A Short Introduction to Cosmology and its Current Status

TL;DR

The notes present a cohesive overview of the $\Lambda$CDM framework, deriving the FRW background from general relativity and exploring both Newtonian and relativistic perturbation theories to understand structure formation. They connect early-universe inflationary initial conditions to the linear and non-linear growth of density perturbations, culminating in predictions for the linear power spectrum, BAOs, and the CMB angular power spectrum. The document then surveys how a suite of observables—galaxy surveys, weak lensing, and the CMB—constrain cosmological parameters, discusses statistical inference, and highlights current tensions such as the $H_0$ discrepancy and potential hints of evolving dark energy. Overall, it argues that cosmology is in a precision era with Stage IV experiments poised to test the robustness of $\Lambda$CDM and potentially reveal new physics.

Abstract

The current cosmological model, known as the $Λ$-Cold Dark Matter model (or $Λ$CDM for short) is one of the most astonishing accomplishments of contemporary theoretical physics. It is a well-defined mathematical model which depends on very few ingredients and parameters and is able to make a range of predictions and postdictions with astonishing accuracy. It is built out of well-known physics - general relativity, quantum mechanics and atomic physics, statistical mechanics and thermodynamics - and predicts the existence of new, unseen components. Again and again it has been shown to fit new data sets with remarkable precision. Despite these successes, we have yet to understand the unseen components of the Universe and there has been evidence for inconsistencies in the model. In these lectures, we lay the foundations of modern cosmology.

Figures (13)

• Figure 1: The Planck 2018 measurements 2020AA...641A...5P of the angular power spectrum of the cosmic microwave background (black lines) which show remarkable agreement with the theoretical predictions of the $\Lambda$CDM model (red line).
• Figure 2: The energy density of radiation, matter and the cosmological constant as a function of scale factor.
• Figure 3: Comparison of three different distance measures in $\Lambda$CDM: comoving distance, $\chi$, angular diameter distance, $D_A$, and the luminosity distance, $D_L$.
• Figure 4: The evolution of the ionisation fraction, $X$, as a function of redshift, $z$, predicted by the Saha equation Eq. (\ref{['eq:saha_eqn']}).
• Figure 5: The evolution of the gravitational potential in $\Lambda$CDM for different values of $k$.