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Recovering the Effective Cosmological Constant in Extended Gravity Theories

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Abstract

In the framework of extended gravity theories, we discuss the meaning of a time-dependent “cosmological constant” and give a set of conditions to recover an asymptotic de Sitter behaviour for a class of cosmological models independently of initial data. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We will deal with scalar-tensor, fourth and higher than fourth-order theories.

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REFERENCES

  1. Weinberg, S. (1989). Rev. Mod. Phys. 61, 1.

    Google Scholar 

  2. Guth, A. (1981). Phys. Rev. D 23, 347; Guth, A. (1982). Phys. Lett. B 108, 389.

    Google Scholar 

  3. Linde, A. D. (1982). Phys. Lett. B 108, 389; (1982). Phys. Lett. B 114, 431; (1983). Phys. Lett. B 129, 177; (1990). Phys. Lett. B 238, 160.

    Google Scholar 

  4. Hoyle, F., and Narlikar, J. V. (1963). Proc. Roy. Soc. Lond. A 273, 1.

    Google Scholar 

  5. Starobinsky, A. A. (1980). Phys. Lett. B 91, 99.

    Google Scholar 

  6. Barrow, J., and Ottewill, A. C. (1983). J. Phys. A: Math. Gen. 16, 2757.

    Google Scholar 

  7. Schmidt, H.-J. (1990). Class. Quantum Grav. 7, 1023; (1996). Phys. Rev. D 54, 7906.

    Google Scholar 

  8. Kluske, S., and Schmidt, H.-J. (1996). Astron. Nachr. 317, 337; Kluske, S. (1996). In New Frontiers in Gravitation, ed. G. Sardanashvily (Hadronic Press, Palm Harbor, Fla.), p. 215.

    Google Scholar 

  9. La, D., and Steinhardt, P. J. (1989). Phys. Rev. Lett. 62, 376; La, D., Steinhardt, P.J., and Bertschinger, E. W. (1989). Phys. Lett. B 231, 231.

    Google Scholar 

  10. Capozziello, S., de Ritis, R., Rubano, C., and Scudellaro, P. (1996). Rivista del Nuovo Cimento 4, 1.

    Google Scholar 

  11. Maeda, K. (1989). Phys. Rev. D 39, 3159.

    Google Scholar 

  12. Rainer, M. (1995). Int. J. Mod. Phys. D 4, 397.

    Google Scholar 

  13. Teyssandier, P., and Tourrenc, P. (1983). J. Math. Phys. 24, 2793.

    Google Scholar 

  14. Wands, D. (1994). Class. Quantum Grav. 11, 269.

    Google Scholar 

  15. Capozziello, S., de Ritis, R., Marino, A. A. (1997). Class. Quantum Grav. 14, 3243.

    Google Scholar 

  16. Kofman, L. A., Linde, A. D., Starobinsky, A. A. (1985). Phys. Lett. B 157, 361; Starobinsky, A. A. (1985). JETP Lett. 42, 152; Gottlöber, S., Müller, V., and Starobinsky, A. A. (1991). Phys. Rev. D 43, 2510; Polarski, D., Starobinsky, A. A. (1992). Nucl. Phys. B 385, 623.

    Google Scholar 

  17. Brandenberger, R. H. (1985). Rev. Mod. Phys. 57, 1; Mukhanov, V. F., Feldman, H. A., and Brandenberger, R. H. (1992). Phys. Rep. 215, 203.

    Google Scholar 

  18. Albrecht, A., and Steinhardt, P. J. (1982). Phys. Rev. Lett. 48, 1220.

    Google Scholar 

  19. Wald, R. M. (1983). Phys. Rev. D 28, 2118.

    Google Scholar 

  20. Hawking, S. W., and Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge).

    Google Scholar 

  21. Capozziello, S., de Ritis, R., Rubano, C., and Scudellaro, P. (1995). Int. J. Mod. Phys. D 4, 767.

    Google Scholar 

  22. Capozziello, S., de Ritis, R., and Marino, A. A. (1997). Nuovo Cimento B 112, 1351.

    Google Scholar 

  23. Cotsakis, S., and Flessas, G. (1993). Phys. Lett. B 319, 69; Burd, A. B., and Barrow, J. D. (1988). Nucl. Phys. B 308, 929; Yokogawa, J., and Maeda, K. (1988). Phys. Lett. B 207, 31; Barrow, J. D., and Götz, G. (1989). Phys. Lett. B 231, 228.

    Google Scholar 

  24. Magnano, G., Ferraris, M., and Francaviglia, M. (1987). Gen. Rel. Grav. 19, 465; Ferraris, M., Francaviglia, M., and Volovich, I. (1993). Nuovo Cimento B 108, 1313.

    Google Scholar 

  25. Zee, A. (1979) Phys. Rev. Lett. 42, 417; Smolin, L. (1979). Nucl. Phys. B 160, 253; Adler, S. (1980). Phys. Rev. Lett. 44, 1567; Birrell, N. D., and Davies, P. C. W. (1982) Quantum Fields in Curved Space (Cambridge University Press, Cambridge).

    Google Scholar 

  26. Vilkovisky, G. (1992). Class. Quantum Grav. 9, 895.

    Google Scholar 

  27. Green, M., Schwarz, J., and Witten, E. (1987). Superstring Theory (Cambridge University Press, Cambridge); Tseytlin, A. A., and Vafa, C. (1992). Nucl. Phys. B 372, 443; Veneziano, G. (1991). Phys. Lett. B 265, 287; Gasperini, M., Maharana, J., and Veneziano, G. (1991). Phys. Lett. B 272, 277; Meissner, K. A., and Veneziano, G. (1991). Phys. Lett. B 267, 33.

    Google Scholar 

  28. Brans, C., and Dicke, R. H. (1961). Phys. Rev 124, 925.

    Google Scholar 

  29. Dirac, P. A. M. (1937). Proc. Roy. Soc. Lond. A 165, 199; Sciama, D. W. (1953). Mon. Not. R. Astr. Soc. 113, 34; Jordan, P. (1959). Z. Phys. 157, 112.

    Google Scholar 

  30. Gottlöber, S., Schmidt, H.-J., and Starobinsky, A. A. (1990). Class. Quantum Grav. 7, 893.

    Google Scholar 

  31. Ruzmaikina, T. V., and Ruzmaikin, A. A. (1970). JETP 30, 372; Stelle, K. S. (1978). Gen. Rel. Grav. 9, 353; Schimming, R., and Schmidt, H.-J. (1990). NTM-Schriftenr. Gesch. Naturwiss. 27, 41.

    Google Scholar 

  32. Buchdahl, H. (1951). Acta Math. 85, 63; Berkin, A., and Maeda, K. (1990). Phys. Lett. B 245, 348; Amendola, L., Battaglia Mayer, A., Capozziello, S., Gottlöber, S., Muller, V., Occhionero, F., and Schmidt, H.-J. (1993). Class. Quantum Grav. 10, L43.

    Google Scholar 

  33. Battaglia Mayer, A., and Schmidt, H.-J. (1993). Class. Quantum Grav. 10, 2441.

    Google Scholar 

  34. Amendola, L., Capozziello, S., Litterio, M., and Occhionero, F. (1992). Phys. Rev. D 45, 417.

    Google Scholar 

  35. Damour, T., and Esposito-Farese, G. (1994). Class. Quantum Grav. 9, 2093.

    Google Scholar 

  36. Magnano, G., and Sokolowski, L. M. (1994). Phys. Rev. D 50, 5039.

    Google Scholar 

  37. Capozziello, S., de Ritis, R., and Scudellaro, P. (1994). Phys. Lett. A 188, 130; Capozziello, S., de Ritis, R., Rubano, C., and Scudellaro, P. (1995). Phys. Lett. A 201, 145; Capozziello, S., de Ritis, R., and Marino, A. A. (1996). Helv. Phys. Acta 69, 241; Capozziello, S., and de Ritis, R. (1997). Gen. Rel. Grav. 29, 1425.

    Google Scholar 

  38. Capozziello, S., and de Ritis, R. (1996). Int. J. Mod. Phys. D 5, 209.

    Google Scholar 

  39. Capozziello, S., and de Ritis, R. (1994). Class. Quantum Grav. 11, 107; Capozziello, S., and de Ritis, R. (1993). Phys. Lett. A 177, 1; Capozziello, S., de Ritis, R., and Scudellaro, P. (1993). Int. J. Mod. Phys. D 2, 463; Capozziello, S., de Ritis, R., and Rubano, C. (1993). Phys. Lett. A 177, 8; Capozziello, S., Demiański, M., de Ritis, R., and Rubano, C. (1995). Phys. Rev. D 52, 3288.

    Google Scholar 

  40. Ellis, G. F. R., and MacCallum, M. A. H. (1969). Commun. Math. Phys. 12, 108; MacCallum, M. A. H. (1979). In General Relativity: An Einstein Centenary Survey, eds. S. W. Hawking and W. Israel (Cambridge University Press, Cambridge); Ryan, M. P., and Shepley, L. C. (1975). Homogeneous Relativistic Cosmologies (Princeton Univ. Press, Princeton).

    Google Scholar 

  41. Barth, N. H., and Christensen, S. M. (1983). Phys. Rev. D 28, 1876.

    Google Scholar 

  42. Müller, V., and Schmidt, H.-J. (1991). Fortschr. Phys. 39, 319.

    Google Scholar 

  43. Capozziello, S., Occhionero, F. and Amendola, L. (1993). Int. J. Mod. Phys. D 1, 615.

    Google Scholar 

  44. Mijić, M. B., Morris, M. S., and Suen, W. M. (1986). Phys. Rev. D 34, 2934.

    Google Scholar 

  45. Vilenkin, A. (1985). Phys. Rev. D 32, 2511

    Google Scholar 

  46. Berkin, A. L., and Maeda, K. (1991). Phys. Rev. D 44, 1691.

    Google Scholar 

  47. Bruni, M., Matarrese, S., Pantano, O. (1995). Phys. Rev. Lett. 74, 1916.

    Google Scholar 

  48. Starobinsky, A. A. (1996). In Cosmoparticle Physics 1, eds. M. Yu. Khlopov et al. (Edition Frontiers).

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Capozziello, S., de Ritis, R. & Marino, A.A. Recovering the Effective Cosmological Constant in Extended Gravity Theories. General Relativity and Gravitation 30, 1247–1272 (1998). https://doi.org/10.1023/A:1026651129626

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