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Springer Handbook of Spacetime pp 673–696Cite as

Exact Approach to Inflationary Universe Models

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Abstract

In this chapter we introduce a study of inflationary universe models that are characterized by a single scalar inflation field . The study of these models is based on two dynamical equations: one corresponding to the Klein–Gordon equation for the inflaton field and the other to a generalized Friedmann equation. After describing the kinematics and dynamics of the models under the Hamilton–Jacobi scheme, we determine in some detail scalar density perturbations and relic gravitational waves. We also introduce the study of inflation under the hierarchy of the slow-roll parameters together with the flow equations. We apply this approach to the modified Friedmann equation that we call the Friedmann–Chern–Simons equation, characterized by F ( H ) = H 2 - α H 4 , and the brane-world inflationary models expressed by the modified Friedmann equation.

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Abbreviations

AdS:

anti-de Sitter

H–J:

Hamilton–Jacobi

WMAP:

Wilkinson microwave anisotropy probe

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  1. Pontificia Universidad Catolica de Valparaiso, Av. Universidad 330, Curauma, Valparaíso, Chile

    Sergio del Campo

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    Abhay Ashtekar

  2. Institute for Foundational Studies Hermann Minkowski, Montreal, Quebec, Canada

    Vesselin Petkov

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del Campo, S. (2014). Exact Approach to Inflationary Universe Models. In: Ashtekar, A., Petkov, V. (eds) Springer Handbook of Spacetime. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41992-8_31

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