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We propose a unified single-field description of the galactic Dark Matter andvarious uniform scalar fields for the inflation and cosmological constant. Thetwo types of effects could originate from a fluid of both spatially andtemporally varying Vacuum Energy if the vacuum has an uneven pressure caused bya photon-like vector field (of perhaps an unstable massive boson). We propose amost general Lagrangian with a {\bf N}on-{\bf u}niform Cosmological Constantfor this vacuum fluid (dubbed as a Nu-Lambda fluid), working within theframework of Einsteinian gravity. This theory includes a continuous spectrum ofplausible dark energy theories and gravity theories, e.g., inflation,quintessence, k-essence, f(R), Generalized Einstein-Aether f(K), MOND, TeVeS,BSTV etc. theories. It also suggests new models such as a certain f(K+R) model,which suggests intriguing corrections to MOND depending of redshift anddensity. Some specific constructions of the Nu-Lambda fluid (e.g., Zhao'sV-$\Lambda$ model) closely resemble the $\Lambda$CDM cosmology on large scale,but fit galaxy rotation curves as good as MOND. Perturbed Einstein Equations ina simple $f(K_4)$ model are solvable and show effects of a DM coupled to DE.Incorporating the perturbation equations here into standard simulations forcosmological structure growth offers a chance to falsify examples of theNu-Lambda theories.

Perturbations In A Non-Uniform Dark Energy Fluid: Equations Reveal Effects of Modified Gravity and Dark Matter