VIII. SPECIAL TOPICS
There are two special topics that are important to GRLCDM, cosmic microwave background and gravitational waves. There are two special topics that are important to NCNG, stability and tests of validity.
A. Cosmic microwave background
There is cosmic microwave background (CMB) radiation in NC and anisotropies (CMBA) as well. The NC version of CMB and CMBA will be developed in this section. CMB radiation consists of relic photons that have traveled since the preceding winter. The observed CMB radiation today has a black body frequency distribution corresponding to \(2.725\,\;K\). Today is \(z = 0\) , where z is the NC cosmological redshift. The histories of Appendix C give z as a function of A (the apex field). One can discover that \(z = 0\) also when \(A = 1.00667\), very near the end of the preceding winter. Thus, the temperature today is \(2.725\,\;K\) because the temperature was \(2.725\,\;K\) in late winter about 20 billion years ago—beyond our ability to observe or calculate.
CMBA depends on the path and timing of a CMB photon (\({\gamma _{cmb}}\)) relative to the brief early spring turning on of local gravity (\({\tau _{on}}\))—the same time everywhere in the universe. Appendix N develops the details of this subject.
One will discover that the NCNG version of CMBA results from a net gravitational wavelength (temperature) shift of a relic \({\gamma _{cmb}}\) passing through or near a canister at \(\tau = {\tau _{on}}\). A canister is a vast and massive collection of matter and an associated gravitational field. The universe is filled with canisters. \({\tau _{on}}\) was about 20 billion years ago, so only the subset of canisters which are close to 20 billion light years away will exhibit a small temperature shift.
It should be possible to observe a sky map of these special canisters (as described in Appendix N). Once done, all of the basic aspects of NCNG could be proven. The internal tensions of GRLCDM have passed the breaking point, and JWST observations will likely increase the tensions. Therefore, it is time to create new observatories to test alternatives to GRLCDM.
B. Gravitational waves
The early observations of LIGO were described by many as proof that general relativity was the only correct theory. That belief was not true, and “proof” evolved into “consistent with”. Any viable gravitational theory will support gravitational waves, and NCNG is no exception. Section IV(B), Eq. (4.13) shows a solution which is a transverse (tensor) plane wave with the same cosmological redshift as electromagnetic waves. These plane waves are what LIGO observes. The difference between NCNG and GR is billions of light years away where the waves are created.
Gravity is so weak that waves cannot be observed unless the distant source is an event that provides a catastrophic amount of energy to be carried away in waves. The best event occurs when two black holes come together to form one black hole. In NCNG the black holes are replaced by CCBOs. Calculations of such events are incredibly complicated for both versions (beyond the scope of this document).
The GR version requires the simultaneous solution of more than 400 nasty equations. The black holes spiral inward toward each other moving at very high velocities (phase1). After the two event horizons come in contact, the two will have only one event horizon (phase 2). LIGO sees phase1 as a wave form of increasing frequency and amplitude. Phase 2 is a wave form of faint frequency and vanishing amplitude. The two phases make a recognizable pattern that denotes an event (if observed by both LIGO observatories).
The NCNG version is similar and every bit as complicated, but for different reasons. The wave formation process is much easier since it will be like electromagnetic waves. The two boundaries will replace event horizons. However, now one needs to calculate the behavior of the two CCBO sources all the way from beginning to end of their wild ride! There are many scenarios. During phase1 for example, a CCBO source will be subject to centrifugal distortion which would deform the boundary as well. It is even possible that such a distortion would destroy the source and cause it to evaporate.
The main difference between GR and NCNG is that NCNG will have a wider range of recognizable patterns than GR. Thus, LIGO will not recognize and record some portion of actual events (using the GR version criterion).
C. Universal stability
Stability is all about energy densities, so a review of this topic is useful. Energy densities are averaged over sufficiently large volumes. There are only three energy densities: \({U_{ax}}(\tau )\) for the apex field, \({U_{ep}}(\tau )\) for the epoch field, and \({U_M}(\tau )\) for “matter” (everything else). There is a universal constraint,
\[{U_{ax}}(\tau ) + {U_{ep}}(\tau ) + {U_M}(\tau ) = {\rm{ univeral~constant}}{\rm{.}}\tag{8.1}\]
The apex and epoch fields are discussed at length in section II. Matter is discussed at length throughout NCNG. Only the most common particles are included: electrons, electron-flavor neutrinos, neutrons, protons, nuclides, photons in flight, and gravitons in flight. Electromagnetic and gravitational fields are also included. The apex and epoch energy densities are negative and matter is positive. There is a basic hierarchy,
\[\left| {{U_{ax}}(\tau )} \right| > \left| {{U_{ep}}(\tau )} \right| > > {U_M}(\tau ),\tag{8.2}\]
where \({U_M}(\tau )\) is thought to be 250 Mev per cubic meter today (suspect value). \({U_M}(\tau )\) has a positive lower limit (a frozen universe), but there is no upper limit (an infinite temperature universe). Eq. (8.1) is the ultimate guarantor of stability, but that is not what this subsection is about. Here, one wants to know if the NCNG universe can run off the tracks.
Derailment means that there is a persistent imbalance which causes the apex and epoch energy densities to steadily become more negative and the matter energy density to steadily increase toward infinity—a disastrous outcome consistent with Eq. (8.1). I have evaded this question till now by insisting that the magnitude of the apex and epoch fields energy density is very much larger than the energy density of matter—an imbalance would take many cycles to derail. To avoid this outcome, it is necessary to study the complex network of energy transfers in NCNG.
An example will illustrate the network. The apex field is the ultimate storehouse of energy, and the epoch field is an important but lesser storehouse. Eq. (2.22) shows that energy can move between the two storehouses only for a very brief period (controlled by \({\Gamma _{ep}}\)) when \(\left| A \right| = {A_{ep}}\). \({\Gamma _{ep}}\) and \({A_{ep}}\) are universal constants tabulated in Appendix Z. This connection only occurs four times in every cycle, so the epoch-field storehouse must handle requirements without help for billions of years.
The epoch field connects with matter via the epoch factor,\(E({\phi _{ep}})\), defined by Eq. (2.17). The epoch factor appears in the LDM for matter via Eq. (3.1), and the connections are manifested by Eq. (7.4) and Eq. (7.5). Thus, any transfer of energy between the epoch field and matter can only occur during brief periods (controlled by \({\Gamma _W}\) or \({\Gamma _G}\)) when \(E({\phi _{ep}}) = {E_W}\) or \(E({\phi _{ep}}) = {E_G}\). \({\Gamma _W}\),
\({\Gamma _G}\), \({E_W}\), and \({E_G}\) are universal constants tabulated in Appendix Z. Both the weak and gravity energy transfers occur four times in each cycle. These specific connections all occur during spring or fall. In spring, the first event is the apex-epoch connection (AE). The second event is the bubble era (not an energy transfer) 2.35 million years later (based on the constants of Appendix Z). The third event is the epoch-gravity connection 5.58 million years after AE. The fourth event is the epoch-weak connection 6.46 million years after AE. In fall, the order is reversed. Thus, the epoch field must endure four matter connections before connecting to the apex field again.
The apex field is also connected directly to matter at all times. The apex field can subtract energy from photons and gravitons in flight via cosmological redshift—\({U_{ax}}(\tau )\) increases. Energy can be added via cosmological blueshift—\({U_{ax}}(\tau )\) decreases. In section III, one learns that the apex field also constantly interacts with all types of matter to empower the (excellently approximated) illusion of special relativity.
This subject is extremely complex (beyond the scope of this document). There are many ways that the apex field can gain or lose energy. Furthermore, the interactions between different types of matter will add even more complications. To move forward, one must estimate the relative importance of the mechanisms and build a model using the most important ones for study. A concordant model will arise from studies. This subject is important, so I believe that a constraint on the universal constants of Appendix Z may be required. It is also possible that some new physics might be required as well.
D. Tests of validity
There are only three universal theories that should be of interest (GRLCDM, MOND, and NCNG). I believe that MOND can be discarded for the following reason. Assume that MOND is a correct theory.
If MOND is a correct theory, then dark matter does not exist. Without dark matter the LCDM cosmology collapses. The minimum requirement for a viable cosmology is the prediction of a correct value of the Hubble constant (accurately known). Therefore, MOND must generate a new cosmology to replace LCDM. I believe that MOND cannot be made to predict the Hubble constant—MOND is not a correct theory.
There are many observations that could compare NCNG predictions with GRLCDM predictions. Unfortunately, most of these observations require equipment that does not exist presently.
JWST may eventually provide some of these observations. NCNG has a maximum cosmological redshift during very early red summer (Appendix C). The oldest JWST object observed as of late 2022 has \(z = 13.2\) [18]. I believe that the accurately determined maximum z will not be much larger than this observation.
There is one important subject which has used existing equipment, spiral-galactic rotation (refer to Appendix D). One will realize that NCNG is the only survivor.