Physical Foundations of Cosmology

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Part I Homogeneous isotropic universe ...

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1Kinematicsanddynamicsofanexpandinguniverse The most importantfeature of our universe is its large scale homogeneity and isotrop ...

4 Kinematics and dynamics of an expanding universe scales greatly exceeding the observable universe. The subject is too seductiv ...

1.1 Hubble law 5 what happens. After we have reached the limits of validity of Newtonian theory, we turn to a proper relativisti ...

6 Kinematics and dynamics of an expanding universe AB θAB a(t) rAB Fig. 1.2. Problem 1.1In order for a general expansion law,v=f ...

1.1 Hubble law 7 is called the scale factor and is the analogue of the radius of the 2-sphere. The integration constant,χBA, is ...

8 Kinematics and dynamics of an expanding universe possess a set of characteristics that can be used to identify them even when ...

1.2 Dynamics of dust in Newtonian cosmology 9 to its energy densityε. (In cosmology the terms “dust” and “matter” are used inter ...

10 Kinematics and dynamics of an expanding universe sphere. The equation of motion, therefore, is mR ̈=− GmM R^2 =− 4 π 3 Gm M ( ...

1.2 Dynamics of dust in Newtonian cosmology 11 sign ofE. As pointed out above, the normalization ofahas no invariant meaning in ...

12 Kinematics and dynamics of an expanding universe Fig. 1.3. special case of =1, orE=0, corresponds to parabolic expansion and ...

1.3 From Newtonian to relativistic cosmology 13 The sign ofqdetermines whether the expansion is slowing down or speeding up. Fin ...

14 Kinematics and dynamics of an expanding universe velocities and having arbitrary pressure. We know that radiation, which has ...

1.3 From Newtonian to relativistic cosmology 15 x y z a r′ φ Fig. 1.4. Substituting this expression into the three-dimensional E ...

16 Kinematics and dynamics of an expanding universe the metric in (1.30) becomes dl^2 = dr′^2 1 −(r′^2 /a^2 ) +r′^2 dφ^2. (1.32) ...

1.3 From Newtonian to relativistic cosmology 17 Problem 1.9By embedding a three-dimensional sphere (pseudo-sphere) in a four-dim ...

18 Kinematics and dynamics of an expanding universe Three-dimensional sphere(k=+1) It follows from (1.39) that in a three- dimen ...

1.3 From Newtonian to relativistic cosmology 19 In fact, since the physical width of an infinitesimal shell isdl=adχ, the volume ...