Anisotropic Cosmological Model with a Generalized Chaplygin Gas

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*Under weak field assumption: we can approximate Finslerianmetric as a perturbation of the FRW metric since in generalrelativity a weak vector field in a space (e.g a magnetic field)can be treated as a first order perturbation of the Riemannmetric tensor.We consider a convenient Finsler metric to approximate thegravitational theories. This metric is reffered as osculatingRiemannian metric( x)gˆ( x,Y )rµ!=µ!connected to the Riemanian one <strong>with</strong> the followingosculating affine connection A ! "µ(x)
*The equation of the geodesics is given by :d2dsx2µ+Aµ"!( x)Y"Y!=0*Under the assumption that the vector fieldsatifies the relationthe Finslerian!!Y; "= 0Y-covariant derivative and the Cartan covariant derivativeof an arbitrary vector field!B ! ( x,Y ( x)B!( x,Y ( x))= B!( x,Y ( ))are equal.;" x#"C000µ ==2CU20000,0
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: In the framework of Finsler geometr
Page 13 and 14: •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 66 and 67:
)]44)(2(ˆˆˆ)4()ˆ[2(4]ˆ31)(219[
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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