Classical Description of the CMB Power Spectrum Without Λ or CDM

In MQ Form

The CMB power distributions are recognized in MQ as temporal divisions of the measurement domain, that which is presently visible Ωvis, that which will be observable Ωobs, their difference, that being the unobserved Ωuobs and that which will never be observed due to the expansion of space Ωdk.

Inputs

  • θsi, 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.

Terms

  • lf, mf and tf are effectively Planck’s Units for length, mass and time, but not precisely the same. In MQ we recognize them as the fundamental units.
  • DU is the diameter of the universe.
  • nT is a count of tf.
  • nL is a count of lf.
  • nTu is a count of tf equal to the age of the universe.
  • nLu is a count of lf equal to the diameter of the universe.
  • vis is the mass that is presently seen from a point in space.
  • obs is the mass that is presently or will eventually be seen from a point in space.
  • uobs is the mass that will eventually be seen from a point in space, but has not presently in view.
  • dk is that domain of the universe that will never be visible.
  • tot is all the mass in the universe.

Calculations


Discussion

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 how we got to this point. 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 temporal 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 parameter free description of early universe events. We will explain.

Initially, the universe has a radius less than one Planck length. This creates a spatial referencing problem. With respect to the internal Measurement Frame of the observer 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 Macr=nTumfθsi3/2 and during the quantum epoch this mass takes the form of a quantum plasma. Once external referencing is possible, 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 related phenomena, but as observational domains representative of our temporal point-of-view. These domains are, first, the visible vis. Next, the observable obs describes what will be visible. The difference between these two describes the unobserved uobs. And that which will never be observed due to the metric expansion of space is described by the dark dk. This last domain is typically associated with the phenomenon dark energy. In the same way, the unobserved domain uobs is partly related to 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.

Distributions.png

Finally, it is because of this rigid and geometrically correlated temporal relation that the peak power spectrum values for each curve 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,

Relativistic Offset.JPG

This last expression describes the frame transform between the Target and Measurement frames, 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. MQ predicts no faster-than-light inflationary period, although there is a very lengthy 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.

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