We extend the notion of phantom energy-which is generally accepted for homogeneously distributed matter with w < −1 in the universe-on inhomogeneous spherically symmetric spacetime configurations. A spherically symmetric distribution of phantom energy is shown to be able to support the existence of static wormholes. We find an exact solution describing a static spherically symmetric wormhole with phantom energy and show that a spatial distribution of the phantom energy is mainly restricted by the vicinity of the wormhole's throat. The maximal size of the spherical region, surrounding the throat and containing the most part of the phantom energy, depends on the equation-of-state parameter w and cannot exceed some upper limit.

We consider a gravitational theory of a scalar field $\phi$ with nonminimal derivative coupling to curvature. The coupling terms have the form $\kappa_1 R\phi_{,\mu}\phi^{,\mu}$ and $\kappa_2 R_{\mu\nu}\phi^{,\mu}\phi^{,\nu}$ where $\kappa_1$ and $\kappa_2$ are coupling parameters with dimensions of length-squared. In general, field equations of the theory contain third derivatives of $g_{\mu\nu}$ and $\phi$. However, in the case $-2\kappa_1=\kappa_2\equiv\kappa$ the derivative coupling term reads $\kappa G_{\mu\nu}\phi^{,mu}\phi^{,\nu}$ and the order of corresponding field equations is reduced up to second one. Assuming $-2\kappa_1=\kappa_2$, 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 depends on the sign of $\kappa$. For negative $\kappa$ 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 $\kappa$ the universe at early stages has the quasi-de Sitter behavior, i.e. $a(t)\sim e^{Ht}$ in the limit $t\to-\infty$, where $H=(3\sqrt{\kappa})^{-1}$. The corresponding scalar field $\phi$ is exponentially growing at $t\to-\infty$, i.e. $\phi(t)\sim e^{-t/\sqrt{\kappa}}$. At late stages the universe evolution does not depend on $\kappa$ at all; namely, for any $\kappa$ 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 $\kappa G_{\mu\nu}\phi^{,mu}\phi^{,\nu}$ is able to explain in a unique manner both a quasi-de Sitter phase and an exit from it without any fine-tuned potential.Comment: 7 pages, 2 figures. Accepted to PR

In this paper, we develop an iterative approach to span the whole set of exotic matter models able to drive a traversable wormhole. The method, based on a Taylor expansion of metric and stress-energy tensor components in a neighbourhood of the wormhole throat, reduces the Einstein equation to an infinite set of algebraic conditions, which can be satisfied order by order. The approach easily allows the implementation of further conditions linking the stress-energy tensor components among each other, like symmetry conditions or equations of state. The method is then applied to some relevant examples of exotic matter characterised by a constant energy density and that also show an isotropic behaviour in the stress-energy tensor or obeying to a quintessence-like equation of state.