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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.

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f(T ) Theories: Status Update

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  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

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  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.

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