Skip to main content
Log in

The Cosmological Constant from the Extended Theory of Gravitation in Clifford Spaces

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

The exploration of the novel physical consequences of the Extended Theory of Gravity in C-spaces (Clifford spaces) is continued. One of the most salient physical feature of the extended gravitational theory in C-spaces is that one can generate an effective stress energy tensor mimicking the effects of “dark” matter/energy. In particular, it is found that the presence of the cosmological constant, along with a plausible mechanism to explain its extremely small value and/or its cancellation, can be understood entirely from a purely Clifford algebraic and geometric perspective. For this reason we believe that this theory may have important consequences in Cosmology and further research in Gravitation and Particle Physics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Baylis W.: Electrodynamics, a Modern Geometric Approach, Boston. Birkhauser, Boston (1999)

    MATH  Google Scholar 

  2. Becker, K., Becker, M., Schwarz, J.: String Theory and M-Theory: A Modern Introduction, pp. 543–545. Cambridge University Press, Cambridge (2007)

  3. Castro C., Pavsic M.: Higher derivative gravity and torsion from the geometry of C-spaces. Phys. Lett. B 559, 74 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  4. Castro C., Pavsic M.: On Clifford algebras of spacetime and the Conformal Group. Int. J. Theor. Phys 42, 1693 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Castro C., Pavsic M.: The extended relativity theory in Clifford-spaces. Progr. Phys. 1, 31 (2005)

    MathSciNet  MATH  Google Scholar 

  6. Castro C.: The extended relativity theory in Born-Clifford phase spaces with a lower and upper length scales and Clifford group geometric unification. Found. Phys. 35(6), 971 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Castro C.: On dual phase space relativity, the machian principle and modifed Newtonian dynamics. Progr. Phys. 1, 20 (2005)

    MATH  Google Scholar 

  8. Castro C.: Lanczos–Lovelock–Cartan gravity from Clifford space geometry. Int. J. Geom. Meth. Mod. Phys. 10, 1350019 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Castro, C.: Extended Lorentz transformations in Clifford space relativity theory. Adv. Appl. Clifford Algebras 25(3), 553–567 (2015)

  10. Castro C.: The extended relativity theory in Clifford phase spaces and modifications of gravity at the Planck/Hubble scales. Adv. Appl. Clifford Algebras 24, 29–53 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Capozziello, S.: De Laurentis M Extended theories of gravity. Phys. Report. (to appear). arXiv:1108.6266

  12. Cayley A.: On the theory of linear transformations. Camb. Math. J. 4, 193 (1845)

    Google Scholar 

  13. Gelfand I., Kapranov M., Zelevinsky A.: Discriminants, Resultants and Determinants. Birkhauser, Boston (1994)

    Book  MATH  Google Scholar 

  14. Guendelman, E.I.: Scale invariance, new inflation and decaying lambda terms. Mod. Phys. Lett. A 14, 1043–1052 (1999). arXiv:gr-qc/9901017

  15. Guendelman, E., Nissimov, E., Pacheva, S.: Metric-independent volume-forms in gravity and cosmology. Bulgar. J. Phys. 42 (2015) (to appear). arXiv:1505.07680

  16. Hehl, F., VonDer Heyde, P., Kerlick, G., Nester, J.: General relativity with spin and torsion: foundations and prospects. Rev. Mod. Phys. 48, 393 (1976)

  17. Hestenes D.: Spacetime Algebra. Gordon and Breach, New York (1996)

    MATH  Google Scholar 

  18. Hestenes D., Sobcyk G.: Clifford Algebra to Geometric Calculus. D. Reidel Publishing Company, Dordrecht (1984)

    Book  Google Scholar 

  19. Kleinert, H.: Nonholonomic mapping principle for classical and quantum mechanics in spaces with curvature and torsion. (2015) (to appear). arXiv:gr-qc/0203029

  20. Lanczos C.: A remarkable property of the Riemann-Christoffel tensor in four dimensions. Ann. Math. 39, 842 (1938)

    Article  MathSciNet  MATH  Google Scholar 

  21. Lovelock D.: The Einstein tensor and its generalizations. J. Math. Phys. 12, 498 (1971)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Nakahara M.: Geometry, Topology and Physics. Institute of Physics Publishing, Bristol (1998)

    MATH  Google Scholar 

  23. Pavsic, M.: The landscape of theoretical physics: a global view, from point particles to the brane world and beyond, in search of a unifying principle. In: Fundamental Theories of Physics, vol. 19. Kluwer, Dordrecht (2001)

  24. Pavsic M.: Kaluza–Klein theory without extra dimensions: curved Clifford space. Phys. Lett. B 614, 85 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Pavsic M.: Spin gauge theory of gravity in Clifford space: a realization of Kaluza–Klein theory in 4-dimensional spacetime. Int. J. Mod. Phys. A 21, 5905 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Pavsic M.: On a unified theory of generalized branes coupled to gauge fields, including the gravitational and Kalb–Ramond fields. Found. Phys. 37, 1197 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Porteous IR.: Clifford Algebras and the Classical Groups. Cambridge University Press, Cambridge (1995)

    Book  MATH  Google Scholar 

  28. Vacaru, S.: Ghost-free massive f(R) theories modelled as effective einstein spaces and cosmic acceleration. Eur. Phys. J. C [Eur. Phys. J.] C 74 (2014) (accepted). arXiv:1401.2882 [physics.gen-ph]

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carlos Castro.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Castro, C. The Cosmological Constant from the Extended Theory of Gravitation in Clifford Spaces. Adv. Appl. Clifford Algebras 26, 913–931 (2016). https://doi.org/10.1007/s00006-015-0594-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-015-0594-1

Keywords

Navigation