Exact cosmological solutions with nonminimal derivative coupling

Sergey V. Sushkov

doi:10.1103/PhysRevD.80.103505

paper

Exact cosmological solutions with nonminimal derivative coupling

arXiv:0910.0980 · doi:10.1103/PhysRevD.80.103505

Abstract

We consider a gravitational theory of a scalar field $ϕ$ with nonminimal derivative coupling to curvature. The coupling terms have the form $κ_{1} R ϕ_{, μ} ϕ^{, μ}$ and $κ_{2} R_{μν} ϕ^{, μ} ϕ^{, ν}$ where $κ_{1}$ and $κ_{2}$ are coupling parameters with dimensions of length-squared. In general, field equations of the theory contain third derivatives of $g_{μν}$ and $ϕ$ . However, in the case $- 2 κ_{1} = κ_{2} \equiv κ$ the derivative coupling term reads $κ G_{μν} ϕ^{, m u} ϕ^{, ν}$ and the order of corresponding field equations is reduced up to second one. Assuming $- 2 κ_{1} = κ_{2}$ , 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 depends on the sign of $κ$ . For negative $κ$ the model has an initial cosmological singularity, i.e. $a (t) \sim (t - t_{i})^{2/3}$ in the limit $t \to t_{i}$ ; and for positive $κ$ the universe at early stages has the quasi-de Sitter behavior, i.e. $a (t) \sim e^{H t}$ in the limit $t \to - \infty$ , where $H = (3 κ)^{- 1}$ . The corresponding scalar field $ϕ$ is exponentially growing at $t \to - \infty$ , i.e. $ϕ (t) \sim e^{- t / κ}$ . At late stages the universe evolution does not depend on $κ$ at all; namely, for any $κ$ one has $a (t) \sim t^{1/3}$ at $t \to \infty$ . Summarizing, we conclude that a cosmological model with nonminimal derivative coupling of the form $κ G_{μν} ϕ^{, m u} ϕ^{, ν}$ is able to explain in a unique manner both a quasi-de Sitter phase and an exit from it without any fine-tuned potential.

7 pages, 2 figures. Accepted to PRD

Exact cosmological solutions with nonminimal derivative coupling

Abstract

References in corpus (5)

Cited by in corpus (201)