Cosmology in symmetric teleparallel gravity and its dynamical system

Jianbo Lu (Department of Physics, Liaoning Normal University, Dalian, 116029, People’s Republic of China) ; Xin Zhao (Department of Physics, Liaoning Normal University, Dalian, 116029, People’s Republic of China) ; Guoying Chee (Department of Physics, Liaoning Normal University, Dalian, 116029, People’s Republic of China)

We explore an extension of the symmetric teleparallel gravity denoted the f(Q) theory, by considering a function of the nonmetricity invariant Q as the gravitational Lagrangian. Some interesting properties could be found in the f(Q) theory by comparing with the f(R) and f(T) theories. The field equations are derived in the f(Q) theory. The cosmological application is investigated. In this theory the accelerating expansion is an intrinsic property of the universe geometry without need of either exotic dark energy or extra fields. And the state equation of the geometrical dark energy can cross over the phantom divide line in the f(Q) theory. In addition, the dynamical system method are investigated. It is shown that there are five critical points in the STG model for taking $$f(Q)=Q+\alpha Q^2$$ f(Q)=Q+αQ2 . The critical points $$P_{4}$$ P4 and $$P_{5}$$ P5 are stable. $$P_{4}$$ P4 corresponds to the geometrical dark energy dominated de Sitter universe ($$w_{tot}^{eff}=-1$$ wtoteff=-1 ), while $$P_{5}$$ P5 corresponds to the matter dominated universe ($$w_{tot}^{eff}=0$$ wtoteff=0 ). Given that $$P_{4}$$ P4 represents an attractor, the cosmological constant problems, such as the fine tuning problem, could be solved in the STG model.

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      "surname": "Zhao", 
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      "surname": "Chee", 
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      "value": "We explore an extension of the symmetric teleparallel gravity denoted the f(Q) theory, by considering a function of the nonmetricity invariant Q as the gravitational Lagrangian. Some interesting properties could be found in the f(Q) theory by comparing with the f(R) and f(T) theories. The field equations are derived in the f(Q) theory. The cosmological application is investigated. In this theory the accelerating expansion is an intrinsic property of the universe geometry without need of either exotic dark energy or extra fields. And the state equation of the geometrical dark energy can cross over the phantom divide line in the f(Q) theory. In addition, the dynamical system method are investigated. It is shown that there are five critical points in the STG model for taking $$f(Q)=Q+\\alpha Q^2$$ <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow><mo>=</mo><mi>Q</mi><mo>+</mo><mi>\u03b1</mi><msup><mi>Q</mi><mn>2</mn></msup></mrow></math> . The critical points $$P_{4}$$ <math><msub><mi>P</mi><mn>4</mn></msub></math>  and $$P_{5}$$ <math><msub><mi>P</mi><mn>5</mn></msub></math>  are stable. $$P_{4}$$ <math><msub><mi>P</mi><mn>4</mn></msub></math>  corresponds to the geometrical dark energy dominated de Sitter universe ($$w_{tot}^{eff}=-1$$ <math><mrow><msubsup><mi>w</mi><mrow><mi>tot</mi></mrow><mrow><mi>eff</mi></mrow></msubsup><mo>=</mo><mo>-</mo><mn>1</mn></mrow></math> ), while $$P_{5}$$ <math><msub><mi>P</mi><mn>5</mn></msub></math>  corresponds to the matter dominated universe ($$w_{tot}^{eff}=0$$ <math><mrow><msubsup><mi>w</mi><mrow><mi>tot</mi></mrow><mrow><mi>eff</mi></mrow></msubsup><mo>=</mo><mn>0</mn></mrow></math> ). Given that $$P_{4}$$ <math><msub><mi>P</mi><mn>4</mn></msub></math>  represents an attractor, the cosmological constant problems, such as the fine tuning problem, could be solved in the STG model."
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Published on:
09 July 2019
Publisher:
Springer
Published in:
European Physical Journal C , Volume 79 (2019)
Issue 6
Pages 1-8
DOI:
https://doi.org/10.1140/epjc/s10052-019-7038-3
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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