Abstract

Every cosmology lecturer these days is confronted with teaching the modern cosmological standard model ΛCDM, and there are many approaches to do this. However, the danger is imminent that it is presented to students as something set into stone, merely to be accepted as a fact based on the plenty of evidences we have. This is even more critical, given that the standard model of cosmology confronts us with entities not yet fully understood, namely a cosmological constant Λ and cold dark matter. In this article, we report on an advanced cosmology course exercise, conducted in computer lab, which was conceived as a means to have students experience first-hand why the ΛCDM model has become so prevalent in the interpretation of modern cosmological data. To this end, we focused on the cosmic microwave background radiation (CMB) and calculated theoretical temperature and matter power spectra, using the modern Boltzmann code CLASS. By comparing and analyzing the outcome for ΛCDM, as well as for three other exotic cosmological models, the students were able to grasp the impact of cosmological parameters on CMB observables, and also to understand some of the complicated CMB physics in a direct way. Our chosen examples are not exhaustive and can be easily modified or expanded, so we express the hope that this article will serve as a valuable resource for interested students and lecturers.

Highlights

  • The cosmological standard model ΛCDM has been confirmed as a ’best-fit model’ by many observations of the last two decades, notably by measurements of the large-scale structure via galaxy surveys (e.g. [1, 2]), the cosmic microwave background radiation (e.g. [3, 4]), and the distance ladder using variable stars and supernovae (e.g. [5, 6, 7, 8])

  • We report on an advanced cosmology course exercise, conducted in computer lab, which was conceived as a means to have students experience firsthand why the ΛCDM model has become so prevalent in the interpretation of modern cosmological data

  • We focused on the cosmic microwave background radiation (CMB) and calculated theoretical temperature and matter power spectra, using the modern Boltzmann code CLASS

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Summary

Introduction

The cosmological standard model ΛCDM has been confirmed as a ’best-fit model’ by many observations of the last two decades, notably by measurements of the large-scale structure via galaxy surveys (e.g. [1, 2]), the cosmic microwave background radiation (e.g. [3, 4]), and the distance ladder using variable stars and supernovae (e.g. [5, 6, 7, 8]). The nature of the two main ingredients of ΛCDM - the cosmological constant Λ and cold dark matter (CDM)-, is still unsettled, despite many past and on-going efforts to reveal their detailed characteristics This is the reason why ΛCDM has been more honestly called the ”current concordance model” in its early days around the turn of the millenium. The students acquire the skill to use modern cosmological software, but they appreciate first-hand why ΛCDM has become so prevalent and important in the interpretation of modern observations There is yet another reason why this exercise was conceived. Various parameter degeneracies made it necessary to focus on certain changes and their impact, as opposed to sampling an exhaustive number of illustrative models With this in mind, I like to emphasize that many more possibilities could be studied with CLASS, in general. In the Appendix, we briefly discuss the two versions of ΛCDM with which we were concerned in our study

Using the CLASS code
Models
Background evolution
CMB temperature power spectrum
Matter power spectrum
Findings
Summary
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