directly to Online Manuscript Submission System of respective journal.

Amazing porn model Belle Delphine nudes on Watch free video collection of Belle Delphine nede leaked

Rare Muslim porn and سكس on Tons of Arab porn clips.

XNXX and Xvideos porn clips free on Best XnXX porn tube channels, categorized sex videos, homemade and amateur porn.

Exlusive russian porn Get uniqe porn clips from Russia

Find out on best collection of Arabain and Hijab سكس

Five Dimensional Exact Solutions of Bianchi Type-I Space-Time in f (R,T) Theory of Gravity

L. S. Ladke1, V. K. Jaiswal2, R. A. Hiwarkar3
  1. Associate Professor & Head, Department of Mathematics, Sarvodaya Mahavidyalaya, Sindewahi , Dist. Chandrapur India
  2. Assistant Professor, Department of Mathematics, Priyadarshini J. L. College of Engineering, Nagpur, India
  3. Assistant Professor, Department of Mathematics, Guru Nanak Institute of Engineering & Technology, Nagpur, India
Related article at Pubmed, Scholar Google

Visit for more related articles at International Journal of Innovative Research in Science, Engineering and Technology


In this paper, we have obtained two five dimensional exact solutions of Bianchi type-I space-time in f (R,T) theory of gravity using assumption of constant deceleration parameter and variation law of Hubble parameter which correspond to two different cosmological models. The first solution yields a singular model for n  0while the second gives a non-singular model for n  0.The physical behavior for both the models have been discussed using some physical quantities..


f (R,T) theory of gravity, five dimensional Bianchi type-I space-time, Vacuum field equations.


Einstein general relativity is the basis to explain most of the gravitational phenomena but it does not seem to resolve some of the important problems in cosmology such as the accelerating expansion of the universe. It is now proved from observational and theoretical fact that our universe is in the phase of accelerated expansion. In order to explain the accelerated expansion, number of cosmological models have been proposed by different authors. f (T) theory of gravity where T is the scalar torsion has been proposed to explain current accelerated expansion without involving dark energy. Ratbay M. [1] has shown that the acceleration of the universe can be understood by f (T) gravity models. M. Sharif et al [2] considered spatially homogeneous and anisotropic Bianchi type–I universe in f (T) gravity theory. Wei H. et al [3] tried to constrain f (T) theories with the fine structure constant. Bamba K. et al [4] studied the cosmological evolution of the equation of state for dark energy with the combination of exponential, logarithmic and f (T) theories. f (R) theory of gravity is the another example of gravity. Many authors have investigated f (R) gravity in different contest. Carrolet. al. [5] explained the presence of late time comic acceleration of the universe in f (R) gravity. Nojiri and Odintsov[6,7] proved that the f (R) theory of gravity provides very natural unification of the early time inflation and late time acceleration. Bertolami et al [8] have poposed a generalization of f (R) modified theory of gravity, by including in the theory an explicit coupling of an arbitrary function of the Ricci scalar R with the matter Lagrangian density Lm. As a result of coupling the motionof the massive particles is non- geodesic and extra force orthogonal to the four velocity arises. Multamaki and Vilja [9,10] investigated static spherically symmetric vacuum solutions of the field equations and non- vacuum solutions by taking fluid respectively. Capozziello et al [11] used Noether symmetries to study spherically symmetric solutions in f (R) theory of gravity. Sharif and Shamir [12] studied exact vacuum solutions in Bianchi type-I and Vspace-times in f (R) ) theory of gravity. Shamir [13] discussed the plane symmetric vacuum Bianchi type-III cosmology in f (R) gravity. Aktas et al [14] have studied anisotropic models in f (R) gravity. Adhav [15] discussed the Kantawski-sachs string cosmological model in f (R) theory. Reddy et al [16] studied vacuum solutions of Bianchi type- I &V models in f (R) gravity with a special form of deceleration parameter.


Higher dimensional cosmological model play a vital role in many aspects of early stage of cosmological problems. The study of higher dimensional space- time provides an idea that our universe is much smaller at early stage of evolution as observed today. There is nothing in the equation of relativity which restrict them to four dimensions. Kaluza and Klein [22, 23] have done remarkable work by introducing an idea of higher dimension space-time. Many researcherinspired to entered in to the field of higher dimension theory to explore knowledge of universe. Wesson [24 ,25] and D.R. K. Reddy {26] have studied several aspects of five dimensional space-time in variable mass theory and bi-metric theory of relativity respectively. Lorentz and Petzold [27], Ibanez and Verdaguer [28] ,Khadekar and Gaikwad [29] ,Adhav et al [30] have studied the multidimensional cosmological models in general relativity and in other alternative theories of gravitations. Ladke L. S. [31] studied the Bianchi type-I (Kasner form) cosmological model in f(R) theory of gravity in five dimensions.
Motivating with the above research work we have obtained five dimensional exact solutions of Bianchi type-I space-time assuming constant deceleration parameter and variation law of Hubble’s parameter proposed by Berman M. S. [32] which corresponds to two different cosmological models. Physical aspects of both the models are also discussed.




In this section we find exact solutions of five dimensional Bianchi type-I space time in f (R) theory of gravity. The line element of Bianchi type-I space-time in 5 V is given by


imagecoefficients A,B, C and volume of the universe increase exponentially with the cosmic time. This shows that the universe expansion take place with zero volume from infinite past. It is seen that,the result obtained here are similar to the results obtained earlier by M. Farasat Shamir et. al (20).


[1]RatbayMyrzakulov : Accelerating universe in f(T) gravity. Eur. phy. J.C (2011)71:1752.

[2]M. Sharif and Shamaila Rani:f(T) Models within Bianchi Type I Universe.arXiv: 1105.6228v1 [gr-qc] 31 May 2011.

[3]Wei H. et al :f(T) theories andvaryingfinestructure constant.Phys. Lett. B 703 (2011) 74-80.

[4]BambaK. et al:Equation of state for dark energy in f(T) gravityJACP 1101 (2011) 021

[5]Carroll, S.M., et al. “Is cosmic speed-up due to new gravitational physics?” Phys. Rev. D, 70, pp.043528, (2004).

[6]Nojiri S and Odintsov S D :Modified gravity and its reconstruction from the universe expansion history”. J.Phys. Conf.Ser. 66, 012005,(2007).

[7]Nojiri S and Odintsov S D :”Future evolution and finite-time singularities in F(R) gravity unifying inflation and cosmic acceleration “. Phys. Rev. D, 78, 046006, (2008).

[8]BertolamiO .et al “Extra force in f(R) modified theories of gravity” . Phys.Rev. D75 (2007) 104016 arXiv:0704.1733 [gr-qc]

[9] Multam¨aki, T. and Vilja, I. : spherically symmetric solution of modified field equations in f(R) theory of gravity, Phys. Rev. D74(2006)064022

[10]Multam¨aki, T. and Vilja,I. :Static spherically symmetric perfect fluid solutions in f (R)theories of gravity, Phys. Rev. D76(2007)064021

[11]Capozziello, S., Stabile, A. and A Troisi. : spherically symmetric solution in f (R) theory of gravity via the Noether symmetry approach, Phys. Rev. D74(2006)064022.Class. QuantumGrav.24(2007)2153.

[12]SharifM. Farasat Shamir : Exact Solutions of Bianchi Types I and V Space-times in f(R) theory of Gravity ,Class. Quant. Grav. 26 (2009) 235020 arXiv:0910.5787 [gr-qc].

[13]Shamir,M.F. “Plane Symmetric Vacuum Bianchi Type III Cosmology in f(R) Gravity” Int. J. Theor. Phys. 50, pp.637-643 (2011).

[14]Aktas, C., et al.” Behaviors of dark energy andmesonic scalar field for anisotropic universe in f (R) gravity”Phys. Lett. B,707, pp.237-242 (2012).

[15] Adhav, K.S.: “Kantowski-sachs string cosmological model in f(R) theory of gravity”.Can.J.Phys,90,119,(2012).

[16]Reddy, D.R.K et al.” Vacuum Solutionsof BianchiType-I and V Models in f(R) Gravity with a Special form of Deceleration parameter” Int .Jou. Sci. Adv. Tech., 4, 3, pp.23-33 (2014).

[17]Harko, T., Lobo, F.S.N., Nojiri, S. and Odintsov, S.D.: “f (R,T) gravity”. Phys. Rev.D84(2011)024020.

[18].Adhav, K.S.: LRS Bianchi type-I cosmological model in f ( R, T) theory of gravity,Astro .phys. Space Sci. 339(2012)365.

[19]Houndjo, M.J.S.: “Reconstruction of f(R, T) gravity describing matter dominated and accelerated phases”,Int. J. Mod. Phys. D21(2012)1250003.

[20]M.“Exact Solutions of Bianchi Types I and V Space-times in f (R,T) Theory of Gravity,arXiv:1207.0708 v1 [gr-qc] 2 July2012.

[21]Reddy D. R. K.and R. shanthikumar “Global journal of science frontier research physics and space science”. Vol. 13 Issue 2(2013)

[22]Kaluza T.:ZumUnitatsproblem. Der physic, Sitzpreuss.Akad.Wiss. D 33, 966-972.

[23] Kelin O.: Quantum Theory and Five-DimensionalTheoryofRelativity (In German and English) Z. Phys. 37 (1926) 895-906.

[24]Wesson P S (1983) :A new approach to scale-invariant gravity, AstronAstrophys., 119, 145- 152.

[25]Wesson P S (1984) :An embedding for general relativity with variable rest mass. Gen. Rel.Grav.Vol.16, Issue 2, pp. 193-203.

[26] Reddy D.R.K. and N. VenkateswaraRao: Non-existence of higher dimensional anisotropic cosmological model in bimetric theory of gravitation. Astrophysics and SpaceScience, Vol. 271, Issue 2, pp 165-169 .(2000)

[27] Lorentz and Petzold;Higher-dimensional Brans-Dicke cosmologies, Gen. Relativ. Grav.17, 1189, (1985).

[28]Ibanez, Z. and Verdaguer,E.: Radiative isotropic cosmologies with extra dimensions,Phys. Rev. D, 34, 1202, (1986).

[29]Khadekar, G.S., and Gaikwad,M.: Proc. Einstein Found Int. 11, 95, (2001)

[30]Adhav. K.S. et al.: Astrophysics and Space Science, 310(3-4), 231, (2007).

[31]Ladke L. S. : Five dimensional Bianchi type- I (Kasner form) Cosmological Model in f(R) theory of gravitation. :OIIRJ Vol. IV Issue .IV July- Aug 2014

[32]Berman , M. S. :NuovoCimentoB 74, 182 91983).