The Crux of the Cosmological Gravitational Field Equation

Abstract
This paper reveals the core issues inherent in Einstein's cosmological field equations and their solutions, the Friedmann equations, through an in-depth analysis. The study found that to construct models of a static or accelerating expanding universe using cosmological field equations, two key assumptions must be introduced: first, the pressure in the equation set may need to be negative; second, the added cosmological constant corresponds to negative mass matter, which can exert repulsive gravity or anti-gravity on ordinary matter. Ordinary fluid pressure and radiation pressure both correspond to positive mass matter, describing states that completely align with cosmological equations built upon Newtonian mechanics and thus cannot explain the phenomenon of the universe's accelerating expansion.The research points out that introducing concepts such as negative pressure and negative mass violate fundamental principles of physics, and thus lack sufficient theoretical support.According to Newton's law of universal gravitation, even if negative mass matter truly existed, based on the positive-negative mass ratio set by current theories of cosmic acceleration, the main constituent of the universe would be negative mass matter—this would only exert attractive universal gravitation on negative mass matter, causing the universe to undergo continuous accelerated contraction rather than expansion. Even from a new perspective of the matter in Newtonian static gravitational field, such negative mass matter cannot be derived. Therefore, the universe cannot possibly accelerate under the repulsive gravity of negative pressure and negative energy matter. By applying Newton's law of universal gravitation, it is proven that the cosmological field equations describing a finite universe cannot accurately depict the true state of the universe and should be completely discarded. Within the framework of the infinite universe hypothesis, applying Newton's law of universal gravitation resolves the Neumann-Seeliger paradox. The established cosmological field equations are Laplace's equations, which can describe an infinite static universe and possess intrinsic harmony. This is entirely consistent with the static universe theory supported by Type Ia supernova Hubble diagrams and light curves.

Keywords
cosmological gravitational field equations, Friedmann's equations, cosmological constant, dark energy, negative mass matter, negative pressure, repulsive universal gravitation, antigravity, Laplace equation

Cite this paper
Zhenglong Xu, The Crux of the Cosmological Gravitational Field Equation , SCIREA Journal of Physics. Volume 11, Issue 4, August 2026 | PP. 206-258. 10.54647/physics140730

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