Cosmological perturbation theory (Lecture 2) by David Wands

PROGRAM

PHYSICS OF THE EARLY UNIVERSE (HYBRID)

ORGANIZERS: Robert Brandenberger (McGill University, Canada), Jerome Martin (IAP, France), Subodh Patil (Leiden University, Netherlands) and L. Sriramkumar (IIT - Madras, India)

DATE: 03 January 2022 to 12 January 2022

VENUE: Online and Ramanujan Lecture Hall

The aim of the School will be to introduce graduate students and postdoctoral fellows to essential ideas and recent developments related to the physics of the early universe. The School will begin with lectures on cosmological perturbation theory and alternative paradigms (such as inflation and the bouncing scenarios) for the generation of the primordial perturbations. They will be followed by lectures on the relation between models of the early universe and particle physics as well as comparison of these models with the available and forthcoming cosmological data. These lectures will be complemented with lectures on topics of considerable interest today such as the nature of dark matter and dark energy and the generation of gravitational waves in the early universe and their observational imprints.

0:00:00 Cosmological perturbation theory
0:01:22 Lecture 2
0:05:40 Metric perturbations
0:11:14 Gravitational waves
0:19:36 Vector perturbations
0:25:06 Scalar metric perturbations
0:26:35 Geometrical interpretation
0:33:11 Vector perturbations
0:37:02 Gravitational waves
0:38:19 Gauge dependence
0:48:28 Linear gauge transformation rules
0:53:03 Linear gauge transformation rules
0:56:12 Gauge-invariant variables
0:58:37 Longitudinal gauge/Conformal Newtonian
1:00:20 Linear gauge transformation rules
1:06:33 Comoving-orthogonal gauge
1:12:14 Uniform-density gauge
1:14:57 Uniform-alpha-density gauge
1:16:20 Spatially-flat gauge
1:18:37 Energy-momentum conservation
1:18:51 Relating gauge-invariant variables
1:20:58 Q&A