Stochastic Properties of Cosmological Perturbations
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The attentive reader must have noticed that, in fact, we have given no actual initial conditions on cosmological perturbations in Chap. 6. What we have done is to give the form of the primordial modes and show how, in the 5 different cases that we investigated, all scalar perturbations are sourced by a single scalar potential. For example, in the adiabatic case we showed in Eq. 6.77 how \(\Phi (\mathbf k)\) is related to \(C_\gamma (\mathbf k)\), which we proved to be equal to \(\zeta (\mathbf k)\) and \(\mathcal R(\mathbf k)\).
- Lyth, D.H., Liddle, A.R.: The Primordial Density Perturbation: Cosmology, Inflation and the Origin of Structure (2009)Google Scholar