Anisotropic Cosmological Model with a Generalized Chaplygin Gas

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)]44)(2(ˆˆˆ)4()ˆ[2(4]ˆ31)(219[)(18222aaaKaaffRRfRfaaRffRffaaPfGPmeff!!!!!!!!!!++!"!!!"!!"!!"!""!!+!"!"=#µ#$)])(43(1)(47)(1)(1)6[(ˆ22aaaaaKaaR!!!!!µ!! "++"+"=B µt! +=
<strong>Generalized</strong> Raychaudhury equation:From fluid motion a congruence (collection) of particles having timelike 4-velocityY aas they fall under their own gravity. it could suffer thefollowing effects:•(a)Expansion/Contraction of volume which is givenby the divergence OfY athat is"! ˆ # #= Y # $ C "# Y !2; = 3 H +Hµ
Page 1 and 2:
Anisotropic Cosmological Modelwith
Page 3 and 4:
Mathematical FormalismA Generalized
Page 5 and 6:
an electromagnetic field or a gauge
Page 7 and 8:
The induced Finslerian metric tenso
Page 9 and 10:
In the framework of Finsler geometr
Page 11 and 12:
*The equation of the geodesics is g
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•A Finsler space is a Riemanian s
Page 15 and 16: Field equations in both formalisms
Page 17 and 18: Conclusion N°1With the same fluid
Page 19 and 20: Conclusion N°2With the same fluid
Page 21 and 22: Exact solutionsH ( t)3= " µ H43! =
Page 23 and 24: w = 0!""chapchapmmAPwP= #=If2000000
Page 25 and 26: 0,0220,020mu/H 0=-0.01a(t)0,0180,01
Page 27 and 28: q-120mu/H 0=-0.01-140-160-180-200-2
Page 29 and 30: 0,0002mu/H 0=0.010,0000-0,0002-0,00
Page 31 and 32: If$Ptottot= $= P+ !(t)" !(t)1!(t)=
Page 33 and 34: !!!!!!!!µµ+""++#+"+=$12010)(11201
Page 35 and 36: If"m* 01A)3(&'34µH2(1 + )0H0%#$1+!
Page 37 and 38: alpha=0.41,000,950,900,850,800,750,
Page 39 and 40: !!!!"#$$$$%&++=+= '= ''= 'µµµ(((
Page 41 and 42: Conservation of momentum-energystre
Page 43 and 44: 1,20mu/H 0=-0.021,151,10density rho
Page 45 and 46: Model3Friedman like equats.8 !G = 1
Page 47 and 48: Near the critical point one can wri
Page 49 and 50: 0))ln(31exp(66)(1)(0)())ln(31)exp((
Page 51 and 52: From Numerical solutions of dynamic
Page 53 and 54: 0mu/H 0=-0.01-20ln(abs(Pchap )-40-6
Page 55 and 56: ))3(1(21411))(3(2)3(1))3(1(6143)(3)
Page 57 and 58: µ!!µ!µ!!µ!µ!!!µ!!µµ!3)52152
Page 60 and 61: )(4 113532122123321311241!!!!!!!bbb
Page 62 and 63: Eigenvalues:""12==! TrM! TrM22+ ( t
Page 64 and 65: A general fourth order theory of gr
Page 68 and 69: •(b) Shear, distortion in shape w
Page 70 and 71: )]4347()26[()](3)(3)(9))()([2()(1ˆ
Page 72 and 73: *The shear tensor measures any tend
Page 74 and 75: Conclusions:The goal is:• Undrsta
Page 76: Thank You
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Anisotropic Cosmological Model with a Generalized Chaplygin Gas

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