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چكيده انگليسي :

The Effect of Entropic Force and Running Gravitational Coupling on the Cosmological Singularities Maryam Aghaei Abchouyeh m aghaei@ph iut ac ir Date of submission 2012 02 19 Department of Physics Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language PersianSupervisor Prof Dr Behrouz Mirza b mirza@cc iut ac irAbstractSpecial and general relativity are introduced at the beginning of this thesis Then the future singular ities of the universe are studied For that propose first it has been shown that Friedmann equationsare derived from solving Einstein equations for the homogenous and isotropic universe which is de scribed by FRW metric Pressure energy density scale factor and Hubble parameter are importantquantities for studying the universe Possibilities of the future singularities are investigated by solvingthe Friedmann equations assuming an accelerating expanding the universe the result will be changedif we consider some new physical effects in this senario The effects of conformal anomalies and bulkviscosity have already been studied in several papers It was shown that the bulk viscosity changesthe time of singularity but conformal anomaly can change the type II singularity to the type III singularity Here we explore the effect of the Entropic force on the singularities Because of the En tropic force two correction terms are added to the Friedmann equations that are the results of surfaceterm in the Einstein Hilbert action These terms are proportional to the Hubble parameter and it sfirst derivative with respect to the time They affect the singularity type II because they change thebehavior of pressure or energy density For some values of the parameters in this theory pressure willbe finite at the singularity time So both the pressure and energy density are finite at the singularitypoint and the singularity type II changes to the type IV For some other values the energy densitywill be infinite at the singularity time so both pressure and energy density are infinite and the suddenfuture singularity type II changes to type III singularity We also consider a running gravitationalcoupling and it s effects on the future singularities of the universe Because of asymptotic safety it snecessary for gravitational coupling to run with an energy scale Here the gravitational coupling G is studied as a function of energy density of the universe Our results show that running gravitationalcoupling changes the type II singularity to a new kind of singularity which is similar to type IV Also the time evolution of the universe will be changed in other cases Then we consider the effectof both Entropic force and running gravitational coupling on the future singularities It is shown thatthe behavior of the pressure and energy density does not change in the type I singularity The singu larity type II changes to a new kind of singularity which is similar to type III If we introduce theeffective Hubble parameter we find that singularity type II clearly changes to type III and type I that is a strong singularity in both Tipler and Krolak definition will changes to the singularity type III which is a strong singularity in Tipler definition but a weak singularity in Krolak definition Keywords Cosmology Singularity Entropic Force Running Gravitational Coupling

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