Academia.eduAcademia.edu

Outline

Title
Abstract
Definitions and Basic Results
Results for Planar Systems
Analysis in the Limit Φ → ∞
Numerical Evidence of the Result of Theorem 26
Case Γ = 1
Conclusion
Cosmological Implications and Discussion: Model 1
Cosmological Implications and Discussion: Model 2
Cosmological Implications and Discussion: Model 3
Cosmological Implications and Discussion: Model 4
Phase-Space Analysis of Hořava-Lifshitz Cosmology
Detailed Balance: Phase-Space Analysis
Case 1: Flat Universe with Λ = 0
Case 2: Non-Flat Universe with Λ = 0
Case 3: Flat Universe with Λ = 0
Finite Analysis
Analysis at Infinity
Beyond Detailed Balance: Phase Space Analysis
Cosmological Implications: Beyond Detailed Balance
Introduction
Phase-Space Analysis
Conclusions
References

Cosmological dynamical systems

Profile image of Carlos R. FadragasCarlos R. Fadragas

Abstract

In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and useful tools from the qualitative theory of dynamical systems. They provide the theoretical basis for the qualitative study of concrete cosmological models. Chapters 1 and 2 are a review of well-known results. Chapters 3, 4, 5 and 6 are devoted to our main results. In these chapters are extended and settled in a substantially different, more strict mathematical language, several results obtained by one of us in arXiv:0812.1013 [gr-qc]; arXiv:1009.0689 [gr-qc]; arXiv:0904.1577[gr-qc]; and arXiv:0909.3571 [hep-th]. In chapter 6, we provide a different approach to the subject discussed in astro-ph/0503478. Additionally, we perform a Poincar\'e compactification process allowing to construct a global phase space containing all the cosmological info...

Related papers

Dynamical systems approach to G 2 cosmology
Claes Uggla

Classical and Quantum Gravity, 2002

In this paper we present a new approach for studying the dynamics of spatially inhomogeneous cosmological models with one spatial degree of freedom. By introducing suitable scale-invariant dependent variables we write the evolution equations of the Einstein field equations as a system of autonomous partial differential equations in first-order symmetric hyperbolic format, whose explicit form depends on the choice of gauge. As a first application, we show that the asymptotic behaviour near the cosmological initial singularity can be given a simple geometrical description in terms of the local past attractor on the boundary of the scale-invariant dynamical state space. The analysis suggests the name "asymptotic silence" to describe the evolution of the gravitational field near the cosmological initial singularity.

View PDFchevron_right
Dynamical system of cosmological models for different possibilities of G and
Chingtham Sonia

2022

The present paper deals with the dynamics of spatially flat Friedmann-LemâıtreRobertson-Walker (FLRW ) cosmological model with a time varying cosmological constant Λ where Λ evolves with the cosmic time t through the Hubble parameter H , that is, Λ(H). We consider that the model dynamics has a reflection symmetry H → −H with Λ(H) expressed in the form of Taylor series with respect to H . Dynamical systems for three different cases based on the possibilities of gravitational constant G and the vacuum energy density ρΛ have been analysed. In case I, both G and ρΛ are taken to be constant. We analyse stability of the system by using the notion of spectral radius, behavior of perturbation along each of the axis with respect to cosmic time and Poincaré sphere. In case II, we have dynamical system analysis for G=constant and ρΛ 6=constant where we study stability by using the concept of spectral radius and perturbation function. In case III, we take G 6= constant and ρΛ 6= constant where ...

View PDFchevron_right
Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar Field
Chingtham Sonia

Advances in High Energy Physics, 2020

The stability criteria for the dynamical system of a homogeneous and isotropic cosmological model are investigated with the interaction of a scalar field in the presence of a perfect fluid. In this paper, we depict the dynamical system perspective to study qualitatively the scalar field cosmology under two special cases, with and without potential. In the absence of potential, we get a two-dimensional dynamical system, and we study the analytical as well as geometrical behavior. For the dynamical system with potential, we analyze different potential forms: simple exponential potential form (Vϕ=Voe−λϕ), double exponential potential form Vϕ=Voexp−Aexp2αϕ, and inverse power law potential form (Vϕ=Voϕ−α). We generate an autonomous system of ordinary differential equations (ASODE) for each case by introducing new dimensionless variables and obtain respective fixed points. We also analyze the type, nature, and stability of the fixed points and how their behavior reflects towards the cosmo...

View PDFchevron_right
Lectures on Mathematical Cosmology
Hans-jürgen Schmidt

We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.

View PDFchevron_right
Matter and dynamics in closed cosmologies
Claes Uggla

Physical Review D, 2005

To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on locally rotationally symmetric Bianchi type IX and Kantowski-Sachs orthogonal perfect fluid models, since such models exhibit a particularly rich dynamical structure and also illustrate typical features of more general cases. For these models, we recast Einstein's field equations into a regular system on a compact state space, which is the basis for our analysis. We prove that models expand from a singularity and recollapse to a singularity when the perfect fluid satisfies the strong energy condition. When the matter source admits Einstein's static model, we present a comprehensive dynamical description, which includes asymptotic behavior, of models in the neighborhood of the Einstein model; these results make earlier claims about "homoclinic phenomena and chaos" highly questionable. We also discuss aspects of the global asymptotic dynamics, in particular, we give criteria for the collapse to a singularity, and we describe when models expand forever to a state of infinite dilution; possible initial and final states are analyzed. Numerical investigations complement the analytical results.

View PDFchevron_right
A Modified Dynamical Model of Cosmology I Theory
Hossein Shenavar

2018

A modified dynamical model of cosmology is derived based on imposing Neumann boundary condition on cosmological perturbation equations. Then, it is shown that a new term appears in the equation of motion which leads to a modified Poisson equation with a new density term. In addition, a modified Hubble parameter due to the presence of this new density term is derived. Moreover, it is proved that, without a cosmological constant, such model has a late time accelerated expansion with an equation of state converging to w<-1. Also, the luminosity distance in the present model is shown to differ from that of the LCDM model at high red shifts. Furthermore, it is found that the adiabatic sound speed squared is positive in radiation dominated era and then converges to zero at later times. We bound the parameters of the model based on Type Ia Supernovae, Hubble parameter data and the age of the oldest stars. Theoretical implications of Neumann boundary condition has been discussed and it i...

View PDFchevron_right
The Dynamic Universe – Space as a Spherically Closed Energy System
Tuomo Suntola

The Dynamic Universe model comprises a holistic view and detailed study of space as a spherically closed 3-dimensional energy system in a 4-dimensional universe. It is based on zero-energy balance of motion and gravitation of space as a 3D surface of a 4-sphere -contracting and expanding in the direction of the 4-radius. Such a dynamic solution shows the rest energy of mass in space as the energy of motion mass possesses due to the expansion. DU shows relativity as a consequence of the conservation of total energy and the zero-energy balance in interactions in space, and allows the derivation of physical and cosmological predictions in relatively simple mathematics -with no need to rely on kinematically derived coordinate transformations. The postulates DU employs do not include the principle of relativity, the equivalence principle, or assumptions about the constancy of the velocity of light. Yet, for local phenomena, including near space, DU predictions are essentially the same as the corresponding predictions given by the special and general theories of relativity. Cosmology predictions in DU fit with observations without the need to free parameters like mass density and dark energy used in Friedman-Lemaître-Robertson-Walker (FLRW) cosmology. The Dynamic Universe model offers plausible basis for philosophical considerations and leads to an intelligible picture of physical reality from quantum phenomena to the cosmological structure and development of space. The universe in this model presents itself as an intricately ordered whole where local structures and expressions of energy and matter are inseparably connected to the rest of space.

View PDFchevron_right
A Modified Dynamical Model of Cosmology
Kurosh Javidan

2018

A modified dynamical model of cosmology is derived based on imposing Neumann boundary condition on cosmological perturbation equations. Then, it is shown that a new term appears in the equation of motion which leads to a modified Poisson equation with a new density term. In addition, a modified Hubble parameter due to the presence of this new density term is derived. Moreover, it is proved that, without a cosmological constant, such model has a late time accelerated expansion with an equation of state converging to w<-1. Also, the luminosity distance in the present model is shown to differ from that of the LCDM model at high red shifts. Furthermore, it is found that the adiabatic sound speed squared is positive in radiation dominated era and then converges to zero at later times. We bound the parameters of the model based on Type Ia Supernovae, Hubble parameter data and the age of the oldest stars. Theoretical implications of Neumann boundary condition has been discussed and it i...

View PDFchevron_right
Cosmology in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>Q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> gravity: A unified dynamical systems analysis of the background and perturbations
JIbitesh Dutta

Physical review, 2023

View PDFchevron_right
Dynamics of the $\Lambda$CDM model of the universe from the aspect of the dynamical systems theory
Zarko Mijajlovic

arXiv (Cornell University), 2022

In this paper we exploit the theory of the dynamical systems to study the dynamics of the standard cosmological model of the universe, which is known as the ΛCDM model. We assume that the matter content in our universe consists of barotropic perfect fluids without mutual interaction. Furthermore, we present the appropriate physical interpretation, as well as new dependencies between the scale expansion factor of the universe and cosmological density parameters.

View PDFchevron_right

References (509)

  1. A. A. Coley. Dordrecht, Netherlands: Kluwer (2003) 200 p.
  2. E. Komatsu et al., arXiv:1001.4538 [astro-ph.CO].
  3. M. Kowalski et al. [Supernova Cosmology Project Collaboration], Astrophys. J. 686, 749 (2008);
  4. S. W. Allen, D. A. Rapetti, R. W. Schmidt, H. Ebeling, G. Morris and A. C. Fabian, Mon. Not. Roy. Astron. Soc. 383, 879 (2008);
  5. K. N. Abazajian et al. [SDSS Collaboration], Astrophys. J. Suppl. 182, 543 (2009);
  6. N. Jarosik et al., arXiv:1001.4744 [astro-ph.CO].
  7. S. Perlmutter et al. Astrophys. J., 517:565-586, 1999.
  8. C. L. Bennett et al. Astrophys. J. Suppl., 148:1, 2003.
  9. M. Tegmark et al. Phys. Rev., D69:103501, 2004.
  10. S. W. Allen, R. W. Schmidt, H. Ebeling, A. C. Fabian, and L. van Speybroeck. Mon. Not. Roy. Astron. Soc., 353:457, 2004.
  11. Max Tegmark et al., Astrophys. J. 606 (2004), 702-740.
  12. E. Komatsu et al., Astrophys. J. Suppl. 148 (2003), 119-134.
  13. G. Hinshaw et al., Astrophys. J. Suppl. 148 (2003), 135.
  14. D. N. Spergel et al., Astrophys. J. Suppl. 148 (2003), 175.
  15. H. V. Peiris et al., Astrophys. J. Suppl. 148 (2003), 213.
  16. Adam G. Riess et al., Astron. J. 116 (1998), 1009-1038.
  17. Adam G. Riess et al., Astrophys. J. 607 (2004), 665-687.
  18. H. K. Jassal, J. S. Bagla, and T. Padmanabhan, Mon. Not. Roy. Astron. Soc. 356 (2005), L11-L16.
  19. W. L. Freedman et al. [HST Collaboration], Astrophys. J. 553, 47 (2001)
  20. J. R. Mould et al., Astrophys. J. 529, 786 (2000)
  21. T. Roy Choudhury and T. Padmanabhan, Astron. Astrophys. 429 (2005), 807.
  22. E. J. Copeland, M. Sami, and S. Tsujikawa. Int. J. Mod. Phys., D15:1753-1936, 2006.
  23. R. R. Caldwell and M. Kamionkowski. Ann. Rev. Nucl. Part. Sci., 59:397-429, 2009.
  24. M. S. Turner and D. Huterer. J. Phys. Soc. Jap., 76:111015, 2007.
  25. U. Alam, V. Sahni, and A. A. Starobinsky. JCAP, 0406:008, 2004.
  26. V. Sahni. Class. Quant. Grav., 19:3435-3448, 2002.
  27. S. M. Carroll, W. H. Press, and E. L. Turner. Ann. Rev. Astron. Astrophys., 30:499- 542, 1992.
  28. V. Sahni and A. A. Starobinsky. Int. J. Mod. Phys., D9:373-444, 2000.
  29. S. Weinberg. Rev. Mod. Phys., 61:1-23, 1989.
  30. S. Tsujikawa. Phys. Rev., D73:103504, 2006.
  31. S. Tsujikawa. Phys. Rev., D72:083512, 2005.
  32. L. Amendola, C. Quercellini, and E. Giallongo. Mon. Not. Roy. Astron. Soc., 357:429-439, 2005.
  33. C. Beck. Physica, A340:459-466, 2004.
  34. I. Maor and R. Brustein. Phys. Rev., D67:103508, 2003.
  35. M. Sami. arXiv: 0901.0756 [hep-th].
  36. J. S. Alcaniz. Braz. J. Phys., 36:1109, 2006.
  37. P. D. Mannheim. Prog. Part. Nucl. Phys., 56:340-445, 2006.
  38. T. Padmanabhan, Current Science, 88 7, 1057, (2005).
  39. T. Matos, de que est hecho el universo? materia oscura y energa oscura, Fondo de Cultura Econmica, S. A., 2004.
  40. K. Freese and M. Lewis, Phys. Lett. B540 (2002), 1-8.
  41. S. Nesseris and L. Perivolaropoulos, JCAP 0701, 018 (2007) [arXiv:astro- ph/0610092].
  42. A. Melchiorri, L. Mersini-Houghton, C. J. Odman, and M. Trodden, Phys. Rev. D68 (2003), 043509.
  43. A. Vikman, Phys. Rev. D71 (2005), 023515.
  44. R. Curbelo, T. Gonzalez, G. Leon, and I. Quiros, Class. Quant. Grav. 23 (2006), 1585-1602.
  45. E. Elizalde, S. Nojiri and S. D. Odintsov, Phys. Rev. D 70, 043539 (2004)
  46. P. S. Apostolopoulos and N. Tetradis, Phys. Rev. D 74, 064021 (2006)
  47. K. Bamba, S. Nojiri and S. D. Odintsov, Phys. Rev. D 77, 123532 (2008)
  48. K. Bamba, C. Q. Geng, S. Nojiri and S. D. Odintsov, Phys. Rev. D 79, 083014 (2009)
  49. M. R. Setare and E. N. Saridakis, JCAP 0903, 002 (2009)
  50. B. Feng, X. L. Wang and X. M. Zhang, Phys. Lett. B 607, 35 (2005);
  51. Z. K. Guo, et al., Phys. Lett. B 608, 177 (2005);
  52. B. Feng, M. Li, Y.-S. Piao and X. Zhang, Phys. Lett. B 634, 101 (2006);
  53. W. Zhao and Y. Zhang, Phys. Rev. D 73, 123509 (2006);
  54. M. R. Setare and E. N. Saridakis, Phys. Lett. B 668, 177 (2008);
  55. M. R. Setare and E. N. Saridakis, JCAP 0809, 026 (2008);
  56. Y. F. Cai, E. N. Saridakis, M. R. Setare and J. Q. Xia, Phys. Rept. 493, 1 (2010).
  57. H. Wei and R. G. Cai, Phys. Lett. B 634, 9 (2006).
  58. H. M. Sadjadi and M. Alimohammadi, Phys. Rev. D 74, 043506 (2006).
  59. M. R. Setare and E. N. Saridakis, JCAP 0809, 026 (2008)
  60. M. R. Setare and E. N. Saridakis, Phys. Rev. D 79, 043005 (2009)
  61. Z.-K. Guo, Y.-S. Piao, X.-M. Zhang, and Y.-Z. Zhang. Phys. Lett., B608:177-182, 2005.
  62. X.-F. Zhang, H. Li, Y.-S. Piao, and X.-M. Zhang. Mod. Phys. Lett., A21:231-242, 2006.
  63. Wei H. and Cai R. G., 2005, Phys. Rev. D 72, 123507 [arXiv:astro-ph/0509328].
  64. Wei H., Cai R. G. and Zeng D. F., 2005, Class. Quant. Grav. 22, 3189 [arXiv:hep- th/0501160].
  65. R. Lazkoz and G. Leon. Phys. Lett., B638:303-309, 2006.
  66. Y. f. Cai, M. z. Li, J. X. Lu, Y. S. Piao, T. t. Qiu and X. m. Zhang, Phys. Lett. B 651, 1 (2007)
  67. S. Zhang and B. Chen, arXiv:0806.4435 [hep-ph].
  68. J. Sadeghi, M. R. Setare, A. Banijamali and F. Milani, Phys. Lett. B 662, 92 (2008).
  69. Y. F. Cai and J. Wang, Class. Quant. Grav. 25, 165014 (2008).
  70. E. N. Saridakis, P. F. Gonzalez-Diaz and C. L. Siguenza, Class. Quant. Grav. 26, 165003 (2009)
  71. Lazkoz R., Leon G. and Quiros I., Phys. Lett. B 649, 103 (2007).
  72. M. Alimohammadi and H. M. Sadjadi, Phys. Lett. B 648, 113 (2007).
  73. M. Alimohammadi, Gen. Rel. Grav. 40, 107 (2008).
  74. M. R. Setare and E. N. Saridakis, Int. J. Mod. Phys. D 18, 549 (2009).
  75. X. Zhang, Int. J. Mod. Phys. D 14, 1597 (2005).
  76. X. Zhang and F. Q. Wu, Phys. Rev. D 72, 043524 (2005)
  77. X. Zhang, Phys. Rev. D 74, 103505 (2006).
  78. E. N. Saridakis, Phys. Lett. B 661, 335 (2008).
  79. M. R. Setare and E. N. Saridakis, Phys. Lett. B 671, 331 (2009).
  80. S. Nojiri and S. D. Odintsov, eConf C0602061, 06 (2006) [Int. J. Geom. Meth. Mod. Phys. 4, 115 (2007)]
  81. S. M. Carroll et al. Phys. Rev., D71:063513, 2005.
  82. S. M. Carroll, V. Duvvuri, M. Trodden, and M. S. Turner. Phys. Rev., D70:043528, 2004.
  83. S. Capozziello, V. F. Cardone, S. Carloni, and A. Troisi. Int. J. Mod. Phys., D12:1969-1982, 2003.
  84. S. Capozziello, S. Carloni, and A. Troisi. Recent Res. Dev. Astron. Astrophys., 1:625, 2003.
  85. S. Capozziello and M. Francaviglia. Gen. Rel. Grav., 40:357-420, 2008.
  86. D. Wands. Class. Quant. Grav., 11:269-280, 1994.
  87. S. Capozziello, A. Stabile, and A. Troisi. Phys. Lett., B686:79-83, 2010.
  88. S. Capozziello, M. De Laurentis, M. Francaviglia, and S. Mercadante. 2009.
  89. S. Capozziello, M. De Laurentis, and V. Faraoni. arXiv: 0909.4672 [gr-qc].
  90. S. Capozziello. PoS, QG-PH:015, 2007.
  91. S. Capozziello, E. Elizalde, S. Nojiri, and S. D. Odintsov. Phys. Lett., B671:193- 198, 2009.
  92. S. Capozziello. Int. J. Mod. Phys., D11:483-492, 2002.
  93. V. Faraoni. Phys. Rev., D72:124005, 2005.
  94. M. Luca Ruggiero and L. Iorio. JCAP, 0701:010, 2007.
  95. A. de la Cruz-Dombriz and A. Dobado. Phys. Rev., D74:087501, 2006.
  96. N. J. Poplawski. Phys. Rev., D74:084032, 2006.
  97. A. W. Brookfield, C. van de Bruck, and L. M. H. Hall. Phys. Rev., D74:064028, 2006.
  98. Y.-S. Song, W. Hu, and I. Sawicki. Phys. Rev., D75:044004, 2007.
  99. B. Li, K. C. Chan, and M. C. Chu. Phys. Rev., D76:024002, 2007.
  100. T. P. Sotiriou. Class. Quant. Grav., 23:5117-5128, 2006.
  101. O. Bertolami and M. Carvalho Sequeira. AIP Conf. Proc., 1241:729-734, 2010.
  102. O. Bertolami and M. Carvalho Sequeira. Phys. Rev., D79:104010, 2009.
  103. O. Bertolami, C. G. Boehmer, T. Harko, and F. S. N. Lobo. Phys. Rev., D75:104016, 2007.
  104. F. Briscese, E. Elizalde, S. Nojiri, and S. D. Odintsov. Phys. Lett., B646:105-111, 2007.
  105. G. Leon, E. N. Saridakis, Class. Quant. Grav. 28, 065008 (2011).
  106. R. Kerner. Gen. Rel. Grav., 14:453-469, 1982.
  107. J. P. Duruisseau and R. Kerner. Class. Quant. Grav., 3:817-824, 1986.
  108. P. Teyssandier. Class. Quant. Grav., 6:219-229, 1989.
  109. G. Magnano, M. Ferraris, and M. Francaviglia. Gen. Rel. Grav., 19:465, 1987.
  110. S. Capozziello, V. F. Cardone, and A. Troisi. JCAP, 0608:001, 2006.
  111. K. Maeda and N. Ohta. Phys. Lett., B597:400-407, 2004.
  112. K. Maeda and N. Ohta. Phys. Rev., D71:063520, 2005.
  113. N. Ohta. Int. J. Mod. Phys., A20:1-40, 2005.
  114. K. Akune, K. Maeda, and N. Ohta. Phys. Rev., D73:103506, 2006.
  115. S. Capozziello, V. F. Cardone, and A. Troisi. Mon. Not. Roy. Astron. Soc., 375:1423-1440, 2007.
  116. S. Carloni, P. K. S. Dunsby, S. Capozziello, and A. Troisi. Class. Quant. Grav., 22:4839-4868, 2005.
  117. S. Carloni, S. Capozziello, J. A. Leach, and P. K. S. Dunsby. Class. Quant. Grav., 25:035008, 2008.
  118. S. Carloni, P. K. S. Dunsby, and A. Troisi. arXiv: 0906.1998 [gr-qc].
  119. S. Carloni, A. Troisi, and P. K. S. Dunsby. Gen. Rel. Grav., 41:1757-1776, 2009.
  120. J. A. Leach, S. Carloni, and P. K. S. Dunsby. Class. Quant. Grav., 23:4915-4937, 2006.
  121. J. A. Leach, P. K. S. Dunsby, and S. Carloni. arXiv: gr-qc/0702122.
  122. N. Goheer, J. A. Leach, and P. K. S. Dunsby. Class. Quant. Grav., 25:035013, 2008.
  123. N. Goheer, J. A. Leach, and P. K. S. Dunsby. Class. Quant. Grav., 24:5689-5708, 2007.
  124. N. Goheer, R. Goswami, and P. K. S. Dunsby. Class. Quant. Grav., 26:105003, 2009.
  125. R. Goswami, N. Goheer, and P. K. S. Dunsby. Phys. Rev., D78:044011, 2008.
  126. J. Miritzis. Phys. Rev., D79: 068501, 2009.
  127. M. Abdelwahab, S Carloni, and P K. S. Dunsby. Class. Quant. Grav., 25:135002, 2008.
  128. L. Randal, R. Sundrum, Phys. Rev. Lett. 83 (1999) 4690.
  129. L. Randal, R. Sundrum, Phys. Rev. Lett. 83 (1999) 3370.
  130. R. M. Hawkins and J. E. Lidsey, Phys.Rev. D63, 041301 (2001), gr-qc/0011060.
  131. G. Huey and J. E. Lidsey, Phys. Lett. B514, 217 (2001), astro-ph/0104006.
  132. G. Huey and J. E. Lidsey, Phys. Rev. D66, 043514 (2002), astro-ph/0205236.
  133. T. Gonzalez, T. Matos, I. Quiros, and A. Vazquez-Gonzalez, Phys. Lett. B676, 161 (2009), 0812.1734.
  134. Y. Leyva, D. Gonzalez, T. Gonzalez, T. Matos, and I. Quiros, Phys. Rev. D80, 044026 (2009), 0909.0281.
  135. W. Fang, Y. Li, K. Zhang, and H.-Q. Lu, Class. Quant. Grav. 26, 155005 (2009), 0810.4193.
  136. R. Garcia-Salcedo, T. Gonzalez, C. Moreno, and I. Quiros, Class. Quant. Grav. 28, 105017 (2011).
  137. P. Horava, arXiv:0811.2217 [hep-th].
  138. P. Horava, JHEP 0903, 020 (2009) [arXiv:0812.4287 [hep-th]].
  139. P. Horava, Phys. Rev. D 79, 084008 (2009) [arXiv:0901.3775 [hep-th]].
  140. P. Hořava, arXiv:0902.3657 [hep-th].
  141. G. Leon. Class. Quant. Grav., 26:035008, 2009.
  142. G. Leon, Pavel Silveira and Carlos R. Fadragas, "Phase-space of flat Friedmann- Robertson-Walker models with both a scalar field coupled to matter and radia- tion", In: Classical and Quantum Gravity: Theory, Analysis and Applications, Editor: Vincent R. Frignanni, ISBN 978-1-61122-957-8, Nova Science Publish- ers, Inc. (2010) [arXiv:1009.0689 [gr-qc]].
  143. G. Leon, Y. Leyva, E. N. Saridakis, O. Martin and R. Cardenas, Falsifying Field- based Dark Energy Models. In Dark Energy: Theories, Developments, and Im- plications, Editor: Karl Lefebvre and Raoul Garcia, ISBN: 978-1-61668-271-2, Nova Science Publishers, Inc. (2010). arXiv:0912.0542 [gr-qc].
  144. D. Escobar, G. Leon, Y. Leyva, [arXiv:1110.1736 [gr-qc]].
  145. E. J. Copeland, A. R. Liddle, and D. Wands, Phys. Rev. D57, 4686 (1998), gr- qc/9711068.
  146. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, San Francisco, W. H. Freeman & Co., 1973.
  147. P. J. E. Peebles, Principles of physical cosmology, Princeton, USA: Univ. Pr. (1993).
  148. A. Campos, R. Maartens, D. Matravers, C. F. Sopuerta, Phys. Rev. D68, 103520 (2003). [hep-th/0308158].
  149. A. Campos, C. F. Sopuerta, Phys. Rev. D64, 104011 (2001). [hep-th/0105100].
  150. A. Campos, C. F. Sopuerta, Phys. Rev. D63, 104012 (2001). [hep-th/0101060].
  151. A. Campos, C. F. Sopuerta, [astro-ph/0102355].
  152. R. Maartens, V. Sahni, and T. D. Saini, Phys. Rev. D63 (2001) 063509, arXiv:0011105.
  153. R. M. Wald, Phys. Rev. D 28, 2118 (1983).
  154. Y. Kitada and K. i. Maeda, Phys. Rev. D 45, 1416 (1992);
  155. Y. Kitada and K. i. Maeda, Class. Quant. Grav. 10, 703 (1993);
  156. J. Ibanez, R. J. van den Hoogen and A. A. Coley, Phys. Rev. D 51, 928 (1995).
  157. S. Cotsakis and G. Flessas, Phys. Lett. B 319, 69 (1993);
  158. S. Capozziello and R. De Ritis, Int. J. Mod. Phys. D 5, 209 (1996);
  159. E. Guzman, Phys. Lett. B 391, 267 (1997);
  160. S. Cotsakis and J. Miritzis, Class. Quant. Grav. 15, 2795 (1998);
  161. T. Singh, Grav. Cosmol. 5, 49 (1999);
  162. B. C. Paul, Phys. Rev. D 66, 124019 (2002).
  163. G. Leon and E. N. Saridakis. JCAP, 0911:006, 2009.
  164. G. Leon and E. N. Saridakis, Phys.Lett. B 693:1, (2010)
  165. G. F. R. Ellis and H. van Elst, NATO Adv. Study Inst. Ser. C. Math. Phys. Sci. 541, 1 (1999)
  166. S. W. Hawking and G. F. R. Ellis, "The Large scale structure of space-time," Cambridge University Press, Cambridge, 1973
  167. R. d'Inverno, "Introducing Einstein's relativity," Oxford, UK: Clarendon (1992).
  168. R. M. Wald, "General Relativity," Chicago, Usa: Univ. Pr. ( 1984).
  169. J. Ehlers, Gen. Rel. Grav. 25, 1225 (1993) [Abh. Akad. Wiss. Lit. Mainz. Nat. Kl. 11, 793 (1961)].
  170. G. F. R. Ellis, "Relativistic cosmology," International School of Physics Enrico Fermi, Course 47: Proceedings. Edited by R.K. Sachs, Academic Press, London, 1971. pp. 104-182
  171. J. A. Wheeler, "Einsteins Vision," Springer, Berlin, 1968.
  172. M. Trodden and S. M. Carroll. arXiv: astro-ph/0401547.
  173. V. Sahni and A. Starobinsky, Int. J. Mod. Phys. D 15, 2105 (2006)
  174. T. Padmanabhan, Physics Reports 380, 235, (2003).
  175. C. F. Kolda and D. H. Lyth, Phys. Lett. B 458, 197 (1999) [arXiv:hep- ph/9811375].
  176. U. Alam, V. Sahni, T. D. Saini and A. A. Starobinsky, Mon. Not. Roy. Astron. Soc. 354, 275 (2004) [arXiv:astro-ph/0311364].
  177. B. Feng, X. L. Wang and X. M. Zhang, Phys. Lett. B 607, 35 (2005) [arXiv:astro- ph/0404224].
  178. R. R. Caldwell, Phys. Lett. B545, 23-29 (2002).
  179. Shin'ichi Nojiri and Sergei D. Odintsov, Phys. Lett. B562, 147-152 (2003).
  180. Sean M. Carroll, Mark Hoffman, and Mark Trodden, Phys. Rev. D68, 023509 (2003).
  181. H. P. Nilles, Phys. Rept. 110, 1 (1984).
  182. J. D. Barrow, Nucl. Phys. B 310, 743 (1988).
  183. M. D. Pollock, Phys. Lett. B 215, 635 (1988).
  184. I. Brevik, S. Nojiri, S. D. Odintsov and L. Vanzo, Phys. Rev. D 70, 043520 (2004).
  185. J. M. Cline, S. Jeon and G. D. Moore, Phys. Rev. D 70, 043543 (2004)
  186. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999).
  187. G. R. Dvali, G. Gabadadze and M. Porrati, Phys. Lett. B 485, 208 (2000).
  188. A. Lue and G. D. Starkman, Phys. Rev. D 70, 101501 (2004).
  189. V. K. Onemli and R. P. Woodard, Class. Quant. Grav. 19, 4607 (2002).
  190. L. P. Chimento and R. Lazkoz, Mod. Phys. Lett. A19, 2479-2484 (2004).
  191. R. R. Caldwell, M. Kamionkowski, and N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003).
  192. L. Fernndez-Jambrina and R. Lazkoz, Phys. Rev. D70, 121503 (2004)
  193. Shin'ichi Nojiri, Sergei D. Odintsov, and Shinji Tsujikawa, Phys. Rev. D71, 063004 (2005).
  194. L. Fernndez-Jambrina y R. Lazkoz, Phys. Rev. D74, 064030 (2006).
  195. Shin'ichi Nojiri and S. D. Odintsov, Phys. Rev. D70, 103522 (2004).
  196. Shin'ichi Nojiri and Sergei D. Odintsov, Phys. Lett. B595, 1-8 (2004).
  197. E. Elizalde, Shin'ichi Nojiri, and S. D. Odintsov, Phys. Rev. D70, 043539 (2004).
  198. B. McInnes, JHEP 08, 029 (2002).
  199. P.-X. Wu and H.-Wei Yu, Nucl. Phys. B727, 355-367 (2005).
  200. P. Singh, M. Sami, and N. Dadhich, Phys. Rev. D68, 023522 (2003).
  201. Z.-K. Guo and Y.-Z. Zhang, Phys. Rev. D71, 023501 (2005).
  202. R.-G. Cai and A. Wang, JCAP 0503, 002 (2005).
  203. C. M. Will. Theory and experiment in gravitational physics. Cambridge, UK: Univ. Pr. (1993) 380 p.
  204. N. Kaloper and K. A. Olive. Phys. Rev., D57:811-822, 1998.
  205. L. Amendola. Phys. Rev., D62:043511, 2000.
  206. L. Amendola, Phys. Rev. D60, 043501 (1999).
  207. R. Bean and J. Magueijo, Phys. Lett. B517, 177-183 (2001).
  208. L. P. Chimento, A. S. Jakubi, D. Pavon, and W. Zimdahl, Phys. Rev. D67, 083513 (2003).
  209. L. P. Chimento, A. S. Jakubi, and D. Pavon, Phys. Rev. D62, 063508 (2000).
  210. L. P. Chimento, A. S. Jakubi, and D. Pavon, Phys. Rev. D67, 087302 (2003).
  211. W. Zimdahl and D. Pavon, Phys. Lett. B521, 133-138 (2001).
  212. T. Gonzalez , G. Leon and I. Quiros, Class. Quant. Grav. 23, 3165 (2006).
  213. G. W. Anderson and S. M. Carroll, arXiv:astro-ph/9711288.
  214. T. Damour, G. W. Gibbons and C. Gundlach, Phys. Rev. Lett. 64, 123 (1990).
  215. J. A. Casas, J. Garcia-Bellido and M. Quiros, Class. Quant. Grav. 9, 1371 (1992)
  216. G. R. Farrar and P. J. E. Peebles, Astrophys. J. 604, 1 (2004).
  217. M. B. Hoffman, arXiv:astro-ph/0307350.
  218. X. Zhang, Mod. Phys. Lett. A 20, 2575 (2005).
  219. G. Leon and E. N. Saridakis, Phys. Lett. B 693:1, (2010)
  220. C. Brans and R. H. Dicke. Phys. Rev., 124:925-935, 1961.
  221. R. V. Wagoner. Phys. Rev., D1:3209-3216, 1970.
  222. J. O' Hanlon. J. Phys., A5:803-811, 1972.
  223. J. O' Hanlon and B. O. J. Tupper. Nuovo Cim., B7:305-312, 1972.
  224. J. D. Bekenstein. Phys. Rev., D15:1458-1468, 1977.
  225. P. G. Bergmann. Int. J. Theor. Phys., 1:25-36, 1968.
  226. K. Nordtvedt, Jr. Astrophys. J., 161:1059-1067, 1970.
  227. M. B. Green, C. M.Hull and P. K. Townsend, Phys. Lett. B 382, 65 (1996).
  228. A. Abramovici et al. Science, 256:325-333, 1992.
  229. A. Serna, J. M. Alimi, and A. Navarro. Class. Quant. Grav., 19:857-874, 2002.
  230. A. Serna and J. M. Alimi. Phys. Rev., D53:3087-3098, 1996.
  231. C. M. Will. Living Rev. Rel., 9:3, 2005.
  232. J. D. Barrow and Paul Parsons. Phys. Rev., D55:1906-1936, 1997.
  233. J. D. Barrow and K. Maeda. Nucl. Phys., B341:294-308, 1990.
  234. V. Faraoni and M. N. Jensen. Class. Quant. Grav., 23:3005-3016, 2006.
  235. A. R. Liddle and D. Wands. Phys. Rev., D45:2665-2673, 1992.
  236. D. La and P. J. Steinhardt. Phys. Rev. Lett., 62:376, 1989.
  237. C. Mathiazhagan and V. B. Johri. Class. Quant. Grav., 1:L29-L32, 1984.
  238. S. J. Kolitch. Ann. Phys., 246:121-132, 1996.
  239. C. Romero and A. Barros. Gen. Rel. Grav., 25:491-502, 1993.
  240. G. Magnano, M. Ferraris, and M. Francaviglia. Class. Quant. Grav., 7:557-570, 1990.
  241. S. Cotsakis. Phys. Rev., D47:1437-1439, 1993; Erratum Phys. Rev. D 49, 1145 (1994).
  242. P. Teyssandier. Phys. Rev., D52:6195-6197, 1995.
  243. H. J. Schmidt. Phys. Rev., D52:6198, 1995.
  244. S. Cotsakis. Phys. Rev., D52:6199-6200, 1995.
  245. S. Capozziello, R. de Ritis, and A. Angela Marino. Class. Quant. Grav., 14:3243- 3258, 1997.
  246. G. Magnano and L. M. Sokolowski. Phys. Rev., D50:5039-5059, 1994.
  247. V. Faraoni, E. Gunzig, and P. Nardone. Fund. Cosmic Phys., 20:121, 1999.
  248. V. Faraoni. Phys. Rev., D75:067302, 2007.
  249. V. Faraoni and S. Nadeau. Phys. Rev., D75:023501, 2007.
  250. Coley A. A., 1999, Gen. Rel. Grav. 31, 1295; Mimoso J. P. and Wands D., 1995, Phys. Rev. D 51, 477.
  251. T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82, 451 (2010).
  252. A. De Felice and S. Tsujikawa, Living Rev. Rel. 13, 3 (2010)
  253. A. D. Rendall. Class. Quant. Grav., 21:2445-2454, 2004.
  254. A. D. Rendall. Class. Quant. Grav., 24:667-678, 2007.
  255. A. D. Rendall. Class. Quant. Grav., 22:1655-1666, 2005.
  256. A. D. Rendall. Class. Quant. Grav., 23:1557-1570, 2006.
  257. L. Macnay. arXiv: 0810.3558 [gr-qc].
  258. R. Bean, D. Bernat, L. Pogosian, A. Silvestri, and M. Trodden. Phys. Rev., D75:064020, 2007.
  259. G. E. Volovik, arXiv:0904.4113 [gr-qc].
  260. R. G. Cai, Y. Liu and Y. W. Sun, arXiv:0904.4104 [hep-th].
  261. R. G. Cai, B. Hu and H. B. Zhang, arXiv:0905.0255 [hep-th].
  262. D. Orlando and S. Reffert, arXiv:0905.0301 [hep-th].
  263. T. Nishioka, arXiv:0905.0473 [hep-th].
  264. R. A. Konoplya, arXiv:0905.1523 [hep-th].
  265. T. P. Sotiriou, M. Visser and S. Weinfurtner, arXiv:0905.2798 [hep-th].
  266. C. Bogdanos and E. N. Saridakis, arXiv:0907.1636 [hep-th].
  267. J. Kluson, arXiv:0907.3566 [hep-th].
  268. N. Afshordi, arXiv:0907.5201 [hep-th].
  269. Y. S. Myung, arXiv:0907.5256 [hep-th].
  270. M. Li and Y. Pang, arXiv:0905.2751 [hep-th].
  271. M. Visser, arXiv:0902.0590 [hep-th].
  272. J. Chen and Y. Wang, arXiv:0905.2786 [gr-qc].
  273. B. Chen and Q. G. Huang, arXiv:0904.4565 [hep-th].
  274. F. W. Shu and Y. S. Wu, arXiv:0906.1645 [hep-th].
  275. C. Charmousis, G. Niz, A. Padilla and P. M. Saffin, JHEP 0908, 070 (2009).
  276. G. Calcagni, JHEP 0909, 112 (2009).
  277. E. Kiritsis and G. Kofinas, Nucl. Phys. B 821, 467 (2009).
  278. H. Lu, J. Mei and C. N. Pope, arXiv:0904.1595 [hep-th].
  279. H. Nastase, arXiv:0904.3604 [hep-th].
  280. E. O. Colgain and H. Yavartanoo, arXiv:0904.4357 [hep-th].
  281. A. Ghodsi, arXiv:0905.0836 [hep-th].
  282. M. Minamitsuji, arXiv:0905.3892 [astro-ph.CO].
  283. A. Ghodsi and E. Hatefi, arXiv:0906.1237 [hep-th].
  284. S. Mukohyama, JCAP 0906, 001 (2009);
  285. B. Chen, S. Pi and J. Z. Tang, JCAP 0908, 007 (2009).
  286. Y. S. Piao, arXiv:0904.4117 [hep-th].
  287. X. Gao, arXiv:0904.4187 [hep-th].
  288. B. Chen, S. Pi and J. Z. Tang, arXiv:0905.2300 [hep-th].
  289. X. Gao, Y. Wang, R. Brandenberger and A. Riotto, arXiv:0905.3821 [hep-th].
  290. A. Wang and R. Maartens, arXiv:0907.1748 [hep-th].
  291. T. Kobayashi, Y. Urakawa and M. Yamaguchi, arXiv:0908.1005 [astro-ph.CO].
  292. S. Mukohyama, K. Nakayama, F. Takahashi and S. Yokoyama, Phys. Lett. B 679, 6 (2009);
  293. T. Takahashi and J. Soda, arXiv:0904.0554 [hep-th].
  294. S. Koh, arXiv:0907.0850 [hep-th].
  295. R. Brandenberger, Phys. Rev. D 80, 043516 (2009);
  296. Y. F. Cai and E. N. Saridakis, JCAP 0910, 020 (2009).
  297. R. H. Brandenberger, arXiv:0905.1514 [hep-th].
  298. Y. F. Cai and E. N. Saridakis, arXiv:0906.1789 [hep-th].
  299. U. H. Danielsson and L. Thorlacius, JHEP 0903, 070 (2009);
  300. R. G. Cai, L. M. Cao and N. Ohta, Phys. Rev. D 80, 024003 (2009);
  301. A. Kehagias and K. Sfetsos, Phys. Lett. B 678, 123 (2009).
  302. R. G. Cai, L. M. Cao and N. Ohta, arXiv:0904.3670 [hep-th].
  303. Y. S. Myung and Y. W. Kim, arXiv:0905.0179 [hep-th].
  304. A. Kehagias and K. Sfetsos, arXiv:0905.0477 [hep-th];
  305. R. G. Cai, L. M. Cao and N. Ohta, Phys. Lett. B 679, 504 (2009);
  306. M. Jamil, E. N. Saridakis and M. R. Setare, JCAP 1011, 032 (2010).
  307. R. B. Mann, arXiv:0905.1136 [hep-th].
  308. G. Bertoldi, B. A. Burrington and A. Peet, arXiv:0905.3183 [hep-th].
  309. A. Castillo and A. Larranaga, arXiv:0906.4380 [gr-qc].
  310. M. Botta-Cantcheff, N. Grandi and M. Sturla, arXiv:0906.0582 [hep-th].
  311. H. W. Lee, Y. W. Kim and Y. S. Myung, arXiv:0907.3568 [hep-th].
  312. E. N. Saridakis, Eur. Phys. J. C 67, 229 (2010).
  313. M. i. Park, arXiv:0906.4275 [hep-th].
  314. A. Wang and Y. Wu, JCAP 0907, 012 (2009).
  315. C. Appignani, R. Casadio and S. Shankaranarayanan, arXiv:0907.3121 [hep-th].
  316. S. S. Kim, T. Kim and Y. Kim, Phys. Rev. D 80, 124002 (2009);
  317. T. Harko, Z. Kovacs and F. S. N. Lobo, arXiv:0908.2874 [gr-qc].
  318. C. B. Netterfield et al., Astrophys. J. 571, 604-614 (2002).
  319. D. J. H. Chung and K. Freese, Phys. Rev. D61, 023511 (2000).
  320. P. Gondolo and K. Freese, Phys. Rev. D68, 063509 (2003).
  321. D. Huterer and A. Cooray, Phys. Rev. D 71, 023506 (2005)
  322. D. Huterer and G. Starkman, Phys. Rev. Lett. 90, 031301 (2003).
  323. Y. Wang and M. Tegmark, Phys. Rev. Lett. 92, 241302 (2004).
  324. Y. Wang and P. Mukherjee, Astrophys. J. 606, 654 (2004).
  325. T. Padmanabhan and T. R. Choudhury, Mon. Not. Roy. Astron. Soc. 344, (2003).
  326. Z. H. Zhu, M. K. Fujimoto and X. T. He, Astron. Astrophys. 417, 833 (2004).
  327. M. Chevallier and D. Polarski, Int. J. Mod. Phys. D 10, 213 (2001).
  328. E. V. Linder, Phys. Rev. Lett. 90, 091301 (2003).
  329. S. Hannestad and E. Mortsell, JCAP 0409, 001 (2004).
  330. J. Q. Xia, B. Feng and X. M. Zhang, Mod. Phys. Lett. A 20, 2409 (2005).
  331. J. Q. Xia, G. B. Zhao, B. Feng, H. Li and X. Zhang, Phys. Rev. D 73, (2006).
  332. J. Q. Xia, G. B. Zhao, B. Feng and X. Zhang, JCAP 0609, 015 (2006).
  333. G. B. Zhao, J. Q. Xia, B. Feng and X. Zhang, Int. J. Mod. Phys. D 16, (2007).
  334. J. Q. Xia, G. B. Zhao, H. Li, B. Feng and X. Zhang, Phys. Rev. D 74, (2006)
  335. J. Q. Xia, G. B. Zhao and X. Zhang, Phys. Rev. D 75, 103505 (2007).
  336. G. B. Zhao, J. Q. Xia, H. Li, C. Tao, J. M. Virey, Z. H. Zhu and X. Zhang, Phys. Lett. B 648, 8 (2007).
  337. Y. Wang and P. Mukherjee, Phys. Rev. D 76, 103533 (2007).
  338. E. L. Wright, Astrophys. J. 664, 633 (2007).
  339. H. Li, J. Q. Xia, G. B. Zhao, Z. H. Fan and X. Zhang, Astrophys. J. 683, L1 (2008).
  340. E. Komatsu et al. [WMAP Collaboration], Astrophys. J. Suppl. 180, 330 (2009).
  341. J. Q. Xia, H. Li, G. B. Zhao and X. Zhang, Phys. Rev. D 78, 083524 (2008).
  342. H. Li et al., arXiv:0812.1672 [astro-ph].
  343. R. R. Caldwell and M. Doran, Phys. Rev. D72, 043527(2005).
  344. V. Sahni and Y. Shtanov, JCAP 0311, 014 (2003).
  345. R.-G. Cai, H.-S. Zhang, and A. Wang, Commun. Theor. Phys. 44, 948 (2005).
  346. R.-G. Cai, Y.-g. Gong, and B. Wang, JCAP 0603, 006 (2006).
  347. I. Ya. Aref'eva, A. S. Koshelev, and S. Yu. Vernov, Phys. Rev. D72, 064017 (2005).
  348. Brett McInnes, Nucl. Phys. B718, 55-82 (2005).
  349. L. Perivolaropoulos, JCAP 0510, 001 (2005).
  350. M.-z. Li, B. Feng, and X.-m. Zhang, JCAP 0512, 002 (2005).
  351. H.-S. Zhang and Z.-H. Zhu, Phys. Rev. D73, 043518 (2006).
  352. H. Wei and R.-G. Cai, Phys. Lett. B634, 9-13 (2006).
  353. W. Hu, Phys. Rev. D71, 047301 (2005).
  354. Y.-H. Wei and Y.-Z. Zhang, Grav. Cosmol. 9, 307-310 (2003).
  355. M. R. Setare and E. N. Saridakis, Phys. Lett. B 668, 177 (2008).
  356. H.J. Poincaré, New Methods of Celestial Mechanics. American Institute of Physics: New York, 1993.
  357. H.J. Poincaré, Acta Mathematica. 13: p. 1-270, 1890.
  358. J. Hadamard, Journ. de Math., 5: p. 27-73, 1898
  359. G.D. Birkhoff, Dynamical systems. American Mathematical Society Colloquium Publications, 1927.
  360. G.D. Birkhoff, Bull. Soc. Math. de France, 60: p. 1-26, 1932.
  361. A.N. Kolmogorov, ed. Theorie generale des sytèmes dynamiques et mecanique classique. Proc. International Congress of Mathematicians. Vol. I.: Amsterdam. 315-333, 1954.
  362. J.K. Moser, Stable and Random Motions in Dynamical Systems. Princeton, New York: Princeton University Press, 1973.
  363. A.M. Liapunov, Probleme general de la stabilite du movement. New York: Aca- demic Press, 1947.
  364. J.P. LaSalle, and S. Lefschetz, Stability by Liapunov's Direct Method. New York: Academic Press, 1961.
  365. M. W. Hirsch and S. Smale. Differential equations, dynamical systems, and linear algebra. New York: Academic Press (1974).
  366. V.I. Arnold, Ordinary differential equations. Cambridge: M.I.T. Press., 1973.
  367. V.I. Arnold, Geometrical Methods in the Theory of Differential Equations. Berlin: Springer, 1988.
  368. V.I. Arnold, Ann. Inst. Fourier (Grenoble). 16: p. 319-361, 1966.
  369. M. R. Setare and D. Momeni. arXiv: 1001.3767 [physics.gen-ph].
  370. V. Cardoso, A. S. Miranda, E. Berti, H. Witek, and V. T. Zanchin. Phys. Rev., D79:064016, 2009.
  371. A. G. Lavkin. Sov. J. Nucl. Phys., 52:759-760, 1990.
  372. T. C. Charters, A. Nunes, and J. P. Mimoso. Class. Quant. Grav., 18:1703-1714, 2001.
  373. I. Ya. Aref'eva, N. V. Bulatov, and S. Yu. Vernov. Theor. Math. Phys., 163:788- 803.
  374. R. Lazkoz, G. Leon and I. Quiros. Phys. Lett., B649:103, 2007.
  375. S. Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer (2003).
  376. D. K. Arrowsmith and C. M. Place. An introduction to Dynamical Systems. Cam- bridge University Press (1990).
  377. J. Miritzis. Gen. Rel. Grav., 41:49-65, 2009.
  378. Lasalle, J. P., J. Diff. Eq., 4, pp. 57-65, 1968
  379. V. G. LeBlanc, D. Kerr, and J. Wainwright. Class. Quant. Grav., 12:513-541, 1995.
  380. J. Mark Heinzle and Claes Uggla. Class. Quant. Grav., 27:513-541, 015009, 2010.
  381. A. A. Coley. arXiv: gr-qc/9910074.
  382. J. R. Munkres. Elementary differential topology, in Lecture given at Mas- sachusetts Institute of Technology, Fall 1961. Massachusetts Institute of Tech- nology, 1961.
  383. J. Hale. Ordinary differential equations. Malabar, Florida: Robert E. Krieger Publishing Co., Inc. (1980).
  384. F. C. Hoppensteadt. Analysis and simulation of chaotic systems. Applied Math- ematical Sciences, F, John, J. E. Marsden, and L. Sirovich (eds). Vol. 94. New York: Springer-Verlag, 305 (1993).
  385. B. Aulbach, Continuous and Discrete Dynamics near Manifolds of Equilibria (Lecture Notes in Mathematics No. 1058, Springer, 1984).
  386. M.W. Hirsch, C.C. Pugh, and M. Shub, Invariant manifolds. Springer Lecture Notes in Mathematics. Vol. 583., New York: Springer-Verlag, (1977).
  387. N. Fenichel, Persistence and smoothness of invariant manifolds for flows. Indiana University Mathematical Journal, 21: p. 193-225 (1971).
  388. S. Wiggins, Normally hyperbolic invariant manifolds in dynamical systems. New York: Springer-Verlag, (1974).
  389. L. Perko. Differential Equations and Dynamical Systems . Springer, Berlin, (1991).
  390. J. Carr. Applications of Center Manifold theory. New York: Springer-Verlag (1981).
  391. J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, New York, (1983).
  392. M. Gasperini. Elements of string cosmology. Cambridge, UK: Cambridge Univ. Pr. (2007) 552 p.
  393. Y. Fujii and K. Maeda. The scalar-tensor theory of gravitation. Cambridge, USA: Univ. Pr. (2003) 240 p.
  394. V. Faraoni. Cosmology in scalar tensor gravity Springer (2004).
  395. T. P. Waterhouse. arXiv: astro-ph/0611816.
  396. D. Tocchini-Valentini and L. Amendola. Phys. Rev., D65:063508, 2002.
  397. A. P. Billyard and A. A. Coley. Phys. Rev., D61:083503, 2000.
  398. S. Tsujikawa, K. Uddin, S. Mizuno, R. Tavakol, and J. Yokoyama. Phys. Rev., D77:103009, 2008.
  399. C. G. Boehmer, G. Caldera-Cabral, R. Lazkoz, and R. Maartens. Phys. Rev., D78:023505, 2008.
  400. Gonzalez A., Matos T. and Quiros I., 2005, Phys. Rev. D 71, 084029.
  401. A. P. Billyard, A. A. Coley, and J. E. Lidsey. J. Math. Phys., 40:5092, 1999.
  402. E. J. Copeland. Lect. Notes Phys., 646:53-107, 2004.
  403. E. J. Copeland, E. W. Kolb, A. R. Liddle, and J. E. Lidsey. Phys. Rev. Lett., 71:219-222, 1993.
  404. E. W. Kolb, J. E. Lidsey, M. Abney, E. J. Copeland, and A. R. Liddle. Nucl. Phys. Proc. Suppl., 43:118-125, 1995.
  405. J. E. Lidsey et al. Rev. Mod. Phys., 69:373-410, 1997.
  406. F. Lucchin and S. Matarrese. Phys. Rev., D32:1316, 1985.
  407. A. B. Burd and J. D. Barrow. Nucl. Phys., B308:929-945, 1988.
  408. L. P. Chimento, A. E. Cossarini, and N. A. Zuccala. Class. Quant. Grav., 15:57- 74, 1998.
  409. Z.-K. Guo, Y.-S. Piao, and Y.-Z. Zhang. Phys. Lett., B568:1-7, 2003.
  410. A. A. Coley and R. J. van den Hoogen. Phys. Rev., D62:023517, 2000.
  411. E. J. Copeland, A. Mazumdar, and N. J. Nunes. Phys. Rev., D60:083506, 1999.
  412. K. A. Malik and D. Wands. Phys. Rev., D59:123501, 1999.
  413. I. P. C. Heard and D. Wands. Class. Quant. Grav., 19:5435-5448, 2002.
  414. Z. G. Huang, H. Q. Lu, W. Fang, and K. F. Zhang. Astrophys. Space Sci., 305:177- 181, 2006.
  415. O. Arias, T. Gonzalez, Y. Leyva, and I. Quiros. arXiv: gr-qc/0307016.
  416. T. Gonzalez, R. Cardenas, I. Quiros, and Y. Leyva. Astrophys. Space Sci., 310:13- 18, 2007.
  417. T. Gonzalez, G. Leon, and I. Quiros. Class. Quant. Grav., 23:3165-3179, 2006.
  418. R. J. van den Hoogen and L. Filion. Class. Quant. Grav., 17:1815-1825, 2000.
  419. T. Damour and G. Esposito-Farese. Class. Quant. Grav., 9:2093-2176, 1992.
  420. S. Foster. Class. Quant. Grav., 15:3485-3504, 1998.
  421. J. Miritzis. Class. Quant. Grav., 20:2981-2990, 2003.
  422. J. Miritzis. J. Math. Phys., 46:082502, 2005.
  423. T. Hertog. Phys. Rev., D74:084008, 2006.
  424. R. Giambo and J. Miritzis. Class. Quant. Grav., 27:095003, 2010.
  425. Chimento L. P. , Jakubi A. S. , Pavon D. and Zimdahl W. ,, Phys. Rev. D 67, 083513 (2003).
  426. E. J. Copeland, A. R Liddle, and D. Wands. Phys. Rev., D57:4686-4690, 1998.
  427. R. J. van den Hoogen, A. A. Coley, and D. Wands. Class. Quant. Grav., 16:1843- 1851, 1999.
  428. J. Wainwright and W. C. Lim. J. Hyperbol. Diff. Equat., 2:437-470, 2005.
  429. A. Albrecht and C. Skordis. Phys. Rev. Lett., 84:2076-2079, 2000.
  430. González D. and Nápoles Y., degree thesis, UCLV, (2008).
  431. R. Giambo. J. Math. Phys., 50:012501, 2009.
  432. E. J. Copeland, S. Mizuno, and M. Shaeri. Phys. Rev., D79:103515, 2009.
  433. D. F. Torres. Cosmology and astrophysics of scalar-tensor gravity. Phd thesis, in Departamento de Fsica, Facultad de Ciencias Exactas, Universidad de La Plata: La Plata, Argentina, 1998.
  434. D. J. Holden and D. Wands, Phys. Rev. D 61, 043506 (2000)
  435. R. Tavakol, Introduction to dynamical systems, in Dynamical systems in cosmol- ogy, J. Wainwright and G. F. R. Ellis (eds) Cambridge University Press, Cam- bridge, England (1997).
  436. A. P. Billyard and A. A. Coley, Phys. Rev D 61, 083503 (2000);
  437. R. Lazkoz and G. Leon, Phys. Lett. B 638, 303 (2006);
  438. T. Gonzalez, G. Leon and I. Quiros, Class. Quant. Grav. 23, 3165 (2006);
  439. B. Wang, Y. G. Gong and E. Abdalla, Phys. Lett. B 624, 141 (2005);
  440. Z. K. Guo, R. G. Cai and Y. Z. Zhang, JCAP 0505, 002 (2005);
  441. A. Nunes, J.P. Mimoso and T.C. Charters, Phys. Rev. D 63, 083506 (2001);
  442. N.J. Nunes and D.F. Mota, Mon. Not. Roy. Astron. Soc. 368, 751 (2006);
  443. T. Clifton and J.D. Barrow, Phys. Rev. D 75, 043515 (2007).
  444. X. m. Chen, Y. g. Gong and E. N. Saridakis, JCAP 0904, 001 (2009).
  445. C. Wetterich, Astron. Astrophys. 301, 321 (1995);
  446. L. Amendola, Phys. Rev. D 60, 043501 (1999);
  447. H. Garcia-Compean, G. Garcia-Jimenez, O. Obre- gon and C. Ramirez, JCAP 0807, 016 (2008);
  448. X. M. Chen and Y.G. Gong, arXiv:0811.1698[gr-qc];
  449. C. G. Böhmer, G. Caldera-Cabral, R. Lazkoz and R. Maartens, Phys. Rev. D 78, 023505 (2008).
  450. G. Leon, Class. Quant. Grav. 26, 035008 (2009).
  451. L. Amendola, M. Quartin, S. Tsujikawa and I. Waga, Phys. Rev. D 74, 023525 (2006).
  452. L. Amendola and D. Tocchini-Valentini, Phys. Rev. D 64, 043509 (2001);
  453. L. Amendola and D. Tocchini-Valentini, Phys. Rev. D 66, 043528 (2002);
  454. M. Pietroni, Phys. Rev. D 67, 103523 (2003);
  455. L. Amendola, Mon. Not. R. As- tron. Soc. 342, 221 (2003).
  456. D. Comelli, M. Pietroni and A. Riotto, Phys. Lett. B 571, 115 (2003);
  457. U. Franca and R. Rosenfeld, Phys. Rev. D 69, 063517 (2004).
  458. S. Nojiri and S. D. Odintsov, Phys. Lett. B 562, 147 (2003);
  459. S. Nojiri and S. D. Odintsov, Phys. Lett. B 571, 1 (2003).
  460. J. P. Kneller and L. E. Strigari, Phys. Rev. D 68, 083517 (2003);
  461. C. R. Watson and R. J. Scherrer, Phys. Rev. D 68, 123524 (2003);
  462. E. N. Saridakis, arXiv:0902.3978 [gr-qc];
  463. E. N. Saridakis, arXiv:0903.3840 [astro-ph.CO].
  464. P.G. Ferreira, M. Joyce, Phys. Rev. Lett. 79, 4740 (1997).
  465. E.J. Copeland, M. Sami, S. Tsujikawa, Int. J. Mod. Phys. D 15, 1753 (2006).
  466. X. m. Chen, Y. g. Gong and E. N. Saridakis, JCAP 0904, 001 (2009).
  467. R. R. Caldwell, Phys. Lett. B 545, 23 (2002);
  468. R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003);
  469. S. Nojiri and S. D. Odintsov, Phys. Lett. B 562, 147 (2003);
  470. V. K. Onemli and R. P. Woodard, Phys. Rev. D 70, 107301 (2004);
  471. X. m. Chen, Y. g. Gong and E. N. Saridakis, JCAP 0904, 001 (2009);
  472. S. Dutta and R. J. Scherrer, Phys. Lett. B 676, 12 (2009);
  473. E. N. Saridakis, Eur. Phys. J. C 67, 229 (2010).
  474. S. Das, P. S. Corasaniti and J. Khoury, Phys. Rev. D 73, 083509 (2006);
  475. M. Kaplinghat and A. Rajaraman, Phys. Rev. D 75, 103504 (2007).
  476. M. R. Setare and E. N. Saridakis, Phys. Lett. B 671, 331 (2009);
  477. S. Capozziello, M. De Laurentis, S. Nojiri and S. D. Odintsov, arXiv:0903.2753 [hep-th].
  478. S. Dutta and E. N. Saridakis, JCAP 1001, 013 (2010);
  479. S. Dutta and E. N. Sari- dakis, JCAP 1005, 013 (2010).
  480. S. Carloni, E. Elizalde and P. J. Silva, Class. Quantum Grav. 27 045004 (2010)(15pp).
  481. E. Kiritsis, Phys. Rev. D 81, 044009 (2010).
  482. D. Blas, O. Pujolas and S. Sibiryakov, Phys. Rev. Lett. 104, 181302 (2010).
  483. T. Clifton and J. D. Barrow, Phys. Rev. D 75, 043515 (2007) [arXiv:gr- qc/0701070].
  484. E. N. Saridakis, Nucl. Phys. B 808, 224 (2009) [arXiv:0710.5269 [hep-th]].
  485. Pedro F. Gonzalez-Diaz, Phys. Rev. D69, 063522 (2004).
  486. V. B. Johri, Phys. Rev. D70, 041303(2004).
  487. S. Hannestad and E. Mortsell, Phys. Rev. D66, 063508 (2002).
  488. P. F. Gonzalez-Diaz and C. L. Siguenza, Nucl. Phys. B697, 363-386 (2004).
  489. L. P. Chimento and R. Lazkoz, Phys. Rev. Lett. 91, 211301 (2003).
  490. H. Stefancic, Phys. Lett. B586, 5-10 (2004).
  491. H. Stefancic, Eur. Phys. J. C36, 523-527 (2004).
  492. V. K. Onemli and R. P. Woodard, Phys. Rev. D70, 107301 (2004).
  493. T. Brunier, V. K. Onemli, and R. P. Woodard, Class. Quant. Grav. 22, 59-84 (2005).
  494. Shin'ichi Nojiri and S. D. Odintsov, Phys. Lett. B571, 1-10 (2003).
  495. M. Szydlowski and W. Czaja, Annals Phys. 320, 261-281 (2005).
  496. R. Lazkoz y G. León, Phys. Rev. D71, 123516, (2005).
  497. A. Nunes and J. P. Mimoso, Phys. Lett. B 488, 423 (2000).
  498. P. J. Steinhardt, L.-M. Wang, and I. Zlatev, Phys. Rev. D59, 123504 (1999).
  499. J.-P. Uzan, Phys. Rev. D59, 123510 (1999).
  500. A. P. Billyard, A. A. Coley, and R. J. van den Hoogen, Phys. Rev. D58, 123501 (1998).
  501. L. P. Chimento, Class. Quant. Grav. 15, 965-974 (1998).
  502. A. R. Liddle and R. J. Scherrer, Phys. Rev. D59, 023509 (1999).
  503. A. Kehagias and G. Kofinas, Class. Quant. Grav. 21, 3871-3886 (2004).
  504. E. J. Copeland, M. R. Garousi, M. Sami, and S. Tsujikawa, Phys. Rev. D71, 043003 (2005).
  505. Y. Wang, K. Freese, P. Gondolo, and M. Lewis, Astrophys. J. 594, 25-32 (2003).
  506. Z.-H. Zhu, M.-K. Fujimoto, and X.-T. He, Astrophys. J. 603, 365-370 (2004).
  507. R. Lazkoz, S. Nesseris, and Leandros Perivolaropoulos, JCAP 0511, 010 (2005).
  508. M. Szydlowski and W. Czaja, Phys. Rev. D69, 083507 (2004).
  509. S. Nesseris and L. Perivolaropoulos, Phys. Rev. D70 (2004), 043531.

Related papers

Dynamical Systems in Cosmology
George Ellis

1997

View PDFchevron_right
CONCEPT OF A COMPACT DYNAMIC UNIVERSE - improved (4.4.2024)
Michal Grenčík

2024

In this work I present a dialectical conception of the world. Among other things, there are no serious problems in this concept (eg with singularities) as in contemporary (at the turn of the 2nd and 3rd millennium) mainstream physics. After the general part, I present a theory of spectral shifts based on this concept.

View PDFchevron_right
Introduction to the application of dynamical systems theory in the study of the dynamics of cosmological models of dark energy
Israel Quiros

European Journal of Physics, 2015

The theory of the dynamical systems is a very complex subject which has brought several surprises in the recent past in connection with the theory of chaos and fractals. The application of the tools of the dynamical systems in cosmological settings is less known in spite of the amount of published scientific papers on this subject. In this paper a -mostly pedagogical -introduction to the application in cosmology of the basic tools of the dynamical systems theory is presented. It is shown that, in spite of their amazing simplicity, these allow to extract essential information on the asymptotic dynamics of a wide variety of cosmological models. The power of these tools is illustrated within the context of the so called ΛCDM and scalar field models of dark energy. This paper is suitable for teachers, undergraduate and postgraduate students from physics and mathematics disciplines.

View PDFchevron_right
Introduction to the application of the dynamical systems theory in the study of the dynamics of cosmological models of dark energy
Daniel Sánchez Guzmán

The theory of the dynamical systems is a very complex subject which has brought several surprises in the recent past in connection with the theory of chaos and fractals. The application of the tools of the dynamical systems in cosmological settings is less known in spite of the amount of published scientific papers on this subject. In this paper a -mostly pedagogical -introduction to the application in cosmology of the basic tools of the dynamical systems theory is presented. It is shown that, in spite of their amazing simplicity, these allow to extract essential information on the asymptotic dynamics of a wide variety of cosmological models. The power of these tools is illustrated within the context of the so called ΛCDM and scalar field models of dark energy. This paper is suitable for teachers, undergraduate and postgraduate students from physics and mathematics disciplines.

View PDFchevron_right
Introduction to the Dynamic Universe
Tuomo Suntola

The Dynamic Universe is a holistic model of physical reality starting from whole space as a spherically closed zero-energy system. Instead of extrapolating the cosmological appearance of space from locally defined field equations, locally observed phenomena are derived from the conservation of the zero-energy balance of motion and gravitation in whole space. The energy structure of space is described in terms of nested energy frames starting from hypothetical homogeneous space as the universal reference and proceeding down to local frames in space. Time is decoupled from space-the fourth dimension has a geometrical meaning as the radius of the sphere closing the three-dimensional space. Relativity in the Dynamic Universe is the measure of the locally available share of total energy-clocks in fast motion or in a strong gravitational field do not lose time because of slower flow of time but because more energy is bound into interactions in space. For local observations, the DU predictions are essentially the same as the corresponding predictions derived from the theory of relativity. At the extremes, at cosmological distances and in the vicinity of local singularities in space however, differences become remarkable-e.g. galactic space in the DU appears in Euclidean geometry, and the magnitudes of high redshift supernovae are explained without assumptions of dark energy or accelerating expansion. Black holes in DU space have stable orbits down to the critical radius. Instead of a sudden Big Bang, the energy buildup in Dynamic Universe is seen as a continuous process from infinity in the past to infinity in the future.

View PDFchevron_right
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved