—————————— read pre-print on research gate (new window) ——————————

• θ_si, is 3.26239 radians or kg m/s (momentum) or no units at all a function of the chosen frame of reference. This is a new constant to modern theory and exists in nearly every equation of the model. It may be measured macroscopically given specific Bell states necessary for quantum entanglement of X-rays such as those carried out by Shwartz and Harris.

• l_f, m_f and t_f are effectively Planck’s Units for length, mass and time, but not precisely the same. In MQ we recognize them as the fundamental units.
• D_U is the diameter of the universe.
• n_T is a count of t_f.
• n_L is a count of l_f.
• n_Tu is a count of t_f equal to the age of the universe.
• n_Lu is a count of l_f equal to the diameter of the universe.
• Ω_vis is the mass that is presently seen from a point in space.
• Ω_obs is the mass that is presently or will eventually be seen from a point in space.
• Ω_uobs is the mass that will eventually be seen from a point in space, but has not presently in view.
• Ω_dk is that domain of the universe that will never be visible.
• Ω_tot is all the mass in the universe.

The Cosmic Microwave Background (CMB) offers physical insight into early universe events. For instance, what properties characterize the earliest epoch? How did this epoch begin? What ends this epoch? Did the CMB form in this epoch or during the first moments of the expansionary epoch? And, how do we match properties of the CMB power spectrum to early universe events?

A Measurement Quantization (MQ) approach to early universe events answers these questions. Importantly, such an analysis provides an understanding of how our universe expands, why it expands and the milestone events that makeup the eveolution of our universe. It also steers us away from our current understanding of the CMB power spectrum as representative of several energy domains (i.e., baryonic, dark matter, dark energy) and instead points to a time-based geometry, as these parameters better define the CMB power curve. Perhaps most important, MQ is a nomenclature, a syntax used with existing classical expression to resolve a first principles description of early universe events. We will explain.

Initially, we can infer there was a time when the universe had a radius less than one Planck length. Such a period would have created a spatial referencing problem. With respect to a discrete Internal Frame of the universe - these properties of measure derived using the Heisenberg uncertainty principle, escape velocity and the speed of light - it is not possible to reference points external to the universe. As such, the universe expands quantumly until reaching a radius of square root of three Planck lengths. This takes 363,312 years. At the same time - across all epochs - mass accretes at a steady rate M_acr=n_Tum_fθ_si^3/2 and during the quantum epoch this mass takes an uncertain form. Once external referencing is possible, a point in time when the radius of the universe reaches the square root of three fundamental lengths, expansion begins and all mass accreted to that point becomes what we see today as the CMB. Calculations match measurement with digit-for-digit correspondence.

Importantly, we find that the power spectrum is not best described as a composite of energy phenomena, but as observational domains representative of our temporal point-of-view. These domains are, first, the visible Ω_vis. Next, the observable Ω_obs describes what will be visible. The difference between these two describes the unobserved Ω_uobs. And that which will never be observed due to the metric expansion of space is described by the dark Ω_dk. This last domain is typically associated with the phenomenon dark energy. In the same way, the unobserved domain Ω_uobs is an important compenent of the dark matter phenomenon.

Importantly, these domains apply to all models of an expanding universe. Conversely, models of non-expanding universes exhibit the visible and observable domains, each which match in magnitude while the unobserved and dark domains do not exist.

Finally, it is because of this rigid and geometrically correlated relation that the peak power spectrum values for each curve of the power spectrum can easily be described. Their x and y coordinates - such that x is a function of y, are

And finally, we account for dilation with respect to the x-coordinate. Each x-value, except the dark domain, must be multiplied by,

This last expression describes the frame transform between the Internal and System Frames of the universe, specifically the dilation between the two epochs. As such, we have a complete picture of the CMB as well as the physical events that transpired during the earliest epoch. Moreover, inflation theory is not described or predicted by the MQ approach to classical expression. MQ predicts no faster-than-light inflationary period, although there is a 363,312 year quantum period.

Finally, all the calculations are classical. The observations presented require no fitting, no new axioms and no new physics. The CMB distributions are correlated to today's best measurements and upon this foundation a straight-forward story that spans from the earliest epoch to the present unfolds.