Grand Relativity: The Scalar Landscape

The standard ΛCDM cosmological model invokes three disconnected components: inflation, cold dark matter, and a cosmological constant. Recent observations reveal significant tensions: the Hubble constant discrepancy and JWST’s discovery of massive galaxies at z ∼ 10 − 14 challenge standard structure formation. We propose these are manifestations of a single mechanism: cosmological evolution of the scalar field ϕ in the Grand Relativity framework. Under the Scaling Concordance (c ∝ ϕ, G ∝ ϕ2, m ∝ ϕ−2), the apparent dark matter fraction evolves as fDM (z) = ϕ0(1+z)1.5 −1, rather than the constant ratio predicted by ΛCDM. We test this against a complete sample of 40 galaxy clusters spanning z = 0 to z = 3. The GRL power-law model yields an excellent fit with χ2 red = 0.72, while the constant ΛCDM model is decisivelyrejected (χ2 red = 2.93, > 9σ tension). The data further supports a “Hierarchical Vacuum” structure, where the scalar baseline shifts from ϕ ≈ 4.0 in shielded galactic environments to ϕ ≈ 5.3 in the intergalactic cluster medium. Remarkably, we demonstrate that the scalar field ϕ represents the dynamical Planck scale of the universe (lp ∝ ϕ−1/2), unifying quantum mechanics with cosmology. We derive the fundamental acceleration equation⃗a = −c 2∇ϕ/ϕ rigorously from the geodesic equation of the effective metric. The scalar field background arises from Mach’s Principle via the Sciama relation, providing a geometric origin for both its primordial amplitude and cosmological decay. Dark energy emerges as the kinetic relaxation of the universe from fine-grained quantum resolution (high confinement energy) to the coarse-grained vacuum of the present day. If validated, GRL suggests the dark sector represents geometric artifacts of quantum scale evolution rather than distinct particles.