On the Reinterpretation of Dark Energy as the Elasticity of Space

In this work, we demonstrate that by treating space as a three dimensional elastic membrane, one can interpret the energy density stored in it as Dark Energy. In particular, we will model space as an infinitely large fundamental 3 brane and show that its vacuum stress energy tensor has the same mathematical form which one expects from the stress energy tensor describing a Lorentz invariant vacuum energy density (Dark Energy). We identify the dark-energy density with the tension of the fundamental 3 brane and thereby establish a direct correspondence between the cosmological constant and brane tension. Finally, we present a brief argument as to why the Cosmological Constant should be treated as a fundamental constant of nature, based on some light ontological discussion regarding the origin of the tension term in the broader framework of String Theory. In a forthcoming work, we will articulate a dynamical mechanism, which will be grounded in Q-theory, Hawking-Wu flux neutralization and broken super-symmetry, demonstrating the precise cancellation of vacuum energy in a manner such that the fundamental brane (spatial) tension remains the unique source of the Cosmological Constant.