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Cosmology for Particle Physicists.pdf

November 8, 2009 · Filed Under Physics  · Tags: , , , ,

Taken from Introduction: Over the past two decades Cosmology has increasingly become a precision science. That the Universe is expanding was an astonishing discovery. Now we know its details to unprecedented precision. An expanding Universe also implied an extremely compact state in the past, and therefore very high temperature. The Particle Physics forces which can now be explored only in accelerator laboratories were in free play in the remote past. Thus the observation of the oldest remnants in the Universe amounts to looking at the results of a Particle Physics experiment under natural conditions.

In these notes we present a selection of topics, each section approximately amounting to one lecture. We begin with a brief recapitulation of General Relativity, and the Standard Model of Cosmology. The study of Cosmology requires General Relativity to be applied only under a highly symmetric situation and therefore it is possible to recast the essentials as Three Laws of Cosmology.

The study of very early Universe brings us squarely into the domain of Quantized Field Theory at given temperature. Intermediate metastable phases through which the Universe passed require an understanding of the effective potential of the field theory in a thermal equilibrium. This formalism is developed in some detail.

The remainder of the notes discuss important signatures of the remote past. These include : (i) inflation, (ii) density perturbations leading to galaxy formation, (iii) study of hot and cold relics decoupled from the remaining constituents, some of which can be candidates for Dark Matter, (iv) finally the baryon asymmetry of the Universe. As we shall see each of these has a strong bearing on Particle Physics and is being subjected to ever more precise observations.

Contents:

  • 1 Introduction
    • General Theory of Relativity : A Recap
    • The Standard Model of Cosmology
    • The Standard Model of Particle Physics
  • 2 Friedmann-Robertson-Walker Metrics
    • Cosmological redshift
    • Luminosity Distance
  • 3 The Three Laws of Cosmology
    • Example : Friedman Universe
    • Parameters of the Universe
  • 4 The Big Bang Universe
    • Thermodynamic Relations
    • Isentropic Expansion
    • Temperature Thresholds
    • Photon Decoupling and Recombination
  • 5 Phase Transitions with Quantum Fields in the Early Universe
    • Legendre Transform
    • Effective action and effective potential
    • Computing Veff
    • Temperature corrections to 1-loop
  • 6 First order Phase transition
    • Tunneling
    • Applications
  • 7 Inflationary Universe
    • Fine tuned initial conditions
    • Horizon problem
    • Oldness-Flatness problem
    • Density perturbations
    • Inflation
    • Resolution of Problems
    • Inflaton Dynamics
  • 8 Density perturbations and galaxy formation
    • Jeans Analysis for Adiabatic Perturbations
    • Jeans Analysis in Expanding Universe
    • Density Fluctuations from Inflation
  • 9 Relics of the Big Bang
    • Boltzmann Equations
    • Dark Matter
  • 10 Missing Dark Energy
  • 11 Baryon asymmetry of the Universe
    • Genesis of the idea of Baryogenesis
    • Sakharov criteria
    • Anomalous violation of B + L number
    • Electroweak baryogenesis
    • Baryogenesis from Leptogenesis
  • 12 Appendix

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