Skip to main content
Log in

Viscous inflationary universe models

  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

The research on viscous cosmological models is reviewed and carried further. Inflationary cosmological models of Bianchi type-I with shear, bulk, and nonlinear viscosity are studied. The inflation field energy is represented by a two-components cosmic fluid consisting of a vacuum fluid and a Zel'dovich fluid. It is shown that there exist models in which the viscous Zel'dovich fluid removes the initial singularity of the corresponding viscosity free models. The mean expansion of a Zel'dovich dominated unvierse is found to be independent of shear viscosity and anisotropy. Bulk viscosity and shear viscosity cause exponential decay of anisotropy, while nonlinear viscosity causes power-law decay of anisotropy.

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

  • Bali, R.: 1984,Astrophys. Space Sci. 107, 155.

    Google Scholar 

  • Bali, R.: 1985,Astrophys. Space Sci. 116, 81.

    Google Scholar 

  • Banerjee, A. K. and Santos, N. O.: 1983,J. Math. Phys. 24, 2689.

    Google Scholar 

  • Banerjee, A. K. and Santos, N. O.: 1984,Gen. Rel. Grav. 16, 217.

    Google Scholar 

  • Banerjee, A. K. and Sanyal, A. K.: 1986,Gen. Rel. Grav. 18, 1251.

    Google Scholar 

  • Banerjee, A. K. and Sanyal, A. K.: 1988,Gen. Rel. Grav. 20, 103.

    Google Scholar 

  • Banerjee, A. K., Duttachoudhury, S. B., and Sanyal, A. K.: 1985,J. Math. Phys. 26, 3010.

    Google Scholar 

  • Banerjee, A. K., Duttachoudhury, S. B., and Sanyal, A. K.: 1986,Gen. Rel. Grav. 18, 461.

    Google Scholar 

  • Banerjee, A. K., Ribeiro, M. B., and Santos, N. O.: 1987,Astrophys. Space Sci. 136, 331.

    Google Scholar 

  • Barrow, J. D.: 1977,Nature 267, 117.

    Google Scholar 

  • Barrow, J. D.: 1986,Phys. Letters 180B, 235.

    Google Scholar 

  • Barrow, J. D.: 1987,Phys. Letters B183, 285.

    Google Scholar 

  • Barrow, J. D.: 1988,Nucl. Phys. B310, 743.

    Google Scholar 

  • Barrow, J. D. and Matzner, R. A.: 1977,Monthly Notices Roy. Astron. Soc. 181, 719.

    Google Scholar 

  • Belinskij, V. A. and Khalatnikov, I. M.: 1975,Soviet Phys. JETP Letters 21, 99.

    Google Scholar 

  • Belinskij, V. A. and Khalatnikov, I. M.: 1976,Soviet Phys. JETP 42, 205.

    Google Scholar 

  • Belinskij, V. A. and Khalatnikov, I. M.: 1977,Soviet Phys. JETP 45, 1.

    Google Scholar 

  • Belinskij, V. A., Nikomarov, E. O., and Khalatnikov, I. M.: 1979,Soviet Phys. JETP 50, 213.

    Google Scholar 

  • Benton, J. B. and Tupper, B. O. J.: 1986,Phys. Rev. D33, 3534.

    Google Scholar 

  • Bernstein, J.: 1987, Rep. No. RU87/B1/88, Rockefeller University, New York.

  • Blau, S. K. and Guth, A. H.: 1987, in S. W. Hawking and W. Israel (eds.), ‘Inflationary Cosmology’,300Years of Gravitation, Chapter 12, Cambridge University Press, Cambridge.

    Google Scholar 

  • Caderni, N.: 1979, in M. Demianski (ed.), ‘Physics of the Expanding Universe’,Lecute, Notes in Physics, Vol. 109, p. 81.

  • Caderni, N. and Fabbri, R.: 1977a,Nuovo Cimento Letters 20, 185.

    Google Scholar 

  • Caderni, N. and Fabbri, R.: 1977b,Phys. Letters 69B, 508.

    Google Scholar 

  • Caderni, N. and Fabbri, R.: 1978a,Nuovo Cimento 44B, 228.

    Google Scholar 

  • Caderni, N. and Fabbri, R.: 1978b,Phys. Letters 67A, 19.

    Google Scholar 

  • Caderni, N. and Fabbri, R.: 1978c,Phys. Letters 68A, 144.

    Google Scholar 

  • Caderni, N. and Fabbri, R.: 1979,Phys. Rev. D20, 1251.

    Google Scholar 

  • Caderni, N., Fabbri, R., van den Horn, L. J., and Siskens, Th. J.: 1978,Phys. Letters 66A, 251.

    Google Scholar 

  • Carswell, R. F.: 1969,Monthly Notices Roy. Astron. Soc. 144, 279.

    Google Scholar 

  • Coley, A. A.: 1989a,Phys. Letters 137A, 235.

    Google Scholar 

  • Coley, A. A.: 1989b,Astrophys. Space Sci. 155, 193.

    Google Scholar 

  • Coley, A. A. and Tupper, B. O. J.: 1983a,Phys. Letters 95A, 357.

    Google Scholar 

  • Coley, A. A. and Tupper, B. O. J.: 1983b,Astrophys. J. 271, 7.

    Google Scholar 

  • Coley, A. A. and Tupper, B. O. J.: 1984a,Astrophys. J. 280, 26.

    Google Scholar 

  • Coley, A. A. and Tupper, B. O. J.: 1984b,Phys. Letters 100A, 495.

    Google Scholar 

  • Coley, A. A. and Tupper, B. O. J.: 1985a,Phys. Letters 111A, 182.

    Google Scholar 

  • Coley, A. A., and Tupper, B. O. J.: 1985b,Astrophys. J. 288, 418.

    Google Scholar 

  • Coley, A. A. and Tupper, B. O. J.: 1986a,J. Math. Phys. 27, 406.

    Google Scholar 

  • Coley, A. A. and Tupper, B. O. J.: 1986b,Can. J. Phys. 64, 204.

    Google Scholar 

  • Collins, C. B. and Stewart, J. M.: 1971,Monthly Notices Roy. Astron. Soc. 153, 419.

    Google Scholar 

  • Davies, P. C. W.: 1987a,Class. Quant. Grav. 4, L225.

    Google Scholar 

  • Davies, P. C. W.: 1987b,Quantum Effects in Background Gravitational Fields, Proc. 26th Liège Int. Astrophys. Colloq., July 1–4, 1986.

  • Davies, P. C. W.: 1988,Ann. Inst. Henri Poicaré 49, 297.

    Google Scholar 

  • Diosi, L., Keszthelyi, B., Lukacs, B., and Paal, G.: 1984,Acta Phys. Pol. B15 909.

    Google Scholar 

  • Diosi, L., Keszthelyi, B., Lukacs, B., and Paal, G.: 1985,Phys. Letters 157B, 23.

    Google Scholar 

  • Doroshkevich, A. G., Zel'dovich, Ya. B., and Novikov, I. D.: 1968,Soviet Phys. JETP 26, 408.

    Google Scholar 

  • Doroshkevich, A. G., Zel'dovich, Ya. B., and Novikov, I. D.: 1969,Astrofizika 5, 539.

    Google Scholar 

  • Ellis, J., Gaillard, M. K., and Nanopoulos, D. V.: 1980,Phys. Letters 90B, 253.

    Google Scholar 

  • Fabbri, R.: 1979,Nuovo Cimento Letters 26, 77.

    Google Scholar 

  • Fabbri, R.: 1980,Nuovo Cimento 56B 125.

    Google Scholar 

  • Fustero, X. and Pavon, D.: 1982,Nuovo Cimento Letters 35, 427.

    Google Scholar 

  • Goenner, H. F. M. and Kowalewski, F.: 1989,Gen. Rel. Grav. 21, 467.

    Google Scholar 

  • Goicoechea, L. J. and Sanz, J. L.: 1984,Astrophys. J. 286, 392.

    Google Scholar 

  • Grøn, Ø: 1985,Phys. Rev. D32, 2522.

    Google Scholar 

  • Grøn, Ø. and Soleng, H.: 1988,Class Quant. Grav. 5, L101.

    Google Scholar 

  • Hageman, T. and van Leeuwen, W. A.: 1987,Physica 146A, 506.

    Google Scholar 

  • Heller, M.: 1978,Acta Cosmologica 7, 7.

    Google Scholar 

  • Heller, M. and Klimek, Z.: 1975,Astrophys. Space Sci. 33, L37.

    Google Scholar 

  • Heller, M. and Suszycki, L.: 1974,Acta Phys. Pol. B5, 345.

    Google Scholar 

  • Heller, M. and Szydlowski, M.: 1983,Astrophys. Space Sci. 90, 327.

    Google Scholar 

  • Heller, M., Klimek, Z., and Suszycki, L.: 1973,Astrophys. Space Sci. 20, 205.

    Google Scholar 

  • Heller, M., Ostrowski, M., and Woszcyna, A.: 1982,Astrophys. Space Sci. 87, 425.

    Google Scholar 

  • Hu, B. L.: 1982,Phys. Letters 90A, 375.

    Google Scholar 

  • Hu, B. L.: 1983a,Adv. Astrophys. 1, 23.

    Google Scholar 

  • Hu, B. L.: 1983b,Phys. Letters 97A, 368.

    Google Scholar 

  • Huang, W. H.: 1988,Phys. Letters 129A, 429.

    Google Scholar 

  • Huang, W. H.: 1989,Phys. Letters 136A, 21.

    Google Scholar 

  • Johri, V. B. and Sudarshan, R.: 1988,Phys. Letters 132A, 316.

    Google Scholar 

  • Johri, V. B. and Sudarshan, R.: 1989,Australian J. Phys. 42, 215.

    Google Scholar 

  • Klimek, Z.: 1974,Acta Cosmologica 2, 49.

    Google Scholar 

  • Klimek, Z.: 1975a,Acta Astron. 25, 79.

    Google Scholar 

  • Klimek, Z.: 1975b,Acta Cosmologica 3, 49.

    Google Scholar 

  • Klimek, Z.: 1976,Nuovo Cimento 35B, 249.

    Google Scholar 

  • Klimek, Z.: 1981,Acta Cosmologica 10, 7.

    Google Scholar 

  • Koijam, M. S.: 1988a,Astrophys. Space Sci. 143, 137.

    Google Scholar 

  • Koijam, M. S.: 1988b,Astrophys. Space Sci. 148, 149.

    Google Scholar 

  • Koppar, S. S. and Patel, L. K.: 1988a,Nuovo Cimento 102B, 419.

    Google Scholar 

  • Koppar, S. S. and Patel, L. K.: 1988b,Nuovo Cimento 102B, 425.

    Google Scholar 

  • Lake, K.: 1982,Phys. Rev. 26D, 518.

    Google Scholar 

  • Liang, E. P. T.: 1975,Monthly Notices Roy. Astron. Soc. 171, 551.

    Google Scholar 

  • Liang, E. P. T.: 1977,Phys. Rev. D16, 3369.

    Google Scholar 

  • Lima, J. A. S., Portugal, R., and Waga, I.: 1988,Phys. Rev. D 37, 2755.

    Google Scholar 

  • Linde, A.: 1987, in S. W. Hawking and W. Israel (eds.), ‘Inflation and Quantum Cosmology’,300 Years of Gravitation, Cambridge University Press, Cambridge.

    Google Scholar 

  • Lorenz-Petzold, D.: 1989,Astrophys. Space Sci. 155, 335.

    Google Scholar 

  • Lukacs, B.: 1976,Gen. Rel. Grav. 7, 635.

    Google Scholar 

  • Lukacs, B.: 1981,Acta Phys. Acad. Sci. Hung. 51, 117.

    Google Scholar 

  • Lukash, V. N. and Starobinskij, A. A.: 1974,Soviet Phys. JETP 39, 742.

    Google Scholar 

  • Lukash, V. N., Novikov, I. D., Starobinskij, A. A. and Zel'dovich, Ya. B.: 1976,Nuovo Cimento 35B, 293.

    Google Scholar 

  • MacIntosh, C. B. G.: 1972,Australian J. Phys. 25, 75.

    Google Scholar 

  • Matzner, R. A.: 1969a,Astrophys. J. 157, 1085.

    Google Scholar 

  • Matzner, R. A.: 1969b,Astrophys. Space Sci. 4, 459.

    Google Scholar 

  • Matzner, R. A.: 1972,Astrophys. J. 171, 433.

    Google Scholar 

  • Matzner, R. A. and Misner, C. M.: 1972,Astrophys. J. 171, 415.

    Google Scholar 

  • Misner, C. W.: 1967,Phys. Rev. Letters 19, 533.

    Google Scholar 

  • Misner, C. W.: 1968,Astrophys. J. 151, 431.

    Google Scholar 

  • Modak, B.: 1987,Class. Quant. Grav. 4, L47.

    Google Scholar 

  • Murphy, G. L.: 1973,Phys. Rev. D8, 4231.

    Google Scholar 

  • Myung, S. and Cho, B. H.: 1986,Mod. Phys. Letters A1, 37.

    Google Scholar 

  • Nayak, B. K. and Sahoo, B. K.: 1989,Gen. Rel. Grav. 21, 211.

    Google Scholar 

  • Neugebauer, G. and Strobel, H.: 1969,Wissen Z. Friedrich-Schiller Universität Jena 18, 175.

    Google Scholar 

  • Nightingale, J. D.: 1973,Astrophys. J. 185, 105.

    Google Scholar 

  • Novello, M. and Araujo, T. A.: 1988,Phys. Rev. D22, 260.

    Google Scholar 

  • Novello, M. and d'Olival, J. B. S.: 1980,Acta Phys. Pol. B11, 3.

    Google Scholar 

  • Oliveira, H. P. and Salim, J. M.: 1988,Acta Phys. Pol. B19, 649.

    Google Scholar 

  • Pacher, T., Stein-Schabes, J. A., and Turner, M. S.: 1987,Phys. Rev. D36, 1603.

    Google Scholar 

  • Padmanabhan, T. and Chitre, S. M.: 1987,Phys. Letters A120, 433.

    Google Scholar 

  • Papini, G. and Weiss, M.: 1985,Nuovo Cimento Letters 44, 612.

    Google Scholar 

  • Papini, G. and Weiss, M.: 1986,J. Math. Phys. 27, 1367.

    Google Scholar 

  • Parnowski, S. L.: 1977,Soviet Phys. JETP 45, 423.

    Google Scholar 

  • Ribeiro, M. B. and Sanyal, A. K.: 1987,J. Math. Phys. 28, 657.

    Google Scholar 

  • Romero, C.: 1988,Rev. Bras. de Fisica 18, 75.

    Google Scholar 

  • Sakai, K.: 1971,Prog. Theor. Phys. 46, 1292.

    Google Scholar 

  • Salvati, G. A. Q., Schelling, E. E., and van Leeuwen, W. A.: 1987,Ann. Phys. 179, 52.

    Google Scholar 

  • Santos, N. O.: 1984,Phys. Letters 106A, 296.

    Google Scholar 

  • Santos, N. O., Dias, R. S., and Banerjee, A.: 1985,J. Math. Phys. 26, 878.

    Google Scholar 

  • Singh, R. K. T. and Singh, N. I.: 1988a,Astrophys. Space Sci. 147, 235.

    Google Scholar 

  • Singh, R. K. T. and Singh, N. I.: 1988b,Astrophys. Space Sci. 150, 65.

    Google Scholar 

  • Singh, R. K. T. and Singh, N. I.: 1988c,Astrophys. Space Sci. 150, 309.

    Google Scholar 

  • Stewart, J. M.: 1968,Astrophys. Letters 2, 133.

    Google Scholar 

  • Stewart, J. M.: 1969,Monthly Notices Roy. Astron. Soc. 145, 347.

    Google Scholar 

  • Straumann, N.: 1976,Helv. Phys. Act. 49, 269.

    Google Scholar 

  • Suszycki, L.: 1978,Acta Cosmologica 7, 147.

    Google Scholar 

  • Szydlowski, M. and Heller, M.: 1983,Acta Phys. Pol. B14, 303.

    Google Scholar 

  • Tauber, G. E.: 1978,Astrophys. Space Sci. 57, 163.

    Google Scholar 

  • Treciokas, R. and Ellis, G. F. R.: 1971,Comm. Math. Phys. 23, 1.

    Google Scholar 

  • Van Leeuwen, W. A. and Salvati, G. A. Q.: 1985,Ann. Phys. 165, 214.

    Google Scholar 

  • Van Leeuwen, W. A., Miedema, P. G., and Wiersma, S. H.: 1989a,Gen. Rel. Grav. 21, 413.

    Google Scholar 

  • Van Leeuwen, W. A., Miedema, P. G., Salvati, G. A. Q., and Wiersma, S. H.: 1989b,Gen. Rel. Grav. 21, 1263.

    Google Scholar 

  • Verwimp, T. A. and Callebaut, D. K.: 1987,Bulk Viscosity and Inflation, Proc. 26th Liège Int. Astrophys. Colloq., July 1–4, 1986, p. 211.

  • Waga, I., Falcao, R. C., and Chandra, R.: 1986,Phys. Rev. D33, 1839.

    Google Scholar 

  • Weinberg, S.: 1971,Astrophys. J. 168, 175.

    Google Scholar 

  • Wolf, C.: 1987,Hadronic J. 10, 59.

    Google Scholar 

  • Wolf, C.: 1988,Phys. Letters A127, 129.

    Google Scholar 

  • Wolf, C.: 1989,Phys. Scripta 40, 9.

    Google Scholar 

  • Woszczyna, A.: 1980,Acta Phys. Pol. B11, 15.

    Google Scholar 

  • Woszczyna, A. and Betkowski, W.: 1982,Astrophys. Space Sci. 82, 489.

    Google Scholar 

  • Zel'dovich, Ya. B.: 1970,Soviet Phys. JETP Letters 12, 307.

    Google Scholar 

  • Zel'dovich, Ya. B.: 1979, in M. Demianski (ed.), ‘Physics of the Expanding Universe’,Lecture Notes in Physics, Vol. 109, p. 60.

  • Zel'dovich, Ya. B. and Novikov, I. D.: 1983,Relativistic Astrophysics, Vol. 2, The University of Chicago Press, Chicago, p. 519.

    Google Scholar 

  • Zel'dovich, Ya. B. and Starobinskij, A. A.: 1972,Soviet Phys. JETP 34, 1159.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grøn, Ø. Viscous inflationary universe models. Astrophys Space Sci 173, 191–225 (1990). https://doi.org/10.1007/BF00643930

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00643930

Keywords

Navigation