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According to general relativity inertial mass and gravitational mass are equivalent. Therefore, inertial acceleration might, like gravitational acceleration, be associated with changing metrical coefficients in the line element of general relativity. This possibility is investigated. If a cosmological reference frame exists, the Minkowskian line element may be modified by a velocity dependent scale factor for which all accelerating motion becomes motion on spacetime geodesics. This might model inertia as a gravitational-type phenomenon.

Three previous papers in this series introduce and discuss the Scale Expanding Cosmos (SEC) theory. This paper proposes a connection between the theory's discrete, stepwise, cosmological scale expansion and quantum mechanics. Very high frequency, small amplitude, temporal excitation in the metrical coefficients of the Minkowski spacetime is modelled in general relativity. DeBroglie type matter-waves are shown to result from motion of spatially confined metrics oscillating at the Compton frequency. The momentum ?guiding function? of Bohm and de Broglie naturally follows from the geodesic equations of general relativity. A clear physical explanation to the double-slit interference experiment is given. Setting part of the Ricci scalar equal to zero gives a wave equation from which the Schr?dinger equation is derived. This possible link between general relativity theory and quantum theory explains the particle-wave duality and suggests that quantum mechanical wave functions are amplitude and phase odulations of very high frequency oscillations in general relativity's metrical coefficients.

In the Scale Expanding Cosmos (SEC) the gravitational potential is modified by the cosmological scale expansion. The range of the gravitational field rolls off close to the Hubble distance and the presence of matter modifies the gravitational vacuum field, which evaluated in the cosmological reference frame contains negative energy that should equal the gravitating mass energy mc². A freely falling particle never reaches the event-horizon, which could prevent the formation of black holes. Although the results presented in this paper are tentative, two definite conclusions may be made in the SEC model:

1. The event-horizon is a true singularity.
2. Any spherically symmetric solution (other than the cosmological line element) of the Einstein's equations necessarily must modify the vacuum energy-momentum tensor generating negative field energy.

In a previous article the author introduced the Scale Expanding Cosmos (SEC) theory and showed that this new theory could resolve several problems with the Standard Cosmological Model. This new theory better agrees with observational data, for example the number count test, the angular size test, the surface brightness test and the supernovae Ia observations. In addition it provides a simple explanation to the Pioneer anomaly. The SEC theory predicts new and testable cosmological features among them cosmic (velocity) drag, which is the subject of this paper. I will show that currently there is substantial evidence for cosmic drag and suggest how this new and unexpected aspect of the universe may be confirmed by observations in the solar system.

A new cosmological theory is presented based on the proposition that all four metrical coefficients of space and time change with the cosmological expansion. Such a universal scale expansion would preserve the four-dimensional spacetime geometry and therefore by general relativity most physical relationships. In addition, if the scale expansion were exponential with time, all epochs would be equivalent. The theory resolves several outstanding problems with the Big Bang theory and better agrees with four observational programs. It also provides a simple explanation to the Pioneer anomaly.