The Dynamical Systems Approach to Modeling: The Universe as a Case Study

  • Ailier Rivero-AcostaEmail author
  • Adrian Linares-Rodriguez
  • Carlos R. Fadragas
Conference paper


The acceleration of the expansion of the Universe, as it is indicated by observations of redshift of light coming from supernovas, anisotropies of cosmological microwave background radiation, and the large-scale structure of the Universe, defines one of the most interesting theoretical problems that is facing the modern cosmology. The aim of this work is to show the analysis of the idea that inflation and dark energy are two subjects closely related, that is, both equivalents to the fundamental scalar field known as the standard model Higgs field. We considered that there exist non-trivial solutions with non-minimal coupling of the Cosmological Higgs Field to gravity. For this condition, an attractive cosmological model was derived. Results from applying the dynamical stability analysis show that the current accelerated expansion of the Universe is one of several possibilities. The future behavior of the Universe could seriously affect the existence of particles and structures that we are made of. For that reason, it is important to do some comments on this idea.


Cosmological Higgs Field Dynamical systems Accelerated expansion 



We want to thank R. Cárdenas for his useful comments and discussions. Furthermore, we thank Jose Monteagudo for information support. This research is partially supported by MES of Cuba.


  1. 1.
    Riess AG et al (1998) [Supernova Search Team Collaboration], Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron J 116:1009–1038. arXiv:astro-ph/9805201v1CrossRefGoogle Scholar
  2. 2.
    Schmidt RW et al (2008) The High-Z supernova search: measuring cosmic deceleration and global curvature of the universe using type Ia supernovae. arXiv:astro-ph/9805200v1
  3. 3.
    Kowalski M et al (2008) Supernova cosmology project collaboration. Astrophys J 686(2):749. arXiv:0804.4142v1
  4. 4.
    Allen S et al (2008) Improved constraints on dark energy from Chandra X-ray observations of the largest relaxed galaxy clusters. Mon Not Roy Astron Soc 383(3):879–896. arXiv:astro-ph/0706.0033v3CrossRefGoogle Scholar
  5. 5.
    Abazajian KN et al (2009) The seventh data release of the sloan digital sky survey. arXiv:astro-ph/0812.0649v2
  6. 6.
    Ade PAR et al (2014) (Planck Collaboration): Planck 2013 results. XXII. Constraints on inflation. arXiv:astro-ph/1303.5082v3
  7. 7.
    Nemiroff RJ, Patla B (2004) Decaying higgs fields and cosmological dark energy. arXiv:astro-ph/0409649v1
  8. 8.
    Englert F, Brout R (1964) Broken symmetry and the mass of gauge vector mesons. Phys Rev Lett 13:321CrossRefGoogle Scholar
  9. 9.
    Bezrukov F, Shaposhnikov M (2007) The standard model higgs boson as the inflation. Phys Lett BGoogle Scholar
  10. 10.
    Fakir R, Unruh WG (1990) Improvement on cosmological chaotic inflation through nonminimal coupling. Phys Rev DGoogle Scholar
  11. 11.
    Rinaldi M (2015) Higgs dark energy. Class Quantum Gravity. arXiv:astro-ph/1404.0532v4
  12. 12.
    Leon G, Fadragas CR (2011) Cosmological dynamical systems and their applications. Lambert Academic Publishing, SarrebruckGoogle Scholar
  13. 13.
    Coley AA (2003) Dynamical systems and cosmology. Dordrecht-KluwerGoogle Scholar
  14. 14.
    Wiggins S (2003) Introduction to applied nonlinear dynamical systems and chaos. Berlin: SpringerGoogle Scholar
  15. 15.
    Coley AA (1999) Dynamical systems in cosmology. arXiv:astro-ph/gr-qc/9910074v1

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Universidad Central “Marta Abreu” de Las VillasSanta ClaraCuba

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