Bianchi Type-V Two-Fluid Dark Energy Cosmological Models in Saez-Ballester Theory of Gravitation

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1 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio Arile T. Viuh *, V. U. M. Ro, M. Vijy Shi, Y. Adiy & Moll Megesh Nigus Depre of Applied Mheis, Adhr Uiversiy, Viskhp, Idi-5 Absr This pper ls ih spilly hoogeeous d isoropi Bihi-V uiverse filled ih broropi fluid d drk eergy i he fre ork of slr esor heory of grviio proposed by Sez d Blleser 986. We osir boh he ses he he drk eergy is iilly oupled o broropi fluid s ell s dire ierio ih i. The ex soluios of he orrespodig field equios re obied d lso soe ipor feures of he ols, hus obied, hve bee disussed i il. Keyords: Bihi-V eri, Sez-Blleser heory, o-fluids, drk eergy, EoS Preer.. Iroduio I he sudy of or osology, e osir h he ol eergy siy of he uiverse is doied by he siies of o opoes: he drk er d he drk eergy. The ree observiol d srogly oive o sudy geerl properies of he osologil ols oiig ore h oe fluid. These uiverses re oled ih perfe fluids d ih ixures of o ierig fluids ur he ssupio h here is o eergy rsfer og he opoes. Bu, suh serios re o ofired by observiol d. This oives us o sudy osologil ols oiig fluids hih ier ih eh oher. I ree yers here hs bee iese ieres i osologil ols ih drk eergy i geerl reliviy beuse of he f h our observble uiverse is urgoig phse of elered expsio, hih hs bee ofired by severl osologil observios suh s ype superov by severl uhors Riess e l. 998; Perluer e l Cldell d Huge 6 hve disussed osi irove bkgroud CMB isoropy d Diel e l. 8 hve sudied he lrge sle sruure d srogly idie h drk eergy doies he prese uiverse, usig osi elerio. Bsed o hese observios, osologiss hve eped he i of drk eergy, hih is fluid ih egive pressure, kig up roud 7 % of he prese uiverse eergy oe o be resposible for his elerio due o repulsive grviio. * Correspoe Auhor: T. Viuh, Depre of Applied Mheis, Adhr Uiversiy, Viskhp, A.P., Idi. E-il: viuhul@gil.o ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

2 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio Cosologiss hve proposed y dides for drk eergy o fi he urre observios suh s osologil os, Thyo, quiessee, pho d so o. Evoluio of he equio of se EoS of drk eergy / rsfers fro i he er ps quiessee p regio o ree sge pho regio. Akrsu d Kili, Ydv, Ydv d Ydv, Prdh e l., b, Prdh d Airhshhi d Ydv e l. hve ivesiged differe spes of drk eergy ols i geerl reliviy ih vrible EoS preer. The oep of drk eergy s proposed for ursdig his urrely elerig expsio of he uiverse, d he is exisee s ofired by severl high preisio observiol experies Tegrk e l., espeilly he Wilkiso Mirove Aisoropy Probe WMAP sellie experie. The WMAP shos h drk eergy oupies bou 7% of he eergy of he uiverse, d drk er bou %. The usul bryo er, hih be sribed by our ko prile heory, oupies oly bou % of he ol eergy of he uiverse. This oives us o sudy osologil ols oiig fluids hih ier ih eh oher. Cldo e l. 8 hve osired he siples o-rivil osologil serios for ierig ixure of o osi fluids sribed by poer-l sle fors, i.e. he expsio s poer-l i ie. Wheres, ierig d o-ierig o-fluid serio for drk eergy i FRW uiverse ih os elerio preer hve bee sribed by Prdh e l.. Adhv e l. hve ivesiged ierig osi fluids i LRS Bihi ype-i osologil ol. Sh e l. revisied o-fluid serio for drk eergy ols i FRW uiverse ivesiged by Airhshhi e l.. Reddy d Shi Kur hve disussed o fluid serio for drk eergy ol i slr-esor heory of grviio. Airhshhi e l. hve sudied ierig o-fluid visous drk eergy ols i o-fl uiverse. Reely Ro e l. 6 hve disussed o-fluid serio for higher diesiol drk eergy osologil ol i Sez-Blleser heory of grviio Sez d Blleser 986 foruled slr-esor heory of grviio i hih he eri is oupled ih diesioless slr field i siple er. This ouplig gives sisfory sripio of he ek fields. I spie of he diesioless hrer of he slr field igrviy regie ppers. This heory lso suggess possible y o solve issig er proble i o fl FRW osologies. The field equios give by Sez- Blleser 986 for he obied slr d esor fields usig geoerized uis ih =, 8πG = re G ij r ' k, i, j gij, k Tij. ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

3 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio d he slr field sisfies he equio r i r ' k, i r,. here Gij Rij R gij T is he sress eergy esor of he er. ij, k is Eisei esor, R is he slr urvure, d r re oss, The eergy oservio equio is ij T, j.. The sudy of osologil ols i he freork of slr-esor heories hs bee he ive re of reserh for he ls fe s. I priulr, Ro e l. 7, Ro e l. 8, Kore e l., Ro e l., Prdh e l., Reddy e l. d Ro & Jysudh 5 re soe of he uhors ho hve ivesiged severl spes of he osologil ols i Sez-Blleser 986 slr-esor heory. Bihi ype osologil ols re ipor i he sese h hese re hoogeeous d isoropi, fro hih he proess of isoropizio of he uiverse is sudied hrough he pssge of ie. Moreover, for he heoreil poi of vie isoropi uiverse hs greer geerliy h isoropi ols. The sipliiy of he field equios d relive ese of soluios Bihi spe ies useful i osruig ols of spilly hoogeeous d isoropi osologies. Bihi ypes V d VII h represe he geerlized ope FRW ols. Moived by bove ivesigios, i his pper e ill disuss Bihi ype V spe-ie filled ih o fluids broropi d drk eergy i slr-esor heory of grviio proposed by Sez-Blleser 986 heory of grviio. The pper is orgized s follos, i seio e disuss eri d field equios. I seio d, e obied soluios for ierig d o-ierig osologil ols respeively. I seio 5, e disuss soe oher ipor feures of he obied ols. The ls seio ois soe disussios d olusios.. Meri d field equios We osir spilly hoogeeous Bihi ype-v eri i he for ds d dx e x dy dz. ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

4 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio here, d re fuios of ie oly d is os. The ol eergy oeu esor for o fluids is give by T ij p u u pg. i j ij here d p p p. Here d broropi fluid d p re eergy siy d pressure of d p re eergy siy d pressure of drk fluid respeively, he four-veloiy of he fluid sisfyig he folloig odiio, i j g ij u u. I oovig oordie syse, e ge i T T T p, T d Tj for j here he quiies d p re fuios of oly. i. The field equios. for he eri. ih he help of. o., be rie s i u is r r.5.6 r.7 r.8.9 r. ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

5 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio The oservio equio yields.. No-ierig o -fluid ol Here e osir h o fluids do o ier ih eh oher. Hee he geerl for of oservio equio. leds us o rie he oservio equios for he drk eergy d broropi fluid seprely s p d p The EoS preer of broropi fluid i.e., p is os Akrsu d Kili,.. os.. So, equio. is iegrble, hile is fuio of ie. I orr o ge eriisi soluio e ke he folloig plusible physil odiio, he sher slr is proporiol o slr expsio, hih leds o he lier relioship beee he eri poeils d, i.e.,. here d re eri poeils d is posiive os., Fro equio.9, e ge ihou loss of geerliy, by kig, e ge.5 Fro equios.5,.6,.7 d.5, e ge..6 Fro equio.6, e ge ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

6 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio,.7 here k d k. k, k re oss of iegrio. Fro equios.5 d.7, e ge..8 Fro equios.,.7 d.8 e ge..9 Fro. e obi he slr field s r r C C log. here C is iegrig os. No, he eri., i his se, be rie s ds d dx e x [ dy dz ]. Fro equio.,. be rie s. here is iegrig os. Usig.9 i., e ge ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

7 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o 98. Fro. d., e ge p. Fro equios., d., e ge pressure d eergy siy for drk eergy s 9 p By usig equios.5 d.6, e fid he EoS preer p of drk eergy s Thus he eri. ogeher ih. d.-.7 osiues Bihi ype-v oierig o fluid osologil ol i Sez - Blleser heory of grviio.

8 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio Fig.: Plo of siy of ordiry er d drk eergy versus ie i oierig ol. Here, k, k,.,. Fig.: Plo of EoS preer of drk eergy versus ie for o-ierig ol. Here, k, k,.,. The behvior of d i ers of osi ie re sho i Fig.. Boh re posiive resig fuio of ie d overge o zero for suffiiely lrge ies. Figure pis he behvior of he EoS preer of drk eergy observed h versus ie. I is begis i he pho regio, ireses d beoes roud =.5 he psses io he quiessee regio d eds o os hih is i he quiessee regio. The expressios for he er-siy d drk-eergy siy re give by Ad he ol siy preer is give by 9. ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

9 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio Fig. : Plo of overll siy preer versus ie i oierig ol. Here, k, k,.,. The vriio of ol eergy siy preer ih osi ie is sho i Figure. I is observed h siy preer is resig fuio of ie d vryig i posiive regio hroughou he evoluio of he uiverse. This resul is opible ih he observiol resuls.. Ierig o-fluid ol No, here e osir he ierio beee drk eergy d broropi fluids. For his purpose e rie he oiuiy equios for drk fluid d broropi fluids s d p Q p Q The quiy Q expresses he ierio beee he drk eergy opoes. Sie e re ieresed i eergy rsfer fro he drk eergy o drk er, e osir Q> hih esures h he seod l of herodyis is fulfilled Pvo d Wg 9. Folloig Aedol e l. 7 d Guo e l. 7, e osir Q H. here is ouplig os. Usig equio. i equio. d iegrig, e obi... here is iegrig os. Usig.9 i., e ge ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

10 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o 98.5 No, he broropi pressure is give by p.6 Fro equios., d.5, e ge pressure d eergy siy for drk eergy s 9 p Usig.7 d.8 e ge he EoS preer p of drk eergy s Thus he eri. ogeher ih. d osiues Bihi ype-v ierig o fluid osologil ol i Sez - Blleser heory of grviio. Fig. : Plo of eergy siy of drk eergy d broropi fluid i ierig ol. Here, k, k,.,,..

11 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio Fig.5: Plo of EoS preer of drk eergy versus ie for ierig ol. Here, k, k,.,,.. Figures d sribe he behvior of siy of drk eergy & broropi fluid d EoS preer of drk eergy i ers of ie. We observed h he behvior of, d i his se is los siilr o o-ierig se. 5. Soe oher ipor properies of he ols The re of expsio i he direio of x, y d z re give by H x, H y, 5. H z. The e Hubble s preer H, expsio slr d sher slr re give by H, 5., ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

12 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio The spil volue V, e isoropy preer foud o be A d elerio preer q re V x e, 5.5 A, 5.6 q d d H. 5.7 Fro equios 5. d 5., e ge Disussio d Colusios I his pper, e hve obied d preseed spilly hoogeeous Bihi ype-v osologil ol filled ih broropi fluid d drk eergy i slr esor heory of grviio proposed by Sez-Blleser 986. The folloig re he observios d olusios: Fro. i be observed h he ols hve o iiil sigulriy i.e.. The volue of he ols vishes d expsio slr eds o ifiiy, hih shos h he Uiverse srs evolvig ih zero volue ih ifiie re of expsio. The spil volue ireses d beoes ifiiely lrge s. We observe h H,,, d diverge d hey ll vish s. The slr field is diverge s d vishes for sll vlues of ie i.e.,. Fro 5.6, oe observe h verge isoropy A for hroughou he hisory of he Uiverse, his idies h hese ols re isoropi. I is observed h i boh ierig d o-ierig ses he behvior of EoS preer of drk eergy is los se, i.e., iresig fuio of osi ie hih explis he le ie elerio of he uiverse. ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

13 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio Fro 5.7 e observed h he elerio preer is posiive d hee he ol obied is elerig iiilly d ill elere i fiie ie due o osi re-ollpse Nojiri d Odisove. The o ols preseed here re isoropi, o-roig, sherig d lso elerig i sdrd y. Hee hey represe o oly he erly sge of evoluio bu lso he prese uiverse. Reeived Oober, 6; Aeped Noveber, 6 Referees Adhv, K.S., D, M.V. d Borikr, S. M., : Ierig osi fluids i LRS Bihi ype-i osologil ols, Bulg. Jour. Phys. 8:7. Akrsu, O., Kili, C.B., : LRS Bihi ype I ols ih isoropi drk eergy d os elerio preer, Ge. Reliv. Grvi. :9. Aedol, L., Crgo Cpos, G., Rosefeld, R., 7: Cosequee of drk er-drk eergy ierio o osologil preers rived fro ype I Superov d, Phys. Rev. D 75:856. Airhshhi, H., Prdh, A., Sh, B., : A ierig o-fluid serio for drk eergy i FRW uiverse, Chi. Phys. Le. 8:98. Airhshhi, H., Prdh, A., Ziuddi, H., : Ierig o-fluid visous drk eergy ols i o-fl uiverse, Reserh i Asro. Asrophysis :9. Cldell, R.R., : A Pho Mee? Cosologil osequees of drk eergy opoe ih super-egive equio of se, Phys. Le. B 55:. Cldo, M, Mell, P, Miig, P, Svedr, J., 8: Ierig osi fluids i poer-l Fried Roberso Wlker osologil ols, Phys. Le. B. 66:. Diel, S.F., e l., 8: Lrge sle sruure s probe of grviiol slip, Phys. Rev. D, 77:5. Guo, Z.K., Oh, N., Tsujik, S. 7: Probig he ouplig beee drk opoes of uiverse, Phys. Rev. D, 76, 58. Hug, Z.Y., e l., 6: Hologrphi explio of i-gle poer orrelio suppressio i he osi irove bkgroud rdiio, J. Cosol. Asropr. Phys., 5:. Kore, S.D., Adhv, K.S., Shikh, A.Y.: Srke, N.K., : Higher Diesiol LRS Bihi ype- I Doi Wlls i Slr-Tesor Theory of Grviio, I. J. Theor. Phys. 9: 58. Nojiri, S., Odisov, S.D. : Modified Grviy Wih Negive d Posiive Poers of Curvure: Uifiio of Uflio d Cosi Aelerio, Phys. Rev. D., 68, 5 Perluer, S., e l., 999: Mesurees of d Fro High Redshif Superove, Asrophys. J.,5: 565. Prdh, A., Airhshhi, H., : Drk Eergy Mol i Aisoropi Bihi Type-III Spe-Tie Wih Vrible EoS Preer, Asrophys. Spe Si. :. ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

14 Prespeie Jourl Deeber 6 Volue 7 Issue 5 pp Viuh, T., Ro, V. U. M., Shi, M. V., Adiy & Nigus, M. M., Bihi Type-V To-Fluid Drk Eergy Cosologil Mols i Sez-Blleser Theory of Grviio Prdh, A., Airhshhi, H., Sh, B., : A Ierig d No-Ierig To-Fluid Cerio for Drk Eergy i FRW Uiverse ih Cos Deelerio Preer, Asrophys. Spe Si. :. Prdh, A., e l., : Bihi Type-I Aisoropi Drk Eergy Mol ih Cos Deelerio Preer; I. J. Theor. Phys. 5:9. Prdh, A., e l., b: A Ne Clss of LRS Bihi Type-II Drk Eergy Mols ih Vrible EoS Preer, Asrophys. Spe Si. :9. Prdh, A., Sigh, A.K.,Chouh, D.S., : Aelerig Bihi Type-V Cosology ih Perfe Fluid d He Flo i Sez-Blleser heory, I. J. Theor. Phys. 5:66. Pvo, D., Wg, B., 9: Le helier-bru Priiple i Cosologil Physis, Ge. Reliv. Grvi. :. Ro, V.U.M., Jysudh, L., 5: Five diesiol spherilly syeri perfe fluid osologil ol i slr-esor heory of grviio, Asrophys Spe Si. 58:8. Ro, V.U.M., Sree Devi Kuri, G., Sireesh, K.V.S., : Aisoropi Uiverse ih Cosi Srigs d Bulk Visosiy i Slr Tesor Theory of Grviio, Asrophys Spe Si. 5:65. Ro, V.U.M., Shi, M. V.,Viuh, T. 8: Ex Bihi Type-II, VIII d IX Perfe Fluid Cosologil Mols i Sez-Blleser Theory of Grviio, Asrophys. Spe Si., 7: 7. Ro, V, U, M., Shi, M. V., Viuh, T. & Adiy, Y. 6: To-Fluid Serio for Higher Diesiol Drk Eergy Cosologil Mol i Sez-Blleser Theory of Grviio., Prespeie Jourl, 7: 9. Ro, V.U.M., Viuh, T., Shi, M. V., 7: A Ex Bihi ype-v Cosologil Mol i Sez- Blleser Theory of Grviio, Asrophys. Spe Si. : 89. Reddy, D.R.K., Bhrhi, D., Vijy Lkshi, G.V., : Koski Shs Bulk Visous Cosologil Mol i Slr Tesor Theory of Grviio, Asrophys Spe Si. 5: 66. Reddy, D.R.K., Shi Kur, R., : To Fluid Serio for Drk Eergy Mol i Slr- Tesor Theory of Grviio, I. J. Theor. Phys. 5:6. Riess, A.G., e l., 998: Observiol Evie fro Superove for Aelerig Uiverse d Cosologil Cos, Asro. J., 6: 9. Sez, D., Blleser, V.J.: A Siple Couplig ih Cosologil Ipliios, Phys. Le. A.,, Sh, B., Airhshhi, H., Prdh A., : To-Fluid Serio for Drk Eergy Mols i FRW Uiverse-Revisied, Asrophys. Spe Si. : 57. Tegrk, M., e l. : Cosologil Preers Fro SDSS d WMAP, Phys. Rev.D., 69, 5. Ydv, A.K., : Soe Aisoropi Drk Eergy Mols i Bihi Type-V Spe-Tie, Asrophys. Spe Si. 5:565. Ydv, A.K., e l., : Drk Eergy Mols ih Vrible Equio of Se Preer, I. J. Theor. Phys. 5:87. Ydv, A.K., Ydv, L., : Bihi Type-III Aisoropi Drk Eergy Mols ih Cos Deelerio Preer, I. J. Theor. Phys. 5:8. ISSN: 5-8 Prespeie Jourl Published by QuuDre, I..prespeie.o

Coefficient Inequalities for Certain Subclasses. of Analytic Functions

Coefficient Inequalities for Certain Subclasses. of Analytic Functions I. Jourl o Mh. Alysis, Vol., 00, o. 6, 77-78 Coeiie Iequliies or Ceri Sulsses o Alyi Fuios T. Rm Reddy d * R.. Shrm Deprme o Mhemis, Kkiy Uiversiy Wrgl 506009, Adhr Prdesh, Idi reddyr@yhoo.om, *rshrm_005@yhoo.o.i