An Introduction to Modern Cosmology

Citation

Liddle, A. (2015). An Introduction to Modern Cosmology (3rd ed.). Wiley.

Chapter Summary

The book is short, about 180 pages of text, and its structure is stated in the preface: a central "spine" of fifteen main chapters that forms a self-contained introduction, plus six Advanced Topic chapters, each with stated prerequisites, that can be added as desired. The author recommends taking an Advanced Topic soon after its prerequisites have been met. The preface also explains the key choice of method: the equations of an expanding universe can be obtained from Newtonian gravity, so that the course can avoid general relativity altogether.

Chapters 1–2: A (Very) Brief History of Cosmological Ideas; Observational Overview

Chapter 1 opens with the cosmological principle, the idea that our place in the Universe is in no way special, and sets it against the long history of Earth-centred pictures. Chapter 2 surveys the Universe in visible light and other wavebands, then homogeneity and isotropy, the expansion, and the particles in the Universe, including thermal distributions and the black-body spectrum.

Chapters 3–5: Newtonian Gravity; The Geometry of the Universe; Simple Cosmological Models

The theoretical core. Chapter 3 derives the Friedmann, fluid and acceleration equations in Newtonian terms and discusses what the expansion means. Chapter 4 describes flat, spherical and hyperbolic geometry, infinite and observable universes and the three values of the curvature parameter k. Chapter 5 turns to Hubble's law, redshift, solutions for matter, radiation and mixtures, number densities and evolution including curvature.

Chapters 6–9: Observational Parameters; The Cosmological Constant; The Age of the Universe; The Density of the Universe and Dark Matter

Chapter 6 introduces the Hubble constant, the density parameter and the deceleration parameter. Chapter 7 introduces Λ and its fluid description and models containing it, and Chapter 8 deals with the age of the Universe. Chapter 9 weighs the Universe by several methods and discusses what dark matter might be and how it is searched for.

Chapters 10–12: The Cosmic Microwave Background; The Early Universe; Nucleosynthesis: The Origin of the Light Elements

Chapter 10 covers the properties of the microwave background, the photon-to-baryon ratio and its origin, with a second, advanced treatment of the origin. Chapter 11 is a short chapter on the early Universe. Chapter 12 covers hydrogen and helium, comparison with observations, and a contrast between decoupling and nucleosynthesis.

Chapters 13–15: The Inflationary Universe; The Initial Singularity; Overview: The Standard Cosmological Model

Chapter 13 states the problems of the hot Big Bang (flatness, horizon, relic particles), describes inflationary expansion and how it solves them, asks how much inflation is needed and relates inflation to particle physics. Chapter 14 is a short discussion of the initial singularity, and Chapter 15 gathers the picture into the standard cosmological model.

Advanced Topics 1–6

The six extension chapters are General Relativistic Cosmology (the metric of space-time and the Einstein equations), Classic Cosmology: Distances and Luminosities, Neutrino Cosmology, Baryogenesis, Structures in the Universe, and Constraining Cosmological Models, which includes "The Standard Cosmological Model: 2014 edition". A bibliography and numerical answers and hints to the problems close the book.

Key Concepts

Chapters 1–5: Observations, Newtonian Gravity, Geometry, Simple Models

• Cosmological principle: the assumption that our location is not special, so that the Universe looks the same everywhere on large scales.
• Friedmann equation: the equation governing the expansion, obtained in Chapter 3 from Newtonian gravity.
• Curvature parameter k: the label for flat, spherical or hyperbolic geometry.
• Redshift and Hubble's law: the relation between the expansion and the observed shifts of light.

Chapters 6–9: Parameters, Λ, Age, Dark Matter

• Density parameter: the density measured against the critical value that separates the three geometries.
• Cosmological constant: the extra term whose fluid description and effect on models Chapter 7 develops.
• Dark matter: matter inferred from several lines of evidence in Chapter 9, such as galaxy rotation curves and cluster composition.

Chapters 10–15: Microwave Background, Nucleosynthesis, Inflation

• Cosmic microwave background: the relic radiation from the time the Universe was denser and hotter.
• Nucleosynthesis: the formation of the light elements, compared with observed abundances.
• Inflation: a period of rapid expansion that addresses the flatness, horizon and relic-abundance problems.

Critical Analysis

Strengths

• A deliberately light prerequisite load. The preface states that the prerequisites are all very standard physics and that the emphasis is on physical intuition rather than mathematical rigour. Taking Newtonian gravity as the starting point avoids a prior course in general relativity.
• A modular structure. The fifteen-chapter spine is self-contained, and the six Advanced Topics, each with listed prerequisites, let a course add depth where it wants it. Chapter 10 itself includes an "advanced" section, so the same pattern appears inside chapters.
• Support for self-study. The publisher describes student problems with hints and numerical answers embedded in the chapters, and the contents show a section of numerical answers and hints at the back. The author maintains a website with errata, updates and full-colour images.
• A short, regularly updated text. At around 180 pages the book can be read in a term. The third edition incorporates results from the Planck mission, according to the publisher, and the preface says each edition has absorbed new discoveries.

Limitations

• Newtonian shortcut. The preface itself calls the derivation "a subtle bit of cheating". General relativity enters only in Advanced Topic 1, a few pages long, so readers who need the metric-based treatment must go elsewhere.
• Intuition over rigour, and little on perturbations. The detailed treatment of microwave-background anisotropies and the origin of structure is confined to Advanced Topic 5, which spans only about a dozen pages; courses on the growth of structure need a more advanced source.
• Observational values date quickly. Advanced Topic 6 presents the standard model as of 2014, and the author says cosmology has no long-settled foundation, so specific numbers will need updating from current data.

Where It Fits in the Course

Liddle's book is the compact, physics-first undergraduate cosmology text in this course list. Fraknoi, Morrison and Wolff's Astronomy 2e and Binney's Astrophysics: A Very Short Introduction come before it as non-calculus or minimal-mathematics surveys, and Maoz's Astrophysics in a Nutshell is a one-semester upper-level course in which cosmology is the closing topic. Carroll and Ostlie's An Introduction to Modern Astrophysics is a comprehensive survey that places cosmology at the end of a much longer book; Liddle gives the subject dedicated treatment in far fewer pages.

Dodelson and Schmidt's Modern Cosmology is the graduate-level next step: it derives the Boltzmann and Einstein equations for perturbations and uses them for the microwave background and galaxy clustering, the material that Liddle only sketches in Advanced Topic 5.

How to Use This Book

According to the preface, the book grew out of a course of about twenty lectures for final-year bachelor's or penultimate-year master's students; the publisher extends the audience to anyone starting research in cosmology. First-year physics with calculus is sufficient; general relativity is not required.

For a short course, read the fifteen main chapters in order, treating Chapters 3–5 as the technical heart: the Newtonian derivation of the expansion equations, geometry and the simple models, which everything afterward uses. Chapters 6–9 connect the models to measurements; Chapters 10–13 cover the microwave background, the early Universe, nucleosynthesis and inflation. Take Advanced Topics 1 and 2 after Chapter 5 if a relativistic treatment and distance measures are wanted, and Advanced Topic 5 after Chapter 10 for structure formation. Use the embedded problems and the hints at the back as you go, and check the author's website for errata and updated observational results.