Physical Foundations of Cosmology

20 Kinematics and dynamics of an expanding universe a homogeneous, isotropic universe. In relativistic theory, there is no absol ...

1.3 From Newtonian to relativistic cosmology 21 is incorporated in Einstein’s equations through the energy–momentum tensor,Tβα. ...

22 Kinematics and dynamics of an expanding universe Problem 1.12Show that the equations of motion for the scalar field, φ;α;α+ ∂ ...

1.3 From Newtonian to relativistic cosmology 23 If the pressurepwithin an expanding sphere of volumeVis significant, then the to ...

24 Kinematics and dynamics of an expanding universe ε(t).The solutions, and hence the future of the universe, depend not only on ...

1.3 From Newtonian to relativistic cosmology 25 This last equation, which corresponds to the trace of the Einstein equations, is ...

26 Kinematics and dynamics of an expanding universe with the Newtonian estimate obtained by ignoring gravity. (HintUse (1.70) to ...

1.3 From Newtonian to relativistic cosmology 27 Problem 1.17Verify that, for a nonflat universe with a mixture of matter and rad ...

28 Kinematics and dynamics of an expanding universe τ r t= const χ= const t= 0, χ = ∞ Fig. 1.7. and hence the Minkowski metric r ...

1.3 From Newtonian to relativistic cosmology 29 time-like world-line. Special Relativity says that the speed measured using rule ...

30 Kinematics and dynamics of an expanding universe (ten parameters in the four-dimensional case). In this book, we pay special ...

1.3 From Newtonian to relativistic cosmology 31 χ= const t= const Fig. 1.8. These coordinates cover the entire hyperboloid for+∞ ...

32 Kinematics and dynamics of an expanding universe t∼= const χ∼= const Fig. 1.9. where+∞> ̄t>−∞and+∞>χ> ̄ −∞.Expres ...

1.3 From Newtonian to relativistic cosmology 33 χ = const t– = const Fig. 1.10. it is recast as ds^2 =−dl^23 d=−dτ^2 −H−^2 ...

34 Kinematics and dynamics of an expanding universe and hence the energy density stays constant during expansion. Substitutingε ...

1.3 From Newtonian to relativistic cosmology 35 k= 1 k= 0 k= − 1 t a(t) Fig. 1.11. then reaches its minimum value, and subsequen ...

36 Kinematics and dynamics of an expanding universe whereHis defined in (1.103). Analyze and discuss the behavior of this solut ...

2 Propagation of light and horizons We obtain most of the information about the universe from light. Over the last century, the ...

38 Propagation of light and horizons In General Relativity, the same must be true in every local inertial coordinate frame. Then ...

2.2 Horizons 39 whereηi(orti) corresponds to the beginning of the universe. At timeη,the infor- mation about events atχ>χp(η) ...