Acceleration is an almost-sterile concept. However, since four-velocity is a four-dimensional (thus reduced) tangent vector field over geometric phase-spacetime (t, xi, ui), it yields a very rich concept of acceleration as a vector-valued 1-form. As in general relativity, the usual concept of acceleration comes out in the wash. By virtue of their nature, constants such as mass and charge are absent from this theory, though there is room for the concept of mass in the “renormalization” of the metric. Since, modulo these constants, force and acceleration become synonymous, the theory of acceleration (TOA) becomes a theory of “shadow” interactions: gravitational, electromagnetic (EM), and a third interaction that we refer to as “Third.” The TOA constitutes part of the theory of all the invariants associated with the above frames, namely, classical differential phase-space time geometry (PSTG). That is its context. The TOA connects with the remainder of PSTG through terms which appear in the acceleration 1-form but which fail to reach the equations of the motion. This absence splits the torsion into one part that we call “electromagnetic + Third” and another part, “Fourth,” which cannot manifest itself as a classical interaction. “Fourth,” which appears to shadow the weak interaction, nevertheless has gravitational effects through its contribution to the source side of Einstein's equations. It is, therefore, dark matter. Cosmological energy appears to be nothing but the energy of this particular type of dark matter, accounting for three quarters of the total. A cosmological term more sophisticated than the one involving the cosmological constant thus results.