BIANCHI TYPE I DUST FILLED UNIVERSE WITH DECAYING VACUUM ENERGY ( ) IN C-FIELD COSMOLOGY

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1 IJRRS 3 (3) December 0 INHI TYPE I DUST FILLED UNIVERSE WITH DEYING VUUM ENERGY () IN -FIELD OSMOLOGY Ra ali & Seema Saraf Deparmen of Mahemaics, Universiy of Raashan, Jaipur balir5@yahoo.co.in Deparmen of Mahemaics, Universiy of Raashan, Jaipur-3000 STRT ianchi Type I dus filled universe (p = 0) wih ime dependen vacuum energy densiy () in he presence of creaion field (-field) is invesigaed. ianchi Type I meric is aken as,, are funcions of -alone. To ge he deerminisic soluion, ds we assume ha 3 dx dy where dz is he eigen value of The condiion (shear ensor) and is he expansion in he model, i leads o = () n. To ge he soluion in erms of cosmic ime, we have assumed n =. The soluion so obained saisfies conservaion equaion 8G T g 0 where i i T v v and T f( g are he energy momenum ensors for maer and -field. (m) i i (c) i i i We find ha -field increases wih ime which agrees wih -field cosmology. The deceleraion parameer (q) > 0, however, if we assume = = hen q < 0. Thus he universe have deceleraing and acceleraing phase. The cosmological consan () decays wih ime which agrees wih he presen day observaions. The oher physical aspecs of he model relaed wih asronomical observaions are also discussed. Key words: ianchi I, Dus, Universe, Decaying vacuum energy, -field.. INTRODUTION ll he invesigaions dealing wih physical process use a model of he universe, usually called a ig bang model. The ig bang models have he following problems: (i) (ii) (iii) (iv) (v) he model has singulariy in he pas and one in fuure. he conservaion of energy is violaed. i leads o a very small paricle horizon in he early epoch of he universe. No consisen scenario exiss wihin he frame work of ig bang model ha explain he origin and evoluion of he universe. i has flaness problem. If a model explains successfully he creaion of posiive energy maer wihou violaing he conservaion of energy, hen i becomes necessary o have some degrees of freedom which acs as a negaive energy mode. Thus negaive energy provides a naural way for creaion of maer. y inroducing a massless and chargeless scalar field, Hoyle and Narlikar [0] adoped a field heoreic approach for creaion of maer. There is no ig bang ype singulariy in -field (reaion field heory). Narlikar and Padmanabhan [3] have invesigaed he soluion of Einsein s field equaions which admi radiaion (= 3p) and negaive-energy massless scalar creaion field as a source where is energy densiy and p he isoropic pressure. They have shown ha he cosmological model based on his soluion saisfies all he observaional ess and hus is a viable alernaive o he ig bang model. ali and Tikekar [6] have invesigaed -field cosmological model for dus disribuion (p = 0) in fla FRW (Friedmann-Roberson-Walker) 800

2 IJRRS 3 (3) December 0 ali & Saraf ianchi Type I Dus Filled Universe model wih variable graviaional consan. ali and Kumawa [7] have invesigaed -field cosmological models for dus disribuion using FRW space-ime for posiive and negaive curvaure wih variable graviaional consan. The non-rivial role of vacuum generaes a cosmological consan () erm in Einsein s field equaions which leads o he inflaionary scenario (bers and Lee []) which prediced ha during an early exponenial phase, he vacuum energy is reaed as large cosmological consan which is expeced by Glashow-Salam-Weinberg and by Grand Unified Theory as menioned by Langacker []. Therefore, he presen day observaions of smallness of cosmological consan 0 56 cm suppor o assume ha cosmological consan is ime dependen. Gibbons and Hawking [9] invesigaed ha cosmological models wih posiive cosmological consan leads o de- Sier space-ime asympoically. Therefore, he cosmological models linking he variaion of cosmological consan having he form of Einsein s field equaions unchanged and preserving he energy-momenum ensor of maer conen, have been sudied by several auhors viz. erman [8], bdussaar and Vishwakarma [], Singh and haubey [6], Pradhan e al. [], ali and Jain [3], ali and Singh [], ali and Tinker [5], Ram and Verma [5]. Moivaed by aforesaid invesigaions, we have invesigaed ianchi Type I dus filled universe wih decaying vacuum energy () in -field cosmology. We find ha reaion field increases wih ime. The universe have deceleraing hen acceleraing phase. The cosmological consan () decays wih ime which agrees wih presen day observaions. The oher physical aspecs of he model relaed wih asronomical observaions are also discussed.. THE METRI ND FIELD EQUTION We consider he ianchi Type I meric given by ds dx dy dz () where,, are funcions of alone and g. Einsein s field equaion by inroducion of -field is modified by Hoyle and Narlikar [] as R Rg 8G [ T T g () i i (m) i (c) i i The energy momenum ensor T for perfec fluid and T (m) i (c) i for creaion field are given by T p v v p g (3) (m) i i i T (c) i f ( i g i where f > 0 is he coupling consan beween maer and creaion field and he meric () lead o 8 G - p f 8 G - p f 8 G - p f 8G f d i i dx (). The field equaion () for (5) (6) (7) (8) 80

3 IJRRS 3 (3) December 0 ali & Saraf ianchi Type I Dus Filled Universe 3. SOLUTION OF FIELD EQUTIONS The conservaion equaion 8G T g 0 i i leads o f f Gf d (0) p being isoropic pressure. Following Hoyle and Narlikar [], we have aken p = 0. The source equaion of -field large r. Thus. n i i f (9) ; leads o = for Using p 0,, equaion (5), (6), (7) and (8) lead o Gf Gf Gf 8G Gf Using equaions () and (3), we have Equaion (5) leads o L where L is consan of inegraion. Equaions () and (3) lead o which leads o M where M is consan of inegraion. To ge he deerminisic value of and, we assume = and / = Using =, equaions (6) and (8) lead o () () (3) () (5) (6)...(7) (8) (9) (0) 80

4 IJRRS 3 (3) December 0 ali & Saraf ianchi Type I Dus Filled Universe d N where N = M L and = which leads o N where is consan of inegraion. Equaions (9) and (0) lead o L Thus equaions () and (3) lead o () () (3) L/N N () where is consan of inegraion. Equaions (9), (0), () and () lead o and (N ) / (5) L/N/) N (6) L/N) N (7) Equaion () leads o k (8) Gf where k. Thus equaion (8) leads o N k (9) where N 5 L and 0 8 N Equaions (), (5), (6), (7) and (9) lead o N 8G (N f (30) Thus he meric (), afer using (5), (6) and (7) leads o ds L/N/) L/N) N dx NT dy NT dz (3) Using equaions (5), (6), (7), (9) and (30) ino Equaion (0), we have d N N (3) (N From equaion (3), we have (N 803

5 IJRRS 3 (3) December 0 ali & Saraf ianchi Type I Dus Filled Universe Thus we have as consan of inegraion, we find Taking creaion field is proporional o ime. (33) (3), which agrees wih he value used in he source equaion. Thus. PHYSIL ND GEOMETRIL SPETS The homogeneous mass densiy (), he creaion field (), cosmological consan () and spaial volume (R 3 ), he deceleraion parameer (q) for he model (3) are given by N 8G N f (35) = N (36) R 3 N q N an h where > 0, > 0. The co-ordinae disance o he horizon ) H saring from infinie pas i.e. ) R () ( H 3 (37) (38) is he maximum disance a null ray could have raveled a ime where R 3 is a scale facor. We could exend he proper ime o in he pas because of non-singular naure of space-ime. Thus H ) 0 3 R ) 0 log(n N (N 0 The inegral a lower limi is infinie which shows ha he model is free from paricle horizon. 5. ONLUSION ND DISUSSION If we assume = = in meric () hen he resuls also saisfies conservaion equaion. The deceleraion parameer q < 0 shows ha he universe is acceleraing. The creaion field () increases wih ime which suppors he resul obained by Hoyle and Narlikar []. The energy densiy > 0. which agrees wih laes asronomical observaions. The spaial volume (R 3 ) increases wih ime and deceleraion parameer (q) < 0 shows ha he model represens acceleraing universe. Thus ianchi Type I dus filled universe in creaion field cosmology saisfies asronomical ess. 80

6 IJRRS 3 (3) December 0 ali & Saraf ianchi Type I Dus Filled Universe 6. REFERENES [] bdussaar and R.G. Vishwakarma, model of he universe wih decaying vacuum energy, Pramana J. Phys. Vol.7, pp.-55 (996). [] E. bers and.w. Lee, Gauge Theories, Phys. Repors, Vol.9, pp.- (973). [3] R. ali, and S. Jain, ianchi Type V magneized sring dus cosmological models in General Relaiviy, In. J. Mod. Phys. D, Vol.6, pp.-0 (007). [] R. ali and J.P. Singh, ulk viscous ianchi Type I cosmological model wih ime dependen cosmological erm, In. J. Theor. Phys., Vol.7, pp (008). [5] R. ali and S. Tinker, ianchi Type V bulk viscous baroropic fluid cosmological model wih variable G and, hin. Phys. Le. Vol.5, pp (008). [6] R. ali and R. Tikekar, -field cosmology wih variable G in fla FRW model, hinese Phys. Le. Vol., pp.7-7 (007). [7] R. ali and M. Kumawa, -field cosmological model wih variable G in FRW space-ime, In. J. Theor. Phys., Vol.8, pp (009). [8] M.S. erman, osmological model wih variable cosmological erm, Gen. Relaiv. Grav. Vol.3, pp (99). [9] G. Gibbons and S.W. Hawking, Non-saionary de-sier cosmological models, Phys. Rev. D, Vol.5, pp (977). [0] F. Hoyle, and J.V. Narlikar, Mach s principle and he creaion of maer, Proc. Roy. Soc. Vol.73, pp.- (963). [] F. Hoyle, and J.V. Narlikar, On he avoidance of singulariies in -field osmology, Proc. Roy. Soc., Vol.78, pp (96) [] P. Langacker, Grand unified Theories and Proon Decays, Phys. Repors, Vol.7, pp (98). [3] J.V. Narlikar and T. Padmanabhan, reaion field cosmology : possible soluion o singulariy, horizon and flaness problems, Phys. Rev. D, Vol.3, pp (985). []. Pradhan, P. Pandey and K. Joania, Some cosmological models wih variable, omm. Theor. Phys. Vol.50, pp (008). [5] S. Ram and M.K. Verma, ulk viscous fluid hyper surface homogeneous cosmological models wih ime varying G and, srophys. and Space-Science, Vol.330, pp.5-56 (00). [6] T. Singh and R. haubey, osmic no-hair conecure in scalar ensor heories, Pramana J. Phys., Vol.67, pp.5-8 (006). 805