MODERN COSMOLOGY

Dynamics of structure formation 47 solution to a potential of unexplained form may seem a retrograde step. However, it is at lea ...

48 An introduction to the physics of cosmology Now, for sufficiently small perturbations, terms containing a product of perturba ...

Dynamics of structure formation 49 linearized equations for conservation of momentum and matter as experienced by fundamental ob ...

50 An introduction to the physics of cosmology be specified in terms of the sound speed c^2 s≡ ∂p ∂ρ Now think of a plane-wave d ...

Dynamics of structure formation 51 For total radiation domination,p =ρc^2 /3, and it is easy to linearize these equations as bef ...

52 An introduction to the physics of cosmology Since∂(a ̇^2 )/∂K=1, this gives the growing and decaying modes as δ∝ { (a ̇/a) ∫a ...

Dynamics of structure formation 53 growth increases smoothly to the Einstein–de Sitterδ∝abehaviour (M ́esz ́aros 1974). The over ...

54 An introduction to the physics of cosmology equation:ρ ̇=−∇·(ρv)in proper units, which obviously takes the same form ρ ̇=−∇·( ...

Dynamics of structure formation 55 (1) Radiation effects. Prior to matter–radiation equality, we have already seen that perturba ...

56 An introduction to the physics of cosmology Figure 2.8.A plot of transfer functions for various models. For adiabatic models, ...

Dynamics of structure formation 57 These expressions assume pure dark matter, which is unrealistic. At least for CDM models, a n ...

58 An introduction to the physics of cosmology This all agrees with what we knew already: at early times the sphere expands with ...

Quantifying large-scale structure 59 properties ofδshould also be homogeneous, even though it is a field that describes inhomoge ...

60 An introduction to the physics of cosmology Alternatively, this sum can be obtained without replacing〈δδ〉by〈δδ∗〉, from the re ...

Quantifying large-scale structure 61 A power-law spectrum implies a power-law correlation function. Ifξ(r)= (r/r 0 )−γ, withγ=n+ ...

62 An introduction to the physics of cosmology Figure 2.9.This figure illustrates how the primordial power spectrum is modified ...

Quantifying large-scale structure 63 2.7.3 Karhunen–Loeve and all that` A key question for these statistical measures is how acc ...

64 An introduction to the physics of cosmology coefficients viaδk=( 1 /N) ∑ iexp(−ik·xi). From this, the expectation power is 〈| ...

Quantifying large-scale structure 65 Suppose we seek to expand the datavector in terms of a set of new orthonormal vectors: d= ∑ ...

66 An introduction to the physics of cosmology are identical, but the idea of choosing an optimal eigenbasis is more general tha ...