Kinetical Inflation and Quintessence by F-Harmonic Map

Affiliation(s)

Faculté des Sciences et Techniques, Université d'Abomey-Calavi, Cotonou, Bénin.

University of Namur, Namur, Belgium.

Faculté des Sciences et Techniques, Université d'Abomey-Calavi, Cotonou, Bénin.

University of Namur, Namur, Belgium.

ABSTRACT

We were interested, along this work, in the phenomena of the quintessence and the inflation due to the F-harmonic maps, in other words, in the functions of the scalar field such as the exponential and trigo-harmonic maps. We showed that some F-harmonic map such as the trigonometric functions instead of the scalar field in the lagrangian, allow, in the absence of term of potential, reproduce the inflation. However, there are other F-harmonic maps such as exponential maps which can’t produce the inflation; the pressure and the density of this exponential harmonic field being both of the same sign. On the other hand, these exponential harmonic fields redraw well the phenomenon of the quintessence when the variation of these fields remains weak. The problem of coincidence, however remains.

We were interested, along this work, in the phenomena of the quintessence and the inflation due to the F-harmonic maps, in other words, in the functions of the scalar field such as the exponential and trigo-harmonic maps. We showed that some F-harmonic map such as the trigonometric functions instead of the scalar field in the lagrangian, allow, in the absence of term of potential, reproduce the inflation. However, there are other F-harmonic maps such as exponential maps which can’t produce the inflation; the pressure and the density of this exponential harmonic field being both of the same sign. On the other hand, these exponential harmonic fields redraw well the phenomenon of the quintessence when the variation of these fields remains weak. The problem of coincidence, however remains.

Cite this paper

A. Kanfon and D. Lambert, "Kinetical Inflation and Quintessence by F-Harmonic Map,"*Journal of Modern Physics*, Vol. 3 No. 11, 2012, pp. 1727-1731. doi: 10.4236/jmp.2012.311213.

A. Kanfon and D. Lambert, "Kinetical Inflation and Quintessence by F-Harmonic Map,"

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[1] P. Binétruy, “Cosmological Constant vs Quintessence,” International Journal of Theoretical Physics, Vol. 39, No. 7, 2000, pp.1859-1875. doi:10.1023/A:1003697832568

[2] J. P. Ostricker and P. J. Steinhard, “The Standard Cosmological Model,” Nature, Vol. 377, 1195, pp. 600-602.

[3] M. S. Turner, G. Steingman and L, Krauss, “The Cosmological Constant,” Physical Review Letters, Vol. 52, No. 23, 1984, pp. 2090-2093. doi:10.1103/PhysRevLett.52.2090

[4] P. Steinhardt, “Critical Problems in Physics,” Princeton University Press, Princeton, 1997.

[5] P. Steinhardt, L. Wang and I. Zlatev, “Cosmological Tracking Solution,” Physical Review D, Vol. 59, No. 12, 1999, pp. 123504-123611. doi:10.1103/PhysRevD.59.123504

[6] C. Armendariz-Picon, T. Darmour and V. Mukanov, “K-Inflation,” Physics Letters B, Vol. 458, 1999, pp. 209-218. doi:10.1016/S0370-2693(99)00603-6

[7] M. Ara, “Geometry of F-harmonic,” Kodai Mathematical Journal, Vol. 22, No. 2, 1999, pp. 243-263. doi:10.2996/kmj/1138044045

[8] M. Ara, “Mathematics Subject Classification,” Primary 58E20, 1991.

[9] M. Ara, “Mathematics Subject Classification”, Primary 58E05, 1991.

[10] M. Ara, “Stability of F-Harmonic Maps into Pinched Manifold,” Hiroshima Mathematical Journal, Vol. 31, No. 1, 2001, pp. 171-181.

[11] T. Chiba, T. Okabe and M. Yamaguchi, “Kinetical Driven Quintessence,” Physical Review D, Vol. 62, No. 2, 2000, pp. 023511-023519. doi:10.1103/PhysRevD.62.023511

[12] Takeshi Chiba, “Tracking kinetically quintessence”, Phys. rev. D, Vol. 66, No. 6, 2002, pp.063514-0635521. doi:10.1103/PhysRevD.66.063514