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Lecture Notes in Cosmology

Oliver F. Piattella

TL;DR

The notes establish a comprehensive framework for cosmology, starting from empirical evidence for an expanding universe and moving through the geometric backbone of the FLRW metric and Friedmann equations. They connect this geometry to observable distances, horizons, and the lookback time, then extend to kinetic theory and the thermal history of the early universe, including BBN and recombination. Central themes include the LambdaCDM concordance model, the roles of dark matter and dark energy, and the suite of distance and horizon measures that link theory to observations. The text emphasizes the interplay between microphysical processes and macroscopic expansion, highlighting tensions, fundamental questions about initial conditions, and the thermal history that shapes present-day cosmological data.

Abstract

The first version of these lecture notes is based on the hand-written notes I prepared for the cosmology course taught to graduate students of PPGFis and PPGCosmo at the Federal University of Espírito Santo (UFES), starting in 2014. The course covers topics ranging from the evidence for the expanding universe to the anisotropies of the Cosmic Microwave Background. The notes are also available on my personal webpage (https://www.oliverfpiattella.eu) and have been published by Springer. The second version extends and updates the material presented in the first version, and typographical errors and mistakes have also been corrected.

Lecture Notes in Cosmology

TL;DR

The notes establish a comprehensive framework for cosmology, starting from empirical evidence for an expanding universe and moving through the geometric backbone of the FLRW metric and Friedmann equations. They connect this geometry to observable distances, horizons, and the lookback time, then extend to kinetic theory and the thermal history of the early universe, including BBN and recombination. Central themes include the LambdaCDM concordance model, the roles of dark matter and dark energy, and the suite of distance and horizon measures that link theory to observations. The text emphasizes the interplay between microphysical processes and macroscopic expansion, highlighting tensions, fundamental questions about initial conditions, and the thermal history that shapes present-day cosmological data.

Abstract

The first version of these lecture notes is based on the hand-written notes I prepared for the cosmology course taught to graduate students of PPGFis and PPGCosmo at the Federal University of Espírito Santo (UFES), starting in 2014. The course covers topics ranging from the evidence for the expanding universe to the anisotropies of the Cosmic Microwave Background. The notes are also available on my personal webpage (https://www.oliverfpiattella.eu) and have been published by Springer. The second version extends and updates the material presented in the first version, and typographical errors and mistakes have also been corrected.

Paper Structure

This paper contains 254 sections, 1987 equations, 47 figures, 5 tables.

Table of Contents

  1. Cosmology
  2. The expanding universe
  3. A bit of history
  4. Olbers's paradox
  5. An exercise
  6. The content of the universe
  7. Photons: the cosmic microwave background radiation
  8. Neutrinos
  9. The accelerated expansion of the universe and dark energy
  10. Dark matter
  11. Rotation curves of disc galaxies.
  12. The dynamics of galaxies in clusters.
  13. The formation of structures in the universe.
  14. The CMB.
  15. Gravitational Lensing and the Bullet Cluster.
  16. ...and 239 more sections

Figures (47)

  • Figure 1: Light-cone for the case $a(t) = (t/t_0)^{2/3}$, using cosmic time and comoving distance.
  • Figure 2: Light-cone for the case $a(t) = (t/t_0)^{2/3}$, using cosmic time and proper distance. The dashed lines represent the Hubble radius $c/H = 3ct/2$. The change of the slope takes place when $D = c/H$.
  • Figure 3: Dimensionless age of the universe $H_0t_0$ as function of $\Omega_\Lambda$, keeping fixed the curvature and radiation content. The value of $\Omega_{\rm m0}$ is then obtained by the closure relation as $\Omega_{\rm m0} = 1 - \Omega_{\Lambda} - \Omega_{\rm r0} - \Omega_{K0}$.
  • Figure 4: Defining the angular diameter distance.
  • Figure 5: The angular diameter distance between two different redshifts.
  • ...and 42 more figures