I have organized series of international coanference, MOGRA, named after "mogura (もぐら)" in Japanese
that means "mole" in English.
The focus of MOGRA series is recent progress in study of gravitational theory, specially modified
gravity theory, and its theoretical and phenomenological applications including:
Past MOGRAs are as follows:
I am now writing the lecture notes on F(R) gravity theory for beginners. Coming soon.
(Last update: December 16, 2024)
The study of gravitational theory began with Galileo, followed by Kepler’s laws of celestial motion and Newton’s law of universal gravitation, and Einstein established general relativity. In the ceaseless research on gravity, alternative theories to general relativity, known as modified gravity, have been investigated. F(R) gravity theory is a modified gravity theory that includes a simple extension to general relativity and has been intensively applied to cosmology and astrophysics. This lecture note covers basics of the F(R) gravity theory and related topics.
Part I (Chapters 1 – 4) summarizes fundamental but essential subjects including basics of GR.
Chapter 1. General Relativity
--- 1.1 Curvature tensor
--- 1.2 Einstein-Hilbert action
--- 1.3 Einstein equation
--- 1.4 Bianchi identity
--- 1.5 Cosmological constant
Chapter 2. F(R) Gravity Theory
--- 2.1 Basic concepts
--- 2.2 Field equation
--- 2.3 Conservation law
--- 2.4 Scalaron field
Chapter 3. F(R) Gravity as Scalar-Tensor
--- 3.1 Scalar-Tensor theory
--- 3.2 In Jordan frame
--- 3.3 Frame transformation
--- 3.4 In Einstein frame
--- 3.5 Chameleon mechanism
Chapter 4. Models in F(R) Gravity
--- 4.1 Modification for what?
--- 4.2 R2 model for inflation
--- 4.3 1/R model for DE
--- 4.4 DE models
--- 4.5 Inflation and DE
Part II (Chapters 5 – 8) is devoted to an overview of practical applications of F(R) gravity.
Chapter 5. Cosmology
--- 5.1 FLRW spacetime
--- 5.2 Friedmann equation in GR
--- 5.3 Modified Friedmann equations
--- 5.4 Another formulation
Chapter 6. Compact Stars
--- 6.1 SSS spacetime
--- 6.2 TOV equation in GR
--- 6.3 Modified TOV equation
--- 6.4 Scalarization
Chapter 7. Gravitational Waves
--- 7.1 Fluctuations of spacetime
--- 7.2 GW in GR
--- 7.3 GW in Jordan frame
--- 7.4 GW in Einstein frame
Chapter 8. Particle Physics
--- 8.1 Dilatonic coupling in Einstein frame
--- 8.2 Coupling to scalar field
--- 8.3 Coupling to fermion field
--- 8.4 Coupling to vector field
Part III (Chapters 9 – 18) covers advanced topics, detailed calculations, and technical matters.
Chapter 9. Mathematical Tools
--- 9.1 Differential geometry
--- 9.2 Parallel transport
--- 9.3 Affine connection
--- 9.4 Levi-Civita connection
--- 9.5 Tensor density
--- 9.6 Covariant derivative for tensor density
Chapter 10. Palatini Formalism
--- 10.1 General connection
--- 10.2 Palatini formalism in GR
--- 10.3 Palatini formalism in F(R) gravity
Chapter 11. Conservation Law
--- 11.1 Generalized Bianchi identity
--- 11.2 Equations of motion of matter fields
--- 11.3 Local and global conservation
Chapter 12. Degrees of Freedom
--- 12.1 Hamiltonian analysis
--- 12.2 ADM formalism
--- 12.3 DOF in GR
--- 12.4 DOF in F(R) gravity
Chapter 13. Weyl Transformation
--- 13.1 Transformation rules
--- 13.2 Ricci scalars in two frames
--- 13.3 Another formulation
--- 13.4 In four-dimensional case
--- 13.5 Frame Equivalence
Chapter 14. Screening Mechanisms
--- 14.1 Long-range fifth force
--- 14.2 Screening mechanism
--- 14.3 Vainshtein mechanism
--- 14.4 K-mouflage
--- 14.5 Chameleon mechanism
--- 14.6 Symmetron mechanism
Chapter 15. Solutions to Friedmann Equation
--- 15.1 Single component
--- 15.2 Two components
--- 15.3 Einstein’s static universe
Chapter 16. Numerical Treatment for TOV Equation
--- 16.1 Junction condition at surface
--- 16.2 Boundary conditions
--- 16.3 Dimensionless quantities
--- 16.4 Models of EOS
--- 16.5 M − R relation
Chapter 17. Perturbations
--- 17.1 Parturbation of metric
--- 17.2 Perturbation in √−g
--- 17.3 Perturbation in Levi-Civita connection
--- 17.4 Perturbation in Curvature Tensor
--- 17.5 Perturbation in Einstein-Hilbert action
Chapter 18. Field Theory in Curved Spacetime
--- 18.1 Vierbein and covariant derivative
--- 18.2 Spin connection
--- 18.3 Spin connection for vector field
--- 18.4 Spin connection for spinor Field
--- 18.5 Scale Anomaly
--- 18.6 Spin and force
Part IV (Chapters A – D) introduces other modified gravity theories related to the F(R) gravity.
Chapter A. Nordström Theory of Gravity
--- A.1 From Newtonian gravity to relativistic gravity
--- A.2 Relativistic scalar theory of gravity
--- A.3 Features of Nordström theory
Chapter B. TEGR, STEGR, and Extensions
--- B.1 GR as quadratic theory of connection
--- B.2 Teleparallel gravity
--- B.3 F(T) gravity
--- B.4 Symmetric teleparallel gravity
--- B.5 F(Q) gravity
Chapter C. Higher-Curvature Gravity
--- C.1 Curvature-squared correction
--- C.2 Critical gravity
--- C.3 F(Rμν) gravity
--- C.4 Eddington-inspired Born-Infeld gravity
Chapter D. Lovelock Theorem
Chapter E. Horndeski Theory
I upload short notes on matters of personal interest. Coming soon.