Boundary term in metric f (R) gravity: Field equations in the metric formalism

General Relativity and Gravitation

Volumn 42, Issue 11, 2010, Pages 2713-2728

  Guarnizo, Alejandro ^a   Castañeda, Leonardo ^a   Tejeiro, Juan M ^a  

^a UNIVERSIDAD NACIONAL DE COLOMBIA   (Colombia)

Author keywords

f (R) gravity; Modified theories of gravity; Variational principles

Indexed keywords

EID: 78649319377     PISSN: 00017701     EISSN: 15729532     Source Type: Journal    
DOI: 10.1007/s10714-010-1012-6     Document Type: Article

References (40)

1. Will C. M.: Theory and Experiment in Gravitational Physics. Cambridge University Press, Cambridge (1993).
2. Misner C. W., Thorne K. S., Wheeler J. H.: Gravitation. W. H. Freeman and Company, Reading (1973).
3. Wald R. M.: General Relativity. The University of Chicago Press, Chicago (1984).
4. Poisson E.: A Relativist's Toolkit-The Mathematics of Black-Hole Mechanics. Cambridge University Press, Cambridge (2004).
5. Padmanabhan T.: Gravitation: Foundations and Frontiers. Cambridge University Press, Cambridge (2010).
6. Weinberg S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York (1972).
7. Carroll S. M.: Spacetime and Geometry: An Introduction to General Relativity. Addison Wesley, San Francisco (2004).
8. Hawking S. W., Ellis J. F. R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973).
9. Gibbons G. W., Hawking S. W.: Action integrals and partition functions in quantum gravity. Phys. Rev. D 15, 27-52 (1977).
10. Hawking S. W., Horowitz G. T.: The gravitational Hamiltonian, action, entropy and surface terms. Class. Quantum. Grav. 13, 1487-1498 (1996) arXiv: gr-qc/9501014.
11. Schmidt H.-J.: Variational derivatives of arbitrarily high order and multi-inflation cosmological models. Class. Quantum Grav. 7, 1023-1031 (1990).
12. Wands D.: Extended gravity theories and the Einstein-Hilbert action Class. Quantum Grav. 11, 269-280 (1994) arXiv: gr-qc/9307034.
13. Farhoudi M.: On higher order gravities, their analogy to GR, and dimensional dependent version of Duff's trace anomaly relation. Gen. Relativ. Gravit. 38, 261-1284 (2006) arXiv: physics/0509210v2.
14. Querella, L.: Variational principles and cosmological models in higher-order gravity. PhD thesis (1998). arXiv: gr-qc/9902044v1.
15. Nojiri S., Odintsov S. D.: Modified gravity as an alternative for Lambda-CDM cosmology. J. Phys. A 40, 6725-6732 (2007) arXiv: hep-th/0610164.
16. Sami, M.: Dark energy and possible alternatives (2009). arXiv: 0901. 0756.
17. Borowiec, A., Godlowski, W., Szydlowski, M.: Dark matter and dark energy as a effects of modified gravity. ECONF C0602061, 09 (2006). arXiv: astro-ph/0607639v2.
18. Durrer R., Maartens R.: Dark energy and dark gravity: theory overview. Gen. Relativ. Gravit. 40, 301-328 (2008).
19. Carroll S. M., Duvvuri V., Trodden M., Turner M. S.: Is cosmic speed-up due to new gravitational physics?. Phys. Rev. D 70, 043528 (2004) arXiv: astro-ph/0306438.
20. Nojiri, S., Odintsov, S. D.: Introduction to modified gravity and gravitational alternative for dark energy. ECONF C0602061, 06 (2006). arXiv: hep-th/0601213.
21. Capozziello S., Francaviglia M.: Extended theories of gravity and their cosmological and astrophysical applications. Gen. Relativ. Gravit. 40, 357-420 (2008) arXiv: 0706. 1146v2.
22. Faraoni, V.: f (R) gravity: successes and challenges (2008). arXiv: 0810. 2602.
23. Sotiriou, T. P.: 6+1 lessons from f (R) gravity. J. Phys. Conf. Ser. 189, 012039 (2009). arXiv: 0810. 5594.
24. Capozziello, S., De Laurentis, M., Faraoni, V.: A bird's eye view of f (R)-gravity (2009). arXiv: 0909. 4672.
25. Sotiriou, T. P., Faraoni, V.: f (R) Theories of gravity (2008). arXiv: 0810. 2602.
26. Buchdahl H. A.: Non-linear Lagrangians and cosmological theory. Mon. Notices R. Astron. Soc. 150, 1-8 (1970).
27. Barth N. H.: The fourth-order gravitational action for manifolds with boundaries. Class. Quantum Grav. 2, 497-513 (1985).
28. Nojiri S., Odintsov S. D.: Brane-world cosmology in higher derivative gravity or warped compactification in the next-to-leading order of AdS/CFT correspondence. JHEP 0007, 049 (2000) arXiv: hep-th/0006232.
29. Nojiri S., Odintsov S. D.: Is brane cosmology predictable? Gen. Relativ. Gravit. 37, 1419-1425 (2005) arXiv: hep-th/0409244.
30. Madsen M. S., Barrow J. D.: De Sitter ground states and boundary terms in generalized gravity. Nucl. Phys. B 323, 242-252 (1989).
31. Fatibene L., Ferraris M., Francaviglia M.: Augmented variational principles and relative conservation laws in classical field theory. Int. J. Geom. Methods Mod. Phys. 2, 373-392 (2005) arXiv: math-ph/0411029v1.
32. Francaviglia M., Raiteri M.: Hamiltonian, energy and entropy in general relativity with non-orthogonal boundaries. Class. Quant. Grav. 19, 237-258 (2002) arXiv: grqc/ 0107074v1.
33. Casadio R., Gruppuso A.: On boundary terms and conformal transformations in curved spacetimes. Int. J. Mod. Phys. D 11, 703-714 (2002) arXiv: gr-qc/0107077.
34. Balcerzak, A., Dabrowski, M. P.: Gibbons-Hawking boundary terms and junction conditions for higher-order brane gravity models (2008). arXiv: 0804. 0855.
35. Nojiri S., Odintsov S. D.: Finite gravitational action for higher derivative and stringy gravities. Phys. Rev. D 62, 064018 (2000) arXiv: hep-th/9911152.
36. Dabrowski, M. P., Balcerzak, A.: Higher-order brane gravity models (2009). arXiv: 0909. 1079.
37. Nojiri S., Odintsov S. D., Ogushi S.: Finite action in d5 gauged supergravity and dilatonic conformal anomaly for dual quantum field theory. Phys. Rev. D 62, 124002 (2000) arXiv: hep-th/0001122v4.
38. Dyer E., Hinterbichler K.: Boundary terms, variational principles and higher derivative modified gravity. Phys. Rev. D. 79, 024028 (2009) arXiv: 0809. 4033.
39. Sotiriou, T. P.: Modified actions for gravity: theory and phenomenology. PhD thesis, International School for Advanced Studies (2007). arXiv: 0710. 4438v1.
40. Sotiriou T. P., Liberati S.: Metric-affine f(R) theories of gravity. Ann. Phys. 322, 935-966 (2007) arXiv: gr-qc/0604006v2.