Physical Foundations of Cosmology

260 Inflation I: homogeneous limit escapes from the maximum not via tunneling, but due to the quantum fluctuations. It then slow ...

5.6 “Menu” of scenarios 261 of the initial conditions problem. We would like to point out, however, that the initial conditions ...

262 Inflation I: homogeneous limit Fig. 5.8. de Sitter space and the lower border for the flat, open or closed Friedmann univers ...

Part II Inhomogeneous universe ...

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6 Gravitational instability in Newtonian theory Measurements of the cosmic microwave background tell us that the universe was ve ...

266 Gravitational instability in Newtonian theory smooth unclustered energy component, like radiation or vacuum energy, influenc ...

6.2 Jeans theory 267 Newton’s force law M·g=Fgr+Fpr (6.7) becomes the Euler equations ∂V ∂t +(V·∇)V+ ∇p ε +∇φ= 0. (6.8) Conserv ...

268 Gravitational instability in Newtonian theory Slightly disturbing the matter distribution, we have: ε(x,t)=ε 0 +δε(x,t), V(x ...

6.2 Jeans theory 269 6.2.1 Adiabatic perturbations First we will assume that entropy perturbations are absent, that is,δS= 0 .Th ...

270 Gravitational instability in Newtonian theory The Jeans lengthλJ∼cstgris the “sound communication” scale over which the pres ...

6.3 Instability in an expanding universe 271 the pressure due to the energy density inhomogeneities is exactly compensated by th ...

272 Gravitational instability in Newtonian theory The Hubble velocityV 0 depends explicitly onxand therefore the Fourier transfo ...

6.3 Instability in an expanding universe 273 6.3.1 Adiabatic perturbations Taking the Fourier transform of (6.46) with respect t ...

274 Gravitational instability in Newtonian theory time-translational-invariant. For smallτ, the time-shifted solutionε 0 (t+τ)ca ...

6.3 Instability in an expanding universe 275 Problem 6.4If we use the redshiftzas a time parameter, then the integral in (6.55) ...

276 Gravitational instability in Newtonian theory In this particular case the perturbation preserves its initial spatial shape a ...

6.3 Instability in an expanding universe 277 We have skipped in (6.64) the term proportional toc^2 sbecause it is determined by ...

278 Gravitational instability in Newtonian theory Problem 6.6Verify that ifw=−1orw=− 1 /3, thenδ∝H is the solution of (6.46) in ...

6.4 Beyond linear approximation 279 to the dark matter. They are tightly coupled to radiation before recombination and perturbat ...