Emergent

We present a covariant effective field theory formulation of the emergent gravity framework of Whitmer (2026a,b). The action combines a k-essence scalar sector with logarithmic kinetic term K(X) = ½a₀²ln(1 + 2X/a₀²), an Einstein-æther coupling through the æther four-acceleration, and a squared cosine potential. Three results follow from a single variational principle: the stochastic field equation with two-point function ⟨η η⟩ = a₀ a_N δ³ derived from Allen & Jacobson (1986) and Starobinsky (1982); the BTFR and rotation curves of Whitmer (2026a) exactly, with f(τ) = 1/(1+τ²) and γ = 2 derived from K’(X); and dark energy w ≈ −0.76 within 2σ of DESI 2024 with no free parameters. The covariant self-consistency of τ is established: τ is defined through the æther four-acceleration magnitude, which Jacobson & Mattingly (2001) show equals a_N in the non-relativistic limit, and the scalar field equation sources that same four-acceleration — constituting a coupled EFT with a well-posed NR initial value problem. The framework is presented as a phenomenological EFT, not a UV-complete theory. Open questions including the CMB spectral index, multi-center treatment, covariant τ generalization beyond the NR limit, and quantum completion are identified explicitly.