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- W2097648045 abstract "We consider a gravitational theory of a scalar field $ensuremath{phi}$ with nonminimal derivative coupling to curvature. The coupling terms have the form ${ensuremath{kappa}}_{1}R{ensuremath{phi}}_{,ensuremath{mu}}{ensuremath{phi}}^{,ensuremath{mu}}$ and ${ensuremath{kappa}}_{2}{R}_{ensuremath{mu}ensuremath{nu}}{ensuremath{phi}}^{,ensuremath{mu}}{ensuremath{phi}}^{,ensuremath{nu}}$, where ${ensuremath{kappa}}_{1}$ and ${ensuremath{kappa}}_{2}$ are coupling parameters with dimensions of length squared. In general, field equations of the theory contain third derivatives of ${g}_{ensuremath{mu}ensuremath{nu}}$ and $ensuremath{phi}$. However, in the case $ensuremath{-}2{ensuremath{kappa}}_{1}={ensuremath{kappa}}_{2}ensuremath{equiv}ensuremath{kappa}$, the derivative coupling term reads $ensuremath{kappa}{G}_{ensuremath{mu}ensuremath{nu}}{ensuremath{phi}}^{,ensuremath{mu}}{ensuremath{phi}}^{,ensuremath{nu}}$ and the order of corresponding field equations is reduced up to second one. Assuming $ensuremath{-}2{ensuremath{kappa}}_{1}={ensuremath{kappa}}_{2}$, we study the spatially-flat Friedman-Robertson-Walker model with a scale factor $a(t)$ and find new exact cosmological solutions. It is shown that properties of the model at early stages crucially depend on the sign of $ensuremath{kappa}$. For negative $ensuremath{kappa}$, the model has an initial cosmological singularity, i.e., $a(t)ensuremath{sim}(tensuremath{-}{t}_{i}{)}^{2/3}$ in the limit $tensuremath{rightarrow}{t}_{i}$; and for positive $ensuremath{kappa}$, the Universe at early stages has the quasi-de Sitter behavior, i.e., $a(t)ensuremath{sim}{e}^{Ht}$ in the limit $tensuremath{rightarrow}ensuremath{-}ensuremath{infty}$, where $H=(3sqrt{ensuremath{kappa}}{)}^{ensuremath{-}1}$. The corresponding scalar field $ensuremath{phi}$ is exponentially growing at $tensuremath{rightarrow}ensuremath{-}ensuremath{infty}$, i.e., $ensuremath{phi}(t)ensuremath{sim}{e}^{ensuremath{-}t/sqrt{ensuremath{kappa}}}$. At late stages, the Universe evolution does not depend on $ensuremath{kappa}$ at all; namely, for any $ensuremath{kappa}$ one has $a(t)ensuremath{sim}{t}^{1/3}$ at $tensuremath{rightarrow}ensuremath{infty}$. Summarizing, we conclude that a cosmological model with nonminimal derivative coupling of the form $ensuremath{kappa}{G}_{ensuremath{mu}ensuremath{nu}}{ensuremath{phi}}^{,ensuremath{mu}}{ensuremath{phi}}^{,ensuremath{nu}}$ is able to explain in a unique manner both a quasi-de Sitter phase and an exit from it without any fine-tuned potential." @default.
- W2097648045 created "2016-06-24" @default.
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- W2097648045 date "2009-11-05" @default.
- W2097648045 modified "2023-10-03" @default.
- W2097648045 title "Exact cosmological solutions with nonminimal derivative coupling" @default.
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- W2097648045 doi "https://doi.org/10.1103/physrevd.80.103505" @default.
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