From inflation to hot big bang -- a tutorial on cosmological perturbations

arXiv:2607.06983 · hep-ph, astro-ph.CO · Submitted 2026-07-08 · Read on arXiv

Mikko Laine, Simona Procacci

hep-ph, astro-ph.CO

Submitted: 2026-07-08

Comments: 241 pages

Journal ref: Lect. Notes Phys. 1047 (2026) pp.1-253

DOI: 10.1007/978-3-032-09893-1

Code: https://github.com/laineprocacci/From-inflation-to-hot-big-bang

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Reheating — 55× in this paper · explained in 2 episodes
• Decoupling — 26× in this paper · explained in 2 episodes
• Trace — 18× in this paper · explained in 2 episodes
• Boltzmann Equation — 14× in this paper · explained in 2 episodes
• Gauge Dependence — 10× in this paper · explained in 2 episodes
• Non-Gaussianity — 10× in this paper · explained in 2 episodes
• Cosmic Microwave Background — 8× in this paper
• Generalization — 8× in this paper · explained in 13 episodes
• alpha — 8× in this paper · explained in 1 episode
• Anisotropy — 6× in this paper · explained in 3 episodes
• Bulk Viscosity — 6× in this paper · explained in 2 episodes
• Quantum fluctuations — 6× in this paper · explained in 2 episodes
• Abundance — 5× in this paper · explained in 1 episode
• Bispectrum — 5× in this paper · explained in 3 episodes
• Spectral Distortions — 5× in this paper · explained in 2 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Consistency — 3× in this paper · explained in 3 episodes
• Cosmic Explorer — 3× in this paper
• Gravitational Lensing — 3× in this paper · explained in 2 episodes
• Homogeneity — 3× in this paper · explained in 2 episodes
• Phase Transitions — 3× in this paper · explained in 2 episodes
• Big Bang Observer — 2× in this paper
• Einstein Telescope — 2× in this paper
• Gauge Freedom — 2× in this paper · explained in 2 episodes
• Primordial non-Gaussianity — 2× in this paper · explained in 2 episodes
• Symmetry Breaking — 2× in this paper · explained in 3 episodes
• pulsar timing arrays — 2× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Conservation Laws — 1× in this paper · explained in 3 episodes
• Cosmic Linear Anisotropy Solving System — 1× in this paper
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Laser Interferometer Space Antenna — 1× in this paper
• Regularization — 1× in this paper · explained in 3 episodes
• Stochastic Dynamics — 1× in this paper · explained in 2 episodes
• Topological Defects — 1× in this paper · explained in 2 episodes

Sources

• Cosmological perturbations
• TASI Lectures on Inflation
• Planck 2018 results. I. Overview and the cosmological legacy of Planck
• On Inflation with Non-minimal Coupling
• Bouncing Cosmologies
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• Constraints on Inflationary Gravitational Waves with Two Years of SPT-3G Data
• Planck 2018 results. VI. Cosmological parameters
• Planck 2018 results. X. Constraints on inflation
• The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $\Lambda$CDM Parameters
• Planck 2018 results. IX. Constraints on primordial non-Gaussianity
• The evolution of CMB spectral distortions in the early Universe
• The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals
• Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array
• Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I
• Terrestrial Very-Long-Baseline Atom Interferometry: Workshop Summary
• Gravitational Wave Astronomy With TianQin
• Current status of space gravitational wave antenna DECIGO and B-DECIGO

Related papers

• Classification of g-modes for neutron stars with a strong transition: Novel universal relation including slow stable hybrid stars
• Higgsino Dark Matter Interpretation of the LUX-ZEPLIN 248 keV Nuclear-Recoil Event
• A Unified Bogoliubov Approach to Primordial Gravitational Waves: From Inflation to Reheating
• Probing Memory-Burdened Primordial Black Holes with High-Energy Neutrinos
• Enhanced Dark Matter Quantum Sensing via Phase-Space Geometric Interferometry
• Axions as Dark Matter, Dark Energy, and Dark Radiation