There is a major taboo in modern cosmology that physicists tend to look away from:
The common belief that "the law of energy conservation does not hold in an expanding universe."
As light from distant galaxies (such as the Cosmic Microwave Background) travels through expanding space, its wavelength is stretched, causing a "redshift." A longer wavelength means the light's energy decreases.
So, where did that lost energy go? It didn't turn into heat, nor did it convert into other particles. Modern physics concludes that "in an expanding system like the universe, energy simply disappears (is not conserved)."
However, the Intergeometric Theory overturns this common sense from the ground up.
Not a single joule of the universe's energy has ever disappeared.
The energy "lost" to redshift has been consistently applied to the universe's "debt repayment to the vacuum," perfectly conserved all along.
1. The Universe's "Credit Line" and the Decay Rate \(\chi_0\)
To understand this mechanism, we must recall the origins of our universe.
Our universe is a "giant virtual particle" existing by borrowing energy in advance from an empty vacuum (See the [Universe as a Virtual Particle] article for details).
Because the universe is borrowing energy, the vacuum's energy (the Higgs vacuum expectation value ν) has decreased from its original state ( \(2M_H\) ) as shown below:
\[\nu=2M_H−\left(\frac{3\chi_0}{81}\right)M_H\]
The \(\chi_0\) here represents the "remaining balance ratio" (cosmic energy decay rate) of the debt held by the universe. (At the moment the universe was born, no repayment had been made, so \(\chi_0=100\%\).
On the other hand, the total energy density of the universe \(\rho_0\) is also linked to this \(\chi_0\) :
\[\rho_0=\frac{\chi_0\left(\frac{t_s}{t_0}\right)^2+2}{81}\times\frac{M_H}{\frac{4\pi}{3}\left(Wl_H\right)^3}\]
(Note: 1 represents matter, and 2 represents dark energy. For why it takes this ratio, see the [True Identity of Dark Energy] article).
What is crucial here is that these two equations demonstrate "perfect coupling (energy conservation)."
When the universe's energy ( \(\rho_0\) ) decreases, the debt balance ( \(\chi_0\) ) decreases, and the vacuum's energy ( ν ) recovers by that exact amount.
Between the universe and the vacuum, energy is exchanged without a single cent of discrepancy.
2. Where Did the Decay Rate "89%" Come From?
So, what exactly is the current debt balance \(\chi_0\) of the universe?
In fact, when back-calculated from the microscopic world of elementary particles (the fine-structure constant and Fermi coupling constant), it is known with extremely high precision that the current \(\chi_0\) is approximately 89%.
However, if "energy is conserved," then calculating it not from microscopic particle constants but from "the macroscopic evolution of the universe (mass reduction)" must also yield the exact same 89%.
Let's do the math.
At the beginning of the universe (just after inflation), the initial energy assigned to one spatial grid (1/81) was " \(M_H/81\)." In the current universe, this has transformed into normal matter (baryons: \(M_{b0}\) ) and dark matter ( \(M_{c0}\) ).
By calculating the ratio of this "current average mass of particles" to the "initial energy," we can find the energy decay rate of the entire universe. (Since the number of dark matter particles is twice that of normal matter, a factor of 2 is applied. See the [Dark Matter] article for details).
\[\frac{\chi_0\times 1\text{(Matter)}+2\text{(Dark Energy)}}{3}\approx\frac{M_{b0}/4+2M_{c0}}{M_H/81}\]
The mass of a baryon ( \(M_{b0}\) ) in the numerator on the right side is known to be about 0.937 GeV based on the hydrogen-to-helium ratio immediately after the Big Bang. (We divide by 4 because protons and neutrons consist of three quarks and one electron, so we convert it per single particle). The mass of dark matter ( \(M_{c0}\) ) is also rigorously calculated from the geometry of this theory to be about 0.628 GeV.
What happens when we rearrange this equation to solve for \(\chi_0\) ?
\[\chi_0\approx 3\times\frac{M_{b0}/4+2M_{c0}}{M_H/81}−2\]
\[\chi_0\approx 89\%\]
Astoundingly, the result calculated from the macroscopic evolution of cosmic mass perfectly matches the "approx. 89%" derived from the microscopic fine-structure constant.
3. The Destination of the "Disappeared" Energy (Light)
A question arises here:
Where did the energy go that decreased from the initial energy ( \(M_H/81\) ) to the current mass ( \(M_{b0}/4+2M_{c0}\) )?
That difference became the energy of light (radiation) known as the "Cosmic Microwave Background (CMB)," the remnant of the Big Bang.
However, this light energy, which once filled the newborn universe with scorching heat, has had its wavelength stretched by the "redshift" accompanying the universe's expansion, drastically reducing to merely "0.005%" of the universe's total energy today.
That is precisely why the calculation above yielded exactly 89% even when completely ignoring the energy of light.
The \(\chi_0\)(the debt) does not decrease the moment matter mass turns into light (burns).
Rather, the process itself, where the emitted light travels through space and "loses energy due to redshift," functions as the repayment of debt to the vacuum (the decrease in \(chi_0\) ).
Even today, nuclear fusion within shining stars causes a minuscule mass defect ( \(E=mc^2\) ), emitting light. Every time that light is lost to redshift, the universe diligently continues to repay its debt to the vacuum.
4. The Absolute Rule that Maintains the Universe
In general relativity, there is no "obligation" for energy to be conserved in an expanding universe. This is why physicists have assumed that "the energy simply disappeared."
However, if energy truly isn't conserved, there is no way to explain why the \(\chi_0\) calculated from current particle constants (fine-structure constant) and the \(\chi_0\) calculated from the history of the universe (mass ratios) both perfectly match at 89%.
The energy of the universe was, after all, strictly conserved.
However, it was not conserved merely within visible matter and light, but as a balance sheet of the entire universe (virtual particle), including the account of "vacuum energy."
No matter how much the universe expands or how cold its light becomes, it continues to uphold the "ledger (rules) for existence" without deviating by a single joule.
