MG13 - Talk detail

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Abstract

The recent discovery of the accelerating expansion of the Universe has raised new problems before theoretical cosmology. As is well established now, any viable cosmological model has to be able to describe several qualitatively different epoches of the Universe evolution, including the primary inflation, the matter-dominated stage, and the present acceleration (or secondary inflation). Moreover, it is also necessary to explain a mechanism providing an epoch change. Attempts to solve these problems have prompted many theoretical speculations. A plethora of models have been postulated and explored in recent years, including Quintessence, K-essence, Ghost Condensates, Dvali-Gabadadze-Porrati gravity, f(R) gravity, and others. We investigate a model containing an usual (barionic) matter and the scalar field with non-minimal derivative coupling to the curvature. Generally, coupling terms have the form $\kappa_1 R\phi_{,\mu}\phi^{,\mu}$ and $\kappa_2 R_{\mu\nu}\phi^{,\mu}\phi^{,\nu}$, and the corresponding field equations contain third derivatives of $g_{\mu\nu}$ and $\phi$. However, in the specific case $\kappa G_{\mu\nu}\phi^{,\mu}\phi^{,\nu}$ the order of field equations is reduced up to second one. The non-minimal derivative coupling provides an essentially new inflationary mechanism. At early times, when $\kappa$-terms are dominating, the cosmological evolution has the quasi-de Sitter character with $a(t)\sim e^{H_K t}$, where $H_K=1/\sqrt{9\kappa}$. Then, in the course of time matter terms become dominating and the inflationary stage is replaced by the matter-dominated epoch. The most likely mechanism of the late-time acceleration of the Universe is a cosmological constant, which is the simplest model and is in good agreement with all observational data. Actually, the cosmological constant $\Lambda$ is negligible at early stages, when the $\kappa$ and matter terms are dominating, but it becomes dominating at large values of the scale factor $a(t)$. At this moment the matter-dominated stage of the Universe evolution is changed by the accelerating phase with $a(t)\sim e^{H_\Lambda t}$, where $H_\Lambda=({\Lambda/3})^{1/2}$. Therefore, in the framework of the model with non-minimal derivative coupling one can naturally obtain the basic stages of the Universe evolution and easily describe transitions from one cosmological phase to another. It is worth also stressing that the model needs no fine-tuned potential.

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