By Viatcheslav Mukhanov
ISBN-10: 051113679X
ISBN-13: 9780511136795
ISBN-10: 0521563984
ISBN-13: 9780521563987
Inflationary cosmology has been constructed over the past two decades to treatment severe shortcomings within the common sizzling massive bang version of the universe. Taking an unique procedure, this textbook explains the foundation of contemporary cosmology and exhibits the place the theoretical effects come from. The ebook is split into components; the 1st offers with the homogeneous and isotropic version of the Universe, the second one half discusses how inhomogeneities can clarify its constitution. confirmed fabric akin to the inflation and quantum cosmological perturbation are awarded in nice aspect.
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Example text
49) is the Ricci tensor expressed in terms of the inverse metric g αγ , defined via g αγ gγβ = δβα , and the Christoffel symbols α γβ = ∂gγβ 1 αδ ∂gγ δ ∂gδβ + − g β γ 2 ∂x ∂x ∂xδ . 50) The symbol δβα denotes the unit tensor, equal to 1 when α = β and 0 otherwise; R = Rαα is the scalar curvature; and = const is the cosmological term. 3 From Newtonian to relativistic cosmology 21 is incorporated in Einstein’s equations through the energy–momentum tensor, Tβα . 52) must coincide with the equations of motion for matter in Minkowski spacetime.
In flat space, however, the normalization of |a 2 | does not have any physical meaning and this factor can be absorbed by redefinition of the coordinates. The generalization of the above consideration to three dimensions is straightforward. Fig. 5. 34) where a 2 is positive and k = 0, ±1. 36) where x¯ = r¯ sin θ cos ϕ, y¯ = r¯ sin θ sin ϕ, z¯ = r¯ cos θ. In many applications, instead of the radial coordinate r , it is convenient to use coordinate χ defined via the relation dχ 2 = It follows that dr 2 .
55) where the equation of state p = p(ε) depends on the properties of matter and must be specified. For example, if the universe is composed of ultra-relativistic gas, the equation of state is p = ε/3. In many cosmologically interesting cases p = wε, where w is constant. 11 Consider a nonrelativistic, dust-like perfect fluid (u 0 ≈ 1, u i p ε) in a flat spacetime. Verify that the equations T αβ ,β = 0 are equivalent to the mass conservation law plus the Euler equations of motion. Another important example of matter is a classical scalar field ϕ with potential V (ϕ).
Physical Foundations of Cosmology by Viatcheslav Mukhanov
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