# Applications of Cosmological Perturbation Theory

@article{Christopherson2011ApplicationsOC, title={Applications of Cosmological Perturbation Theory}, author={Adam J. Christopherson}, journal={arXiv: Cosmology and Nongalactic Astrophysics}, year={2011} }

Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, specifically, to the early universe. Starting with some background material introducing the well-tested 'standard model' of cosmology, we move on to…

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## 13 Citations

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## References

SHOWING 1-10 OF 165 REFERENCES

Covariant generalization of cosmological perturbation theory

- Physics
- 2007

We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we…

Relativistic second-order perturbations of the Einstein-de Sitter Universe

- Physics
- 1998

We consider the evolution of relativistic perturbations in the Einstein-de Sitter cosmological model, including second-order effects. The perturbations are considered in two different settings: the…

Second-order perturbations of the Friedmann world model

- Physics
- 2004

We consider the instability of the Friedmann world model to second order in perturbations. We present the perturbed set of equations up to second order in the Friedmann background world model with a…

Cosmological magnetic fields from nonlinear effects

- Physics
- 2007

In the standard cosmological model, magnetic fields and vorticity are generated during the radiation era via second-order density perturbations. In order to clarify the complicated physics of this…

Perturbations of spacetime : gauge transformations and gauge invariance at second order and beyond

- Physics
- 1997

We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second- and higher-order perturbations. We…

Cosmological matching conditions for gravitational waves at second order

- Physics
- 2009

We compute the second-order matching conditions for tensor metric perturbations at an abrupt change in the equation of state. For adiabatic perturbations on large scales the matching hypersurface…

Can cosmological perturbations produce early universe vorticity

- Physics
- 2010

In this special issue paper, based on the talk with the same title as in session B5 (Theoretical and Mathematical Cosmology) at GR19, we review the case of vorticity generation in cosmology using…

Perturbations in generalized multi-field inflation

- Physics
- 2008

We study the linear perturbations of multi-field inflationary models governed by a Lagrangian which is a general function of the scalar fields and of a global kinetic term combining their spacetime…