16,234 research outputs found

    Cosmological perturbations

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    We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology. We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear and curvature of constant-time hypersurfaces and the orthogonal timelike vector field. We give the gauge transformation rules for metric and matter variables at first and second order. We show how gauge invariant variables are constructed by identifying geometric or matter variables in physically-defined coordinate systems, and give the relations between many commonly used gauge-invariant variables. In particular we show how the Einstein equations or energy-momentum conservation can be used to obtain simple evolution equations at linear order, and discuss extensions to non-linear order. We present evolution equations for systems with multiple interacting fluids and scalar fields, identifying adiabatic and entropy perturbations. As an application we consider the origin of primordial curvature and isocurvature perturbations from field perturbations during inflation in the very early universe.Comment: 96 pages, submitted to Phys. Rep; v2: minor changes, typos corrected, references added, 1 figure added, corresponds to published versio

    Numerical calculation of second order perturbations

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    We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source term and argue that our method is extendable to the full equation. We consider two standard single field models and find that the results agree with previous calculations using analytic methods, where comparison is possible. Our procedure allows the evolution of second order perturbations in general and the calculation of the non-linearity parameter f_NL to be examined in cases where there is no analytical solution available.Comment: 18 pages, 12 figures; v2 version published by JCA
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