Asymptotics of the gravitational field for a homogeneous phase of a gas of thin tubes of a massless scalar field.

The problem of the cosmological constant and the fundamental nature of dark energy remain among the key challenges for modern physics. Observed anomalies, in particular, cosmological tensions within the standard LCDM model related to large-scale structure growth rates and the pronounced heterogeneity of the visible Universe, require the development of radically new theoretical approaches. In this work, we research the concept of a gas of thin tubes of a massless scalar field (TToMSF) as a promising alternative within dynamical dark energy and unified dark fluid models. The TToMSF gas possesses an interesting property: its equation of state parameter w depends on the density of the medium. In the rarefied limit, the gas exhibits behavior characteristic of dark energy, whereas compression drives the system into a stiff matter state. Such dynamics make it possible to realize local equations of state that can mitigate existing cosmological contradictions. Furthermore, local gravitational interaction within the TToMSF gas can generate particles with an effective non-zero rest mass, allowing the TToMSF gas to be classified as a unified dark fluid model. In this study, we analyzed the temporal evolution of the geometry of the gravitational field generated by the homogeneous phase of the TToMSF gas. In this work, the asymptotics of the gravitational field is understood as its behavior under long-term time averaging. We have shown that as a result of such time averaging, the metric tensor of the homogeneous TToMSF gas phase tends toward flat Minkowski spacetime. The Minkowski solution as the time asymptotics confirms the dynamic stability of the homogeneous TToMSF gas phase and forms a fundamental basis for subsequent analysis of local perturbations.