Cosmological solutions in Hořava-Lifshitz scalar field theory

  • 1 Institute of Systems Science, Durban University of Technology, Durban, 4000, South Africa
  • 2 Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla, 1280, Chile
Andronikos PaliathanasisORCID iD: https://orcid.org/0000-0002-9966-5517
  • Institute of Systems Science, Durban University of Technology, Durban, 4000, South Africa
  • Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla, 1280, Antofagasta, Chile
  • orcid.org/0000-0002-9966-5517
  • Search for other articles:
  • degruyter.comGoogle Scholar
and Genly Leon
  • Corresponding author
  • Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla, 1280, Antofagasta, Chile
  • Email
  • Search for other articles:
  • degruyter.comGoogle Scholar

Abstract

We perform a detailed study of the integrability of the Hořava-Lifshitz scalar field cosmology in a Friedmann-Lemaître-Robertson-Walker background space-time. The approach we follow to determine the integrability is that of singularity analysis. More specifically, we test whether the gravitational field equations possess the Painlevé property. For the exponential potential of the scalar field, we are able to perform an analytic explicit integration of the field equations and write the solution in terms of a Laurent expansion and more specifically write the solution in terms of right Painlevé series.

  • [1]

    P. Horava, Phys. Rev. D, vol. 79, no. 1, 2009, Art no. 084008.

  • [2]

    W. Donnelly and T. Jacobson, Phys. Rev. D, vol. 82, 2010, Art no. 064032.

  • [3]

    W. Donnelly and T. Jacobson, Phys. Rev. D, vol. 82, 2010, Art no. 081501 .

  • [4]

    I. Carruthers and T. Jacobson, Phys. Rev. D, vol. 83, 2011, Art no. 024034.

  • [5]

    D. Garfinkle and T. Jacobson, Phys. Rev. Lett., vol. 107, 2011, Art no. 191102.

  • [6]

    T. Jacobson, Phys. Rev. D, vol. 81, 2010, Art no. 10502, Erratum: Phys. Rev. D, vol. 82, 2010, Art no. 129901.

  • [7]

    J.D. Barrow, Phys. Rev. D, vol. 85, 2012, Art no. 047503.

  • [8]

    A.R. Solomon and J.D. Barrow, Phys. Rev. D, vol. 89, 2014, Art no. 024001.

  • [9]

    X. Meng and X. Du, Phys. Lett. B, vol. 710, 2012, pp. 493.

    • Crossref
    • Export Citation
  • [10]

    A. Wang, Int. J. Mod. Phys. D, vol. 26, 2017, Art no. 1730014.

  • [11]

    N. A. Nilsson and E. Czuchry, Phys. Dark Univ., vol. 23, 2019, Art no. 100253.

  • [12]

    O. Luongo, G. Battista Pisani and H. Quevedo, Phys. Rev. D, vol. 93, 2016, Art no. 064057.

  • [13]

    O. Luongo, M. Muccino and H. Quevedo, arXiv: Phys. Dark Univ., vol. 25, 2019, Art no. 100313.

  • [14]

    G. Calgani, JHEP, vol. 09, 2009, pp. 112.

  • [15]

    E. Kiritsis and G. Kofinas, Nucl. Phys. B, vol. 821, 2009, pp. 467.

    • Crossref
    • Export Citation
  • [16]

    S. Mukohyama, Class. Quantum Grav., vol. 27, 2010, Art no. 223101.

  • [17]

    E.N. Saridakis, IJMPD, vol. 20, 2011, pp. 1485.

  • [18]

    T. Christodoulakis and N. Dimakis, J. Geom. Phys., vol. 62, 2012, pp. 2401.

    • Crossref
    • Export Citation
  • [19]

    B. Vakili and V. Kord, Gen. Rel. Gravit., vol. 45, 2013, pp. 1313.

    • Crossref
    • Export Citation
  • [20]

    D. Saez-Gomez, J. Phys. Conf. Ser., vol. 314, 2011, Art no. 012055.

  • [21]

    M. Fukushima, Y. Misonoh, S. Miyashita and S. Sato, Phys. Rev. D, vol. 99, 2019, Art no. 064004.

    • PubMed
    • Export Citation
  • [22]

    H. Shababi and P. Pedram, IJMPD, vol. 26, 2017, Art no. 1750081.

  • [23]

    G. Leon and A. Paliathanasis, Extended phase-space analysis of the Hořava-Lifshitz cosmology, EPJC, vol. 79, 2019, pp. 746.

    • Crossref
    • Export Citation
  • [24]

    V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, Springer, second edition, 1989.

  • [25]

    J. Llibre and C. Valls, J. Nonl. Math. Phys., vol. 20, 2013, pp. 394.

    • Crossref
    • Export Citation
  • [26]

    A. Gierzkiewicz and Z.A. Golda, J. Nonl. Math. Phys., vol. 23, 2016, pp. 494.

    • Crossref
    • Export Citation
  • [27]

    A. Paliathanasis and P. G. L. Leach, Phys. Lett. A, vol. 381, 2017, pp. 1277.

    • Crossref
    • Export Citation
  • [28]

    N. Dimakis, P.A. Terzis, and T. Christodoulakis, Phys. Rev. D, vol. 99, 2019, Art no. 023536.

    • PubMed
    • Export Citation
  • [29]

    A. Paliathanasis, Class. Quantum Grav., vol. 33, 2012, Art no. 075012.

  • [30]

    M. Tsamparlis and A. Paliathanasis, Symmetry, vol. 10, 2018, pp. 233.

    • Crossref
    • Export Citation
  • [31]

    A. Zampeli, T. Pailas, P.A. Terzis, and T. Christodoulakis, JCAP, vol. 16, 2016, pp. 066.

  • [32]

    N. Dimakis, P.A. Terzis, A. Zampeli, and T. Christodoulakis, Phys. Rev. D, vol. 94, 2016, Art no. 064013.

  • [33]

    A. Paliathanasis, A. Zampeli, T. Christodoulakis, and M.T. Mustafa, Class. Quantum Grav., vol. 35, 2018, Art no. 125005.

  • [34]

    T. Christodoulakis, A. Karagiorgos, and A. Zampeli, Symmetry, vol. 10, 2018, pp. 70.

    • Crossref
    • Export Citation
  • [35]

    M.J. Ablowitz, A. Ramani, and H. Segur, Lettere al Nuovo Cimento, vol. 23, 1978, pp. 333.

    • Crossref
    • Export Citation
  • [36]

    M.J. Ablowitz, A. Ramani, and H. Segur, J. Math. Phys., vol. 21, 1980, pp. 715.

    • Crossref
    • Export Citation
  • [37]

    M.J. Ablowitz, A. Ramani, and H. Segur, J. Math. Phys., vol. 21, 1980, pp. 1006.

    • Crossref
    • Export Citation
  • [38]

    J. Miritzis, P.G.L. Leach, and S. Cotsakis, Grav. Cosmol., vol. 6, 2000, pp. 282.

  • [39]

    A. Helmi and H. Vucetich, Phys. Lett. A, vol. 230, 1997, pp. 153.

    • Crossref
    • Export Citation
  • [40]

    S. Cotsakis and P.G.L. Leach, J. Phys A, vol. 27, 1994, pp. 1625.

    • Crossref
    • Export Citation
  • [41]

    P.G.L. Leach, S. Cotsakis, and J. Miritzis, Grav. Cosmol., vol. 7, 2000, pp. 311.

  • [42]

    J. Demaret and C. Scheen, J. Math. Phys. A: Math. Gen., vol. 29, 1996, pp. 59.

    • Crossref
    • Export Citation
  • [43]

    F. Christiansen, H.H. Rugh, and S.E. Rugh, J. Phys. A: Math. Gen., vol. 28, 1995, pp. 657.

  • [44]

    T. Bountis and L. Drossos, On the non-integrability of the mixmaster universe model. In: Simó C. (eds) Hamiltonian Systems with Three or More Degrees of Freedom. NATO ASI Series (Series C:Mathematical and Physical Sciences), vol. 533. Springer, Dordrecht, 1999.

  • [45]

    S. Cotsakis, J. Demaret, Y. De Rop, and L. Querella, Phys. Rev. D, vol. 48, 1993, pp. 4595.

    • Crossref
    • Export Citation
  • [46]

    A. Paliathanasis and P.G.L. Leach, Phys. Lett. A, vol. 380, 2016, pp. 2815.

    • Crossref
    • Export Citation
  • [47]

    A. Paliathanasis, EPJC, vol. 77, 2017, pp. 438.

  • [48]

    A. Paliathanasis, J.D. Barrow, and P.G.L. Leach, Phys. Rev. D, vol. 94, 2016, Art no. 023525.

  • [49]

    A. Paliathanasis, J.D. Barrow, and S. Pan, Phys. Rev. D, vol. 95, 2017, Art no. 103516.

  • [50]

    S. Cotsakis, G. Kolionis, and A. Tsokaros, Phys. Lett. B, vol. 721, 2013, pp. 1.

    • Crossref
    • Export Citation
  • [51]

    S. Cotsakis, S. Kadry, G. Kolionis, and A. Tsokaros, Phys. lett. B, vol. 755, 2016, pp. 387.

    • Crossref
    • Export Citation
  • [52]

    G. Leon and E. N. Saridakis, JCAP, vol. 911, 2009, pp. 006.

  • [53]

    J. Latta, G. Leon, and A. Paliathanasis, JCAP, vol. 11, 2016, pp. 051.

  • [54]

    R. Conte, The Painlevé approach to nonlinear ordinary differential equations, in R. Conte (eds) The Painlevé Property: One Century Later, CRM Series in Mathematics, Springer-Verlag, New York, 1999.

  • [55]

    A. Ramani, B. Grammaticos, and T. Bountis, Phys. Rep., vol. 180, 1989, pp. 159.

    • Crossref
    • Export Citation
Purchase article
Get instant unlimited access to the article.
$42.00
Log in
Already have access? Please log in.


or
Log in with your institution

Journal + Issues

A Journal of Physical Sciences: Zeitschrift für Naturforschung A (ZNA) is an international scientific journal which publishes original research papers from all areas of experimental and theoretical physics. In accordance with the name of the journal, which means “Journal for Natural Sciences”, manuscripts submitted to ZNA should have a tangible connection to actual physical phenomena.

Search