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《中国物理C》（英文）编辑部
2024年10月30日
Chinese Physics C> 2017, Vol. 41> Issue(12) : 125103 DOI: 10.1088/1674-1137/41/12/125103

Generic phase portrait analysis of finite-time singularities and generalized teleparallel gravity

  • 1.

     Centre for Theoretical Physics, The British University in Egypt, P. O. Box 43, El Sherouk City, Cairo 11837, Egypt

  • 2.

     Egyptian Relativity Group(ERG), Cairo University, Giza 12613, Egypt

  • 3.

     Mathematics Department, Faculty of Science, Ain Shams University, Cairo 11566, Egypt

  • 4.

     Egyptian Relativity Group(ERG), Cairo University, Giza 12613, Egypt

  • We analyze the four common types of finite-time singularity using a generic framework of the phase portrait geometric approach. This technique requires the Friedmann system to be written as a one-dimensional autonomous system. We employ a scale factor that has been used widely in the literature to realize the four finite-time singularity types, then we give a detailed discussion for each case showing possible novel models. Moreover, we show how different singularity types can play essential roles in different cosmological scenarios. Among several modified gravity theories, we show that the f(T) cosmology is compatible with the phase portrait analysis, since the field equations include Hubble derivatives only up to first order. Therefore, we reconstruct the f(T) theory which generates these phase portraits. We also perform a complementary analysis using the effective equation of state. Furthermore, we investigate the role of the torsion fluid in realizing the cosmic singularities.
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El Hanafy and G. G. L. Nashed. Generic phase portrait analysis of finite-time singularities and generalized teleparallel gravity[J]. Chinese Physics C, 2017, 41(12): 125103. doi: 10.1088/1674-1137/41/12/125103
El Hanafy and G. G. L. Nashed. Generic phase portrait analysis of finite-time singularities and generalized teleparallel gravity[J]. Chinese Physics C, 2017, 41(12): 125103.  doi: 10.1088/1674-1137/41/12/125103 shu
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Received: 2017-08-16
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    Supported by the Egyptian Ministry of Scientific Research (24-2-12)

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Generic phase portrait analysis of finite-time singularities and generalized teleparallel gravity

    Corresponding author: El Hanafy,
    Corresponding author: G. G. L. Nashed,
  • 1. Centre for Theoretical Physics, The British University in Egypt, P. O. Box 43, El Sherouk City, Cairo 11837, Egypt
  • 2. Egyptian Relativity Group(ERG), Cairo University, Giza 12613, Egypt
  • 3. Mathematics Department, Faculty of Science, Ain Shams University, Cairo 11566, Egypt
  • 4. Egyptian Relativity Group(ERG), Cairo University, Giza 12613, Egypt
  • Received Date: 2017-08-16
  • Available Online: 2017-12-05
Fund Project:  Supported by the Egyptian Ministry of Scientific Research (24-2-12)

Abstract: We analyze the four common types of finite-time singularity using a generic framework of the phase portrait geometric approach. This technique requires the Friedmann system to be written as a one-dimensional autonomous system. We employ a scale factor that has been used widely in the literature to realize the four finite-time singularity types, then we give a detailed discussion for each case showing possible novel models. Moreover, we show how different singularity types can play essential roles in different cosmological scenarios. Among several modified gravity theories, we show that the f(T) cosmology is compatible with the phase portrait analysis, since the field equations include Hubble derivatives only up to first order. Therefore, we reconstruct the f(T) theory which generates these phase portraits. We also perform a complementary analysis using the effective equation of state. Furthermore, we investigate the role of the torsion fluid in realizing the cosmic singularities.

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