- Some evidence for gauge field condensation in gauge theories is reviewed. The gravitational effects of gauge field condensates, in particular those associated with four-index field strengths are analyzed, paying special attention to their effect on the cosmological constant problem (CCP) and on the matching of different phases of the theory. Gauge fields composed of elementary scalars and their role in the CCP are studied. In particular such gauge fields can define a composite measure of integration which is a total derivative leading to the invariance under changes in the Lagrangian density L, L → L + constant. In such models, when gravity is formulated in the first order formalism, gauge field condensates define and control particle physics dynamics and drive inflation while the true vacuum of the theory is one with zero cosmological constant. It is also shown that models of gauge fields composed of elementary scalars, like the "No Scale Nonlinear σ Model" can produce a new geometrical-type solution of the strong CP problem, which is possible when a condensate of a composite gauge field is present. It is shown that the theory without the cosmological constant problem explained here has a scale invariance, spontaneously broken by the expectation value of a four-index field strength. However, no massless "dilaton" appears as a result of this SSB.