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Lectures on the Theory of Cosmological Perturbations

  • Part I The Very Early Universe and High Precision Cosmology
  • Chapter
  • First Online:
The Early Universe and Observational Cosmology

Part of the book series: Lecture Notes in Physics ((LNP,volume 646))

Abstract

The theory of cosmological perturbations has become a cornerstone of modern quantitative cosmology since it is the framework which provides the link between the models of the very early Universe such as the inflationary Universe scenario (which yield causal mechanisms for the generation of fluctuations) and the wealth of recent high-precision data on the spectrum of density fluctuations and cosmic microwave anisotropies. In these lectures, I provide an overview of the classical and quantum theory of cosmological fluctuations.

Crucial points in both the current inflationary paradigm [1,2] of the early Universe and in proposed alternatives such as the Pre-Big-Bang [3] and Ekpyrotic [4] scenarios are that, first, the perturbations are generated on microscopic scales as quantum vacuum fluctuations, and, second, that via an accelerated expansion of the background geometry (or by a contraction of the background), the wavelengths of the fluctuations become much larger than the Hubble radius for a long period of cosmic evolution. Hence, both Quantum Mechanics and General Relativity are required in order to understand the generation and evolution of fluctuations.

As a guide to develop the physical intuition for the evolution of inhomogeneities, I begin with a discussion of the Newtonian theory of fluctuations. applicable at late times and on scales smaller than the Hubble radius. The analysis of super-Hubble fluctuations requires a general relativistic analysis. I first review the classical relativistic theory of fluctuations, and then discuss their quantization. I conclude with a brief overview of two applications of the theory of cosmological fluctuations: the trans-Planckian “problem” of inflationary cosmology and the current status of the study of the back-reaction of cosmological fluctuations on the background space-time geometry. Most of this article is based on the review [5] to which the reader is referred to for the details omitted in these lecture notes.

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  1. Brown University Physics Department, Providence, RI 02912, USA.

    Robert H. Brandenberger

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Nora Bretón Jorge Luis Cervantes-Cota Marcelo Salgado

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Brandenberger, R.H. Lectures on the Theory of Cosmological Perturbations. In: Bretón, N., Cervantes-Cota, J.L., Salgado, M. (eds) The Early Universe and Observational Cosmology. Lecture Notes in Physics, vol 646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40918-2_5

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