1 / 19

f(T ) Theories: Status Update

f(T ) Theories: Status Update. 王元君 Ong Yen Chin Graduate Institute of Astrophysics & LeCosPA. Teleparallel Gravity: Einstein’s Other Theory of Gravity.

neila
Télécharger la présentation

f(T ) Theories: Status Update

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. f(T) Theories: Status Update 王元君 Ong Yen Chin Graduate Institute of Astrophysics & LeCosPA

  2. Teleparallel Gravity: Einstein’s Other Theory of Gravity “In the tranquility of my sickness, I have laid a wonderful egg in the area of general relativity. Whether the bird that will hatch from it will be vital and long-lived only the gods know. So far I am blessing my sickness that has endowed me with it.” - Einstein, 1928. • Originated from an attempt to unify general relativity and electromagnetism. • Failed: Teleparallel gravity doesn’t have extra degree of freedom. It is in fact, equivalent to GR. 2 of 13

  3. Teleparallel Gravity: An Introduction Teleparallel Gravity = General Relativity

  4. Teleparallel Gravity: Introduction • Contortion [Not contorsion!]: Also define • Torsion Scalar: • Einstein-Hilbert Action: 4 of 13

  5. Teleparallel Cosmology • Flat FRW Cosmology: • [Canonical] Tetrad: • Torsion: 5 of 13

  6. f(T) Cosmology • Friedmann Equation • Acceleration Equation Effective dark energy density 6 of 13

  7. Teleparallel Gravity is equivalent to GR; f(T) is NOT equivalent to f(R) That is, R = T + (Total Divergence Terms). f(R) NOT equal to f(T) + (Total Divergence Terms) 7 of 13

  8. f(T) Cosmology Numerous models have been proposed, including those with phantom line crossing. 8 of 13

  9. f(T) Cosmic Evolution Suitable f(T) models exist in which the universe is able to evolve from a radiation dominated era to a matter dominated one, and finally enter an exponential expansion phase. astro-ph/1008.1250 9 of 13

  10. 10 of 13

  11. Problems for f(T) Theories • Not Local Lorentz Invariance: T is not a Lorentz scalar; with different choice of basis tetrad, extra degree of freedom might be introduced into the theory. [Barrow et al.] There is however no extra degree of freedom in the canonical choice of tetrad. There is also no massive graviton. [Dent et al.]. 11 of 13

  12. Problems for f(T) Theories f(T) theories admit Schwarzschild-(anti)-de Sitter black hole solution but do not admit Reissner-Nordström black hole solution [at least in Gullstrand–Painlevé tetrad]. C.f. f(R) theories: both Schwarzschild-(anti)-de Sitter and charged solutions, as well as more general solutions exist. Static Solution with Spherical Symmetry in f(T) Theories, Tower Wang, gr-qc/1102.4410 1. f(R) Black Holes, Taeyoon Moon, Yun Soo Myung, Edwin J. Son, gr-qc/1101.1153 2. Static Spherically Symmetric Solutions in F(R) Gravity, Lorenzo Sebastiani, Sergio Zerbini, gr-qc/1012.5230 2 of 13

  13. Future Prospects 1. f(T ) theory can give very similar background evolution like that of ΛCDM, although they have completely different theoretical basis. 2. How shall we interpret the coordinate transformations in general f(T ) theories; are there extra degree of freedom? 13 of 13

  14. Observational Constraints Observational constraints on f(T) theory, Puxun Wu and Hongwei Yu, gr-qc/ 1006.0674v5

  15. Growth of Perturbations Cosmological perturbations in f(T) gravity, James B. Dent, Sourish Dutta, Emmanuel N. Saridakis [astro-ph:1008.1250] • Matter Overdensity

  16. Growth of Perturbations As nincreases, there is a suppression of growth at smaller redshifts, which can act as a clear distinguishing feature of these models.

  17. Growth of Perturbations Larger scales are more strongly affected than smaller ones. • For this model, on large subhorizon scales (O(100 Mpc) or larger), the evolution of the matter overdensity differs markedly from CDM.

More Related