Mikko Laine had PhD 1994 in Helsinki, was postdoc in Helsinki, Heidelberg, and CERN, and professor of theoretical physics in Bielefeld 2003-2012 and Bern 2012-today. He has published over 150 scientific articles, mostly on thermal field theory and particle cosmology. Mikko Laine is a co-author of the book "Basics of thermal field theory" (Springer, 2016).Simona Procacci had PhD 2023 in Bern, and a postdoc in Geneva 2023-today. She has published close to 10 scientific articles on inflationary cosmology, cosmological phase transitions, and gravitational wave physics. Simona Procacci got the faculty prize for the best PhD thesis in physics at the University of Bern in 2023, which served as an inspiration for this book.

• Einstein equations and the cosmological background solution.- Observable signatures beyond the background solution.- Evolution equations for first order perturbations.- Gauge transformations and different gauges.- Solution with vacuum initial conditions in de Sitter spacetime.- Solution for a general cold inflation scenario.- Evolution equations in the presence of a thermalizing plasma.- What happens when the modes exit the Hubble horizon?.- What happens when the modes re enter the Hubble horizon?.- Gravitational-wave probes of the inflationary period.