According to Kroupa, the Lambda-CDM model is now ruled out. Is there considerable uncertainty about dark matter particles? (According to my speculations, the Riofrio model need a Koide cutoff and a Lestone cutoff.)
According to contemporary scientific thought, the diameter of the observable universe is about 93 billion light years. However, if the Riofrio cosmological model is correct, the radius of our universe is constant, the speed of light in a perfect vacuum is steadily decreasing, and dark matter particles do not exist. If the Riofrio model is empirically valid, the universe is far smaller than most astrophysicists now believe it to be. The question is: How much smaller?
Let us assume that the fundamental basis of nature is an Einstein-Riofrio duality principle, in which string theory with the infinite nature hypothesis corresponds to the (original) Einsteiniian field equations with dark matter particles (Einstein part of the duality), and string theory with the finite nature hypothesis corresponds to modified field equations with the Riofrio cosmological model and without dark matter particles (Riofriio part of the duality). There is a serious problem in understanding the Riofrio model because all the cosmological data is presented in terms of the paradigm with dark matter particles. I speculate that the way to overcome this problem is to assume that ordinary matter is steadily converted into dark matter particles (which might, or might not, exist).
A 3-sphere with radius r has 3-dimensional cubic hyperarea = (2 pi^2) * (r^3).
3-sphere, Wikipedia
The Planck time is approximately 5.39 * 10^-44 seconds.
Planck time, Wikipedia
Our universe is approximately 13.82 billion years old.
Age of the universe, Wikipedia
Hypothesis 1: Assuming that the Einstein-Friedmann model is valid and dark matter exists, the mass-density of our universe is approximately 9.9 * 10^-30 g/cm^3 . (See the WMAP data.)
Hypothesis 2: Wolfram's Reset recurs every (81.6±.1.7) billion years.
Hypothesis 3: During each Planck time interval, precisely one unit of Fredkin-Wolfram energy is converted from ordinary matter to dark matter (which is equivalent to the loss of precisely one unit of Fredkin-Wolfram energy from the boundary of the multiverse into the interior of the multiverse). Here the assumption is made that astronomical time is different from atomic time. See the article "On the compatibility of a proposed explanation of the Pioneer anomaly with the cartography of the solar system" by Antonio Fernández-Rañada and Alfredo Tiemblo-Ramos, 2009.
Step 1: Calculate mass-energy of our universe at the beginning of the Big Bang (assuming that dark matter particles exist) and almost all of the mass-energy at the time of the Big Bang consisted of ordinary matter.
(Planck mass) * (81.6±1.7 billion years)/ (Planck time) =
(4.733 ±.14) * 10^61 = (1.02±.02) * 10^57 grams .
Step 2. Assuming that ordinary matter is steadily converted to dark matter, calculate how much ordinary matter is converted to dark matter in 13.8 billion years.
(1.02±.02) * 10^57 g * 13.8/(81.6±1.7) = (.17±.01) * 10^57 g = (1.7±.1) * 10^56 g .
Step 3. Calculate how much mass-energy in non-converted form now exists, according to the various hypotheses assumed. The answer is roughly 8 * 10^56 grams.
Step 4. Estimate the radius of our universe (assuming the Riofrio model).
(2 pi^2) * (r^3) = (8±.5) * 10^56 g / (9.9 * 10^-30 g/cm^3) = (8±.6) * 10^86 cm^3 =
(8±.6) * 10^80 m^3 .
r = (3.4±.15) * 10^26 m = approximately (36±3) billion light-years. This is considerably less than the diameter of the OBSERVABLE universe, according to the Einstein-Friedmann paradigm. There are a number of speculative hypotheses in the preceding estimate, so the estimate might be completely wrong and misrepresent the Riofrio model, even though the Riofrrio model is empirically valid.