Taishi Katsuragawa's Webpage

International Conference on Modified Gravity (MOGRA)

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:

MOGRA 2023
  • Period: November 18 - 20, 2023
  • Website: MOGRA 2023
  • Place: Junyi Dynasty Hotel, Wuhan, China
  • Supported by the Institute of Astrophysics at Central China Normal University. (Website)
MOGRA 2018
  • Period: August 8 - 10, 2018
  • Website: MOGRA 2018
  • Place: KMI Symposia, Nagoya University, Japan
  • Supported by the Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI) at Nagoya University. (Website)

Lectures on F(R) Gravity Theory

I am now writing the lecture notes on F(R) gravity theory for beginners. Coming soon.

(Last update: December 2, 2024)

Contents of lecture note (planned)

Part I. Rudiments

Part I (Chapters 1 – 4) summarizes fundamental but essential subjects including basics of GR.

Check Chapters/Sections

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. Scalar-Tensor Descriptions
--- 3.1 Scalar-Tensor theory of gravity
--- 3.2 F(R) gravity in Jordan frame
--- 3.3 Frame transformation
--- 3.4 F(R) gravity in Einstein frame
--- 3.5 Effective mass and chameleon mechanism
Chapter 4. Models in F(R) Gravity
--- 4.1 Modification for what?
--- 4.2 R2 model
--- 4.3 1/R model
--- 4.4 DE models
--- 4.5 Unified models

Part II. Applications

Part II (Chapters 5 – 8) is devoted to an overview of practical applications of F(R) gravity.

Check Chapters/Sections

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. Advanced Topics

Part III (Chapters 9 – 18) covers advanced topics, detailed calculations, and technical matters.

Check Chapters/Sections

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

Part IV. Appendix

Part IV (Chapters A – D) introduces other modified gravity theories related to the F(R) gravity.

Check Chapters/Sections

Chapter A. TEGR, STEGR, and Extensions
--- A.1 GR as quadratic theory of connection
--- A.2 Teleparallel gravity
--- A.3 F(T) gravity
--- A.4 Symmetric teleparallel gravity
--- A.5 F (Q) gravity
Chapter B. Higher Curvature Gravity
Chapter C. Lovelock Theorem
Chapter D. Horndeski Theory

KT3 Projects

I upload short notes on matters of personal interest. Coming soon.

ページのトップへ戻る