The Breathing Universe: 704_Cosmological Evolution of the Scalar Vacuum-Tension Background

This paper develops a cosmological extension of the effective field formulation of vacuum-tension dynamics within the Breathing Universe framework. The analysis investigates how the scalar order parameter H(x), previously introduced as a coarse-grained measure of vacuum-tension imbalance relative to the canonical zero-line equilibrium, evolves on cosmological scales in an expanding universe. Using a homogeneous and isotropic background geometry, the vacuum-tension field is treated as a spatially uniform scalar degree of freedom whose dynamics are governed by the covariant scalar–tensor effective action derived in earlier work. The coupled scalar and gravitational field equations are specialized to a cosmological background, yielding evolution equations for the time-dependent vacuum-tension background H(t) and its contribution to the cosmic energy–momentum budget. The analysis shows that vacuum-tension dynamics can produce distinct cosmological regimes depending on the effective parameters of the scalar potential and the background expansion rate. In particular, the vacuum-tension field may behave as a slowly varying background component capable of influencing late-time cosmic acceleration while remaining compatible with the effective field theory interpretation of gravity. The framework preserves general covariance and reduces to the standard Friedmann evolution equations when the vacuum-tension field approaches the zero-line equilibrium. The resulting cosmological dynamics provide a bridge between the local vacuum-tension formulation and large-scale cosmic evolution. The model generates testable consequences through its impact on the expansion history of the universe and on the propagation of gravitational waves across cosmological distances, thereby connecting vacuum-tension dynamics with observational cosmology.