Phantom Matter and the Cosmological Constant

TL;DR

The paper investigates scalar fields with negative kinetic energy (phantoms) as a mechanism for cosmic acceleration and explores their gravitational coupling. It proves that any solution of the Einstein equations with a cosmological constant, $R_{\alpha\beta}=\Lambda g_{\alpha\beta}$, also solves the phantom+fluid system provided $\rho - P = {\Lambda \over 4\pi G}$, revealing a non-unique, steady-state-like matter content for a given metric. It presents static anti-gravitating configurations—including a zero ADM-mass Einstein–Rosen wormhole and repulsive multi-object solutions—as well as extensions to higher-spin phantom fields and bi-metric theories, illustrating broad consequences of negative-energy sectors. The results suggest considerable indeterminacy in the matter content compatible with a fixed spacetime geometry and point to potential implications for dark energy modeling, modified gravity, and high-derivative theories, while underscoring cautions about causality and stability. ($\rho - P = {\Lambda \over 4\pi G}$; $L = {1\over 2}y$ phantoms; anti-self-gravitating solutions; wormholes; higher-spin phantoms$)$

Abstract

Motivated by some recent speculative attempts to model the dark energy, scalar fields with negative kinetic energy coupled to gravity without a cosmological constant are considered. It is shown that in the presence of an ordinary fluid, any solution of the vacuum Einstein equations with cosmological constant is a solution provided $ρ-P={Λ\over 4 πG}$. The solutions can be interpreted as a steady state in which matter or entropy is being continuously created (or destroyed). The motion of the matter is not determined by the background Einstein spacetime, many different matter flows can be found giving rise to the same metric. Solutions without ordinary matter are also considered. Anti-gravitating multi-solutions and repulsive solutions which can chase ordinary matter or black holes are exhibited. These results may also have applications to gravity theories with higher derivatives.