The flat Friedmann universes filled by stiff fluid and a nonminimally coupled material scalar field with polynomial potentials of the fourth degree are considered in the framework of the Einstein-Cartan theory. Exact general solution is obtained for arbitrary positive values of the coupling constant . A comparative analysis of the cosmological models with and without stiff fluid is carried out. Some effects of stiff fluid are elucidated. It is shown that singular models with a de Sitter asymptotic and with the power-law asymptotic at late times are possible. It is found that is a specific value of the coupling constant. It is demonstrated that the bouncing models without the particle horizon and with an accelerated expansion by a de Sitter law of an evolution at late times are admissible. 1. Introduction Recent cosmic observations [1–6] favor an isotropic spatially flat Universe, which is at present expanding with acceleration. The source of this expansion is an unknown substance with negative pressure called dark energy (DE). Establishment of the origin of DE has become an important problem. Different theoretical models of DE have been put forward (see, e.g., the reviews [7–10] and references therein). Among these models various modifications of general relativity (GR) were considered, the Einstein-Cartan theory (ECT) in particular [11–13]. This theory [14–17] is an extension of GR to a space time with torsion, and it reduces to GR when the torsion vanishes. The ECT is the simplest version of the Poincaré gauge theory of gravity (PGTG). It should be noted that the ECT contains a nondynamic torsion, because its gravitational action is proportional to the curvature scalar of the Riemann-Cartan space-time. In this sense, the ECT is a degenerate gauge theory [17–20]. This drawback is absent in the PGTG since its gravitational Lagrangian includes invariants quadratic in the curvature and torsion tensors. Nevertheless the ECT is a viable theory of gravity whose observational predictions are in agreement with the classical tests of GR, and it differs significantly from GR only at very high densities of matter [17, 21, 22]. The ECT finds applications in cosmology [23–28], particle theory [19, 29, 30], and the theory of strong interactions [31, 32]. From some time past, the interest to ECT has grown in connection with the fact that torsion arises naturally in the supergravity [33–35], Kaluza-Klein [36–38], and syperstring [39–41] theories. gravity with torsion has been developed [42–45] as one of the simplest extensions of the ECT. In [43] it has been
A. G. Riess, L.-G. Sirolger, J. Tonry et al., “Type Ia supernova discoveries at from the hubble space telescope: evidence for past deceleration and constraints on dark energy evolution,” The Astrophysical Journal, vol. 607, article 665, 2004.
E. Komatsu, J. Dunkley, M. R. Nolta et al., “Five-year Wilkinson microwave anisotropy probe observations: cosmological interpretation,” The Astrophysical Journal Supplement Series, vol. 180, no. 2, article 330, 2009.
W. M. Wood-Vasey, G. Miknaitis, C. W. Stubbs et al., “Observational constraints on the nature of dark energy: first cosmological results from the essence supernova survey,” Astrophysical Journal Letters, vol. 666, no. 2, pp. 694–715, 2007.
M. Tegmark, M. R. Blanton, M. A. Strauss et al., “The three-dimensional power spectrum of galaxies from the sloan digital sky survey,” Astrophysical Journal Letters, vol. 606, no. 2, pp. 702–740, 2004.
P. Astier, J. Guy, N. Regnault et al., “The supernova legacy survey: measurement of and w from the first year data set,” Astronomy & Astrophysics, vol. 447, no. 1, pp. 31–48, 2006.
A. H. Jaffe, P. A. R. Ade, A. Balbi et al., “Cosmology from MAXIMA-1, BOOMERANG, and COBE DMR cosmic microwave background observations,” Physical Review Letters, vol. 86, no. 16, pp. 3475–3479, 2001.
A. M. Galiakhmetov, “Exact isotropic scalar field cosmologies in Einstein-Cartan theory,” Classical and Quantum Gravity, vol. 27, no. 5, Article ID 055008, 2010.
A. M. Galiakhmetov, “Cosmology with polynomial potentials of the fourth degree in Einstein-Cartan theory,” Classical and Quantum Gravity, vol. 28, no. 10, Article ID 105013, 2011.
é.. Cartan, “Sur les espaces à connexion affine et la théorie de la relativité généralisée, partie I,” Annales Scientifiques de l'école Normale Supérieure, vol. 40, supplement, p. 325, 1923.
E. Cartan, “Sur les varietes à connexion et la theorie de la relativité généralisée (suite),” Annales Scientifiques de l'école Normale Supérieure, vol. 41, supplement, pp. 1–25, 1924.
E. Cartan, “Sur les espaces à connexion affine et la théorie de la relativité généralisée partie II,” Annales Scientifiques de l'école Normale Supérieure, vol. 42, supplement, pp. 17–88, 1925.
F. W. Hehl and Y. N. Obukhov, “Elie Cartan's torsion in geometry and in field theory, an essay,” Annales de la Fondation Louis de Broglie, vol. 32, p. 157, 2007.
F. W. Hehl, P. Von Der Heyde, G. D. Kerlick, and J. M. Nester, “General relativity with spin and torsion: foundations and prospects,” Reviews of Modern Physics, vol. 48, no. 3, pp. 393–416, 1976.
V. N. Ponomarev, A. O. Barvinsky, and N. Yu. Obuhov, Geometrodynamics Methods and Gauge Approach in the Theory of Gravity, Energoatomizdat, Moscow, Russia, 1985.
A. V. Minkevich and A. S. Garkun, “Analysis of inflationary cosmological models in gauge theories of gravitation,” Classical and Quantum Gravity, vol. 23, no. 12, article 4237, 2006.
A. Trautman, “Einstein-Cartan theory,” in Encyclopedia of Mathematical Physics, J. P. Fran？oise, G.-L. Naber, and S. T. Tsou, Eds., pp. 189–195, Elsevier, Oxford, UK, 2006.
P. Baekler and F. W. Hehl, “Beyond Einstein-Cartan gravity: quadratic torsion and curvature invariants with even and odd parity including all boundary terms,” Classical and Quantum Gravity, vol. 28, no. 21, Article ID 215017, 2011.
J. Tafel, “Cosmological models with a spinor field,” Bulletin de L'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 25, p. 593, 1977.
V. Krechet, Problems of gravitational interaction of the phisical fields in an affine connected spaces [PhD thesis], Yaroslavl State Pedagogical University, 1984.
S. D. Odintsov, “The nonsingular quantum cosmological models with nontrivial topology in conformal (Super) gravity,” Europhysics Letters, vol. 8, no. 4, article 309, 1989.
I. L. Buchbinder and S. D. Odintsov, “The behaviour of effective coupling constants in “Finite” grand unification theories in curved space-time with torsion,” Europhysics Letters, vol. 8, no. 7, article 595, 1989.
M. W. Kalinowski, “On a generalization of the Einstein-Cartan theory and the Kaluza-Klein theory,” Letters in Mathematical Physics, vol. 5, p. 489, 1958.
S. Yu. Vladimirov and A. D. Popov, “Compound torsion and spontaneous compactification in Kaluza-Klein theories,” Vestnik Moskovskogo Universiteta, Fizika, Astronomiya, vol. 29, no. 4, pp. 28–32, 1988.
K. Akdeniz, A. Kizilersu, and E. Rizaoglu, “Instanton and eigenmodes in a two-dimensional theory of gravity with torsion,” Physics Letters B, vol. 215, no. 1, pp. 81–83, 1988.
P. Kuusk, “The heterotic string and the geometry of the supersymmetric Einstein-Yang-Mills background,” General Relativity and Gravitation, vol. 21, no. 2, pp. 185–200, 1989.
S. Capozziello, R. Cianci, C. Stornaiolo, and S. Vignolo, “F(R) gravity with torsion: the metric-affine approach,” Classical and Quantum Gravity, vol. 24, no. 24, pp. 6417–6430, 2007.
K. Bamba, C. Q. Geng, C. C. Lee, and L. W. Luo, “Equation of state for dark energy in f(T) gravity,” Journal of Cosmology and Astroparticle Physics, vol. 2011, article 021, 2011.
S. Carloni, S. Capozziello, J. A. Leach, and P. K. S. Dunsby, “Cosmological dynamics of scalar-tensor gravity,” Classical and Quantum Gravity, vol. 25, no. 3, Article ID 035008, 2008.
A. O. Barvinsky, A. Y. Kamenshchik, C. Kiefer, A. A. Starobinsky, and C. Steinwachs, “Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field,” Journal of Cosmology and Astroparticle Physics, vol. 2009, article 003, 2009.
R. Gannouji, D. Polarski, A. Ranquet, and A. A. Starobinsky, “Scalar-tensor models of normal and phantom dark energy,” Journal of Cosmology and Astroparticle Physics, vol. 2006, article 016, 2006.
M. Szydlowsky and O. Hrycyna, “Scalar field cosmology in the energy phase-space—unified description of dynamics,” Journal of Cosmology and Astroparticle Physics, vol. 2009, article 039, 2009.
A. Yu. Kamenshchik, A. Tronconi, and G. Venturi, “Dynamical dark energy and spontaneously generated gravity,” Physics Letters B, vol. 713, no. 4-5, pp. 358–364, 2012.
J. Garcia-Bellido and A. Linde, “Stationarity of inflation and predictions of quantum cosmology,” Physical Review D, vol. 51, no. 2, pp. 429–443, 1995.
G. Felder, A. Frolov, L. Kofman, and A. Linde, “Cosmology with negative potentials,” Physical Review D, vol. 66, no. 2, Article ID 023507, 26 pages, 2002.
M. Cataldo and L. P. Chimento, “Crossing the phantom divide with a classical Dirac field,” Astrophysics and Space Science, vol. 333, no. 1, pp. 277–285, 2011.
V. G. Krechet and D. V. Sadovnikov, “Cosmology in an affine-metric theory of gravity with a scalar field,” Gravitation and Cosmology, vol. 3, pp. 133–1140, 1997.
M. Yu. Khlopov and A. S. Sakharov, “Cosmoparticle physics: as a probe for the theory of physical space-time,” Gravitation and Cosmology, vol. 1, pp. 164–176, 1995.
I. L. Buchbinder, S. D. Odintsov, and I. L. Shapiro, “Nonsingular cosmological model with torsion induced by vacuum quantum effects,” Physics Letters B, vol. 162, no. 1–3, pp. 92–96, 1985.
K. Bamba, S. Capozziello, S. Nojiri, and S. D. Odintsov, “Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests,” Astrophysics and Space Science, vol. 342, no. 1, pp. 155–228, 2012.