A Dynamic Dark Energy Consistent with DESI and DES: Information Dark Energy

1. Introduction

Landauer’s principle [1,2] states that each bit of information in a system at temperature, T, has a minimum equivalent energy of k_B T ln 2. We can put this small quantity into perspective by considering the present ~10 zetabytes held worldwide in the cloud/ AI/ data centres. The data storage and networking aspects of these centres already use ~2 % of the total electricity generated worldwide. However, if all the 10 zetabytes in world data centres were to be erased, the total Landauer energy released as heat at ~300K is miniscule by comparison, only ~200 Joules. This is just the amount used by one electric kettle in 1/10 second. Landauer’s principle has now been proven experimentally [3,4,5,6] and, linking information to thermodynamics, also provides an important solution to the problem of Maxwell’s demon [7].

Despite the little impact that Landauer information energy has on our every day lives, it does nevertheless represent a major source of energy within the universe. A “Foundational Principle” proposed by Anton Zeilinger [8] considers the attributes of all particles, at their most fundamental level, correspond to elemental systems. These are effectively simple 1bit, ‘yes’/’no’, results of experimental inquiry. In a simple universe without star formation, the Landauer equivalent energy of a Zeilinger elemental particle attribute has been shown [9] to be defined exactly the same as the characteristic energy of a cosmological constant [10]. Moreover, the Landauer equivalent energy has been shown to contribute a significant Information Dark Energy, IDE [11,12,13,14,15,16] to the universe. The total information energy carried by matter, or represented by matter, is at a similar level to the total mc² equivalent energy of the 10⁵³ kg baryons in the universe (Figure 7 of [16]). Strong contributions are made by stellar heated gas and the intra-cluster gas within galaxy clusters.

The key to identifying the physical source of dark energy is in determining the dark energy density variation over the history of the universe. The latest results of the Dark Energy Spectrograph Instrument, DESI, [17] and the Dark Energy Survey, DES, [18] provide evidence for a dynamic dark energy, evidence that excludes the previously assumed cosmological constant at a level >3 σ.

A previous IDE publication [16] only compared IDE against the initial data from DESI and DES, whereas the present work applies the updated final published DESI and DES results. Two versions of the relation between temperature and mass of astrophysical objects are applied; one from a survey of galaxy and galaxy cluster measurements, and one derived from the DESI and DES results, assuming the IDE source of dark energy. This work also extends the Stellar Mass Density (SMD) measurements to higher redshifts. We compare the IDE prediction from the SMD measurement survey against the DES and DESI results. We also compare the SMD variation required to explain the DES and DESI measured values against the survey of SMD measurements, assuming an IDE source of dark energy.

2. Information Dark Energy

2.1. Temperature Dependence

The Landauer equivalent energy of each bit in any system is solely dependent on the system’s temperature. We find that the temperatures, T, of several astrophysical structures ranging in mass, M, from 0.1 solar mass, M_⊙, to >10¹⁵ M_⊙ , each follow a similar relation. The results of a large survey of measured galaxy, galaxy group, and galaxy cluster temperatures [19] have been shown, on average, to closely follow the T α M^p relation over the range <10¹² M_⊙ to >10¹⁵ M_⊙ , illustrated in Figure 1 B & Figure 1C, where p=0.606. In Figure 1 A we see that the temperature of stars, from 10^-1 M_⊙ to 3 x 10¹ M_⊙ in the seven main sequence spectral classes also follow the same relation with the same power, p. Note that the previous work on IDE [16] simply considered the values p=0.5, and p=1.0. In this work we also extend the survey of stellar mass density, SMD(a), measurements [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47] used previously to include measurements at universe scale sizes, a<0.2, [48,49] where a is related to redshift, z, by a=1/(1+z).

2.2. CPL ω₀-ω_a Parameters

The time variation of the dark energy density is proportional to a^-3(1+ω) , where ω is the dark energy equation of state parameter. Any dynamic form of dark energy requires a time varying value of ω(a). In order to account for a dynamic dark energy most experimental measurements of dark energy have adopted the common CPL [50] parameters: ω(a)= ω₀ + (1-a) ω_a . As the most recent DES and DESI dark energy results are published in ω₀ - ω_a parameter space, it is convenient to predict the IDE source of dark energy also in terms of ω₀ - ω_a space.

2.3. Predicted IDE in ω₀ – ω_a Space

The Stellar Mass Density is a universe-wide average mass density that changed with time and thus a function of universe scale size: SMD(a). We expect that IDE(a), being proportional to temperature, to vary as IDE(a) ∝ SMD(a)^p. At the same time a CPL approximation of IDE energy density variation describes IDE(a) α a^{-3(1+ ω0 + ( 1 – a ) ωa)} . Each ω₀ - ω_a combination describes the curve of dark energy density as a function of scale size. Assuming an IDE source of dark energy, the p value transfers that to a SMD(a) curve whose measure of fit to all the measured SMD(a) values [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49] is given by a R² coefficient of determination. R² is defined as R²=1-(RSS/TSS), where RSS is the residual sum of squares, and TSS is the total sum of squares.

There are four DESI and DES dark energy derived ω₀ - ω_a combinations listed in Table 1. DESI combines BAO and CMB with three different sets of supernova measurements, Union3, DESY5, and Pantheon plus, to provide three ω₀ -ω_a values [17]. The most constrained DES ω₀ -ω_a value is listed for a combination of Baryon Acoustic Oscillation, BAO, Supernovae, SN, and Cosmic Microwave Background, CMB, measurements [18].

In Figure 2. the value of R² is plotted as a function of p for each of the four experimentally derived DESI and DES ω₀ - ω_a values. The grey line is the average R² of the four values. Shown below are the values of p determined from the temperatures and masses of galaxies and clusters using X-ray and lensing measurements [19]. Figure 2. enabled us to select two data driven values of p to better illustrate the similarity of dark energy history to star formation history. The value p=0.606 was determined directly by actual mass and temperature measurements of galaxy and clusters [19]. The value p=0.461 is determined from the maximum R² of the average of all four DES and DESI measurements, assuming IDE. Note that the value p=0.606 also coincides with the maximum of the single DES measurement, and the value p=0.461 coincides with the maximum of the DESI BAO+CMB+Union3 measurement.

For all combinations of ω₀ and ω_a values in steps of 0.01, over the wide range +0.9 to -3.0, we found the best fit to SMD(a) measurements (maximum R² ) that are also listed in Table 1 for the two chosen values of p. Both of these ω₀ - ω_a values lie well within the range determined by DESI and DES. These maximum R², best fit values are listed in Table 2, together with the R² values for the four DES & DESI ω₀ - ω_a values. The DES R² values at p=0.606 and the DESI/Union3 at p=0.641 are high at 0.947, close to the maximum of 0.953 of all ω₀ - ω_a space for fits to this survey of SMD(a) measurements.

In Figure 3 we further illustrate the similarity between star/structure formation and dark energy histories. For each of the two selected values of p we provide 2 plots. The right-hand plot shows the four DESI and DES 68% and 95% likelihood plots as a function of ω₀ and ω_a . Superimposed are the >0.90 and >0.94 R² contours of IDE over all ω₀–ω_a space derived solely from the survey of measured SMD(a). The location of centre points of DESI and DES plots (listed in Table 1) are highlighted together with the point of maximum R² of the IDE plot. The left-hand plots illustrate how well the curves corresponding to those highlighted ω₀ - ω_a values fit the survey of stellar mass density measurements.

3. Discussion

It is clear from Figure 3 (Left-hand plots) and from the R² values in Table2 that the DES most constrained result and the DESI BAO+CMB+Union 3 result both make a good fit to the SMD(a) measurement survey with curves closely following the highest R² red curve. Moreover, the range in ω₀ – ω_a space that fits SMD(a) measurements with R² >0.94 makes a good fit to the DESI and DES dark energy measurements (Figure 3. Right-hand plots). This suggests that the dark energy history is directly related to the history of astrophysical structure temperature and formation, as we expect for an IDE source.

Figure 4 provides an interpretation of predicted IDE and DES & DESI measurements.

Both the IDE prediction and DESI/DES measurements are consistent with a dark energy that was phantom (increasing energy density) throughout the majority of universe history but is now starting to decrease after recently reaching a maximum. The IDE prediction and DESI/DES measurements are also both consistent with a maximum located in the range 0.2 < z < 0.6.

Figure 3 (right-hand side) illustrates a difference of IDE contours in ω₀ - ω_a space between the two selected values of p. Figure 4 (thick black line) further illustrates this by showing how the maximum R² point moves over a wider range of p values.

While the use of CPL parameters has facilitated comparisons between different experiments, and between experiments and theory, there is no reason to expect that the actual dark energy can be fully described by any particular CPL ω₀ - ω_a combination. It is worth noting the following caveat regarding its use. The relevant curves in Figure 3. (left-hand side plots) emphasize how small the decrease is since the maximum. The curves considered in Figure 3. make a good fit to the majority of data, located beyond the maximum. But we note that much closer to z=0 these CPL curves mostly lie below the SMD data points. Furthermore, other surveys of SMD measurements do not show a distinct peak at low z [51,52,53]. As the star formation rate has fallen rapidly in recent times, SMD ceases to increase and has lead to a near-constant value at very low redshifts. If the same effect applies to the dark energy measurements, then the highest dark energy density to date might be occurring now at z=0. Then the perceived recent peak in dark energy density at 0.2<z<0.6 might be just an illusion created by the best CPL parameter fit being primarily determined by higher z data.

The expanding universe has lead to overall matter and radiation energy densities naturally falling as a^-3 and a^-4 respectively. In contrast, the stellar mass density and the dark energy density have both increased over time, in a way that is consistent with IDE being the dark energy source driven by star and structure formation. This work emphasizes simplicity, wielding Occam’s razor, and naturalness, relying on mostly proven physics, with a strong dependence on data. The potential of IDE to solve problems of cosmology has been covered before (see [16]) and is listed briefly again here for completeness and summarised in Table 3:

• Information/entropy estimates show that IDE can account for the value of the present dark energy density (see Figure 7 of [16]).
• Figure 2, Figure 3 and Figure 4 show that the history of IDE is consistent with the latest DESI and DES ω₀ – ω_a results describing the history of dark energy.
• As IDE fits the latest ω₀ – ω_a experiment data much better than Ʌ, then the Cosmological Constant problem could be resolved by assuming Ʌ=0, a more likely value [54].
• As the maximum star formation has only occurred recently (now?), this is the most likely time for intelligent beings to have evolved to live in the dark energy dominated epoch, effectively resolving the “Why now?” Cosmological Coincidence problem.
• The primarily phantom time history of IDE is similar to several dark energy histories [55,56,57] that have been shown capable of resolving both H₀ and σ₈ tensions.
• As the information energy of matter is clumped in astrophysical structures at a similar energy density to matter, IDE may account for some dark matter attributed effects.
• The location of baryons in galaxies has been shown to fully specify the location of dark matter attributed effects [58,59] as to be expected if IDE accounts for such effects.

4. Summary

The approach taken here has been primarily driven by data and indicates a strong similarity between stellar mass density and dark energy histories. We have shown that IDE predicts a dark energy history that matches the dark energy measurements of DESI and DES with a clear overlap in ω₀ – ω_a space. Equally, the SDM(a) variation required for an IDE source of dark energy to provide the experimentally measured dark energy ω₀ – ω_a combinations matches the measured SDM(a) measurements. The fit between IDE prediction and the latest DES and DESI results, combined with IDE’s ability to resolve many dark side problems and tensions, suggests IDE should be considered a strong candidate for the source of observed dark energy.