Course

PHYS-427: Relativity and cosmology I

Lectures in this course (88)

Cosmological Evolution: Matter and Radiation

Covers the evolution of the universe with a focus on matter and radiation contributions.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Tensors and Normal Coordinates

Introduces one-forms, tensors, normal coordinates, and metric tensors in differential geometry.

Coordinate Transformations in General Relativity

Covers exercises on coordinate transformations in general relativity, emphasizing conceptual understanding and straightforward calculations for the exam.

Dark Energy and Cosmological Constant

Explores dark energy, the cosmological constant, and their impact on the universe's expansion under various scenarios.

Differential Forms: Basics and Applications

Introduces the concept of differential forms and their applications in n-dimensional manifolds, including the Levi-Civita tensor and volume form.

Tensor Properties

Covers the properties of tensors and their applications in various fields.

Hodge Duality and Covariant Derivatives

Introduces Hodge duality, covariant derivatives, and key concepts in differential geometry.

Covariance: Understanding the Concepts

Explores the concept of covariance, its meanings, and practical applications in tensor transformation laws.

Relativity and Cosmology II: Hubble Law and Universe Curvature

Covers the Hubble law derivation and cosmological parameter determination from supernova observations.

Parallel Transport and Geodesics

Explores parallel transport along curves and geodesics maximizing proper time between points.

Rotating Frame, Geodesics and Maxwell Equations

Covers exercises on rotating frame, geodesics, and Maxwell equations to deepen understanding of tensor quantities.

Big Bang Theory Foundations

Explores the foundations of the Big Bang Theory, including thermal equilibrium, radiation-dominated stage, and the prediction of the Cosmic Microwave Background (CMB).

Exponential Map and Curvature Tensor

Covers the exponential map, covariant derivatives, connection coefficients, and Riemann curvature tensor.

Gravitational Field Equations

Covers the formulation of gravitational field equations and the motion of particles in gravitational fields.

Gravity and Motion

Explores force of motion, dimensions, gravity, tensor fields, and equivalence principle.

Riemann Tensor and Ricci Scalar

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Neutrino Decoupling in Early Universe

Explores neutrino decoupling in the early universe and its implications on cosmic evolution.

Gravitational Theory: Light Bending & Geodesic Motion

Explores gravitational theory, light bending, geodesic motion, and electromagnetism in gravitational fields through practical problem-solving.

Symmetries and Conservation Laws

Explores Killing vectors, conserved quantities, symmetric spaces, and the Riemann curvature tensor properties.