1. From Inversion of View to a Testable Model
In the article GIEST: The Core Concept, the Universe was described “from the other side”: not as matter inside spacetime, but as an Informational Capsule. Space, time, and matter were treated as derivatives of a deeper Layer of Laws, and the Boundary between Information and Matter appeared as an informational–energetic singularity — a horizon where mass is converted into pure informational potential.
If this inversion of view is more than a metaphor, it should have quantitative consequences. In particular, if information is stored on boundaries, then cosmological horizons should behave like informational shells. Their entropy should not be a secondary detail, but a primary quantity from which cosmic dynamics can be derived.
Black hole thermodynamics gives us exactly this handle. The Bekenstein–Hawking relation tells us that the entropy S of a horizon scales with its area A, not with the volume it encloses. For a cosmological horizon with characteristic size L proportional to the inverse Hubble scale H, we have:
S \propto A \propto L^2 \propto H^{-2}so the informational content of the cosmic Boundary can be expressed directly through the Hubble parameter H(a).
In standard ΛCDM cosmology, late-time acceleration is explained by introducing a separate substance — dark energy — with an equation of state w \simeq -1. In the GIEST perspective, we can invert this logic:
instead of postulating dark energy, we postulate a law of growth of horizon entropy S(a), and treat geometry and effective “energy content” as derived from it.
The rest of this note makes this idea explicit. We first show how the effective equation of state w_{\mathrm{eff}}(a) can be written directly in terms of the logarithmic growth of horizon entropy, and then give a simple example where a saturating S(a) reproduces both a matter-like era and a late-time accelerated expansion — without introducing dark energy as an independent fluid.
2. Postulate: Horizon Entropy as the Primary Variable
Consider a spatially flat FRW Universe with scale factor a(t) and Hubble parameter:
H(t) = \dfrac{\dot{a}}{a}.We associate to the Universe an effective horizon of size L \sim H^{-1} (Hubble or event horizon, depending on context). Motivated by the Bekenstein–Hawking area law, we postulate that the informational content of the Universe at cosmic time t is encoded in the entropy S of this horizon via:
S \propto A \propto L^2 \propto H^{-2},so that, up to a constant factor,
S(a) = \dfrac{\sigma}{H(a)^2},with \sigma > 0 a fixed constant (containing k_B, c, G, \hbar, etc.).
GIEST Postulate (cosmological form). On large scales, the effective dynamics of the Universe is governed not by a separate “dark energy” fluid, but by a law of growth of horizon entropy S(a). Geometry and effective equation of state are derived from S(a).
3. From Horizon Entropy to the Effective Equation of State
In a homogeneous, isotropic Universe with a single effective component (or an effective sum), the FRW equations imply:
w_{\mathrm{eff}} = -1 - \dfrac{2}{3}\,\dfrac{\dot{H}}{H^2}.Using S \propto H^{-2}, we can write:
\ln H = -\dfrac{1}{2}\,\ln S + \text{const}.Taking derivatives with respect to \ln a,
\dfrac{d \ln H}{d \ln a} = -\dfrac{1}{2}\,\dfrac{d \ln S}{d \ln a}.Since \dot{H} / H^2 = d \ln H / d \ln a, we obtain:
w_{\mathrm{eff}}(a) = -1 - \dfrac{2}{3}\,\dfrac{d \ln H}{d \ln a} = -1 + \dfrac{1}{3}\,\dfrac{d \ln S}{d \ln a}.Thus the effective equation of state of the Universe is fully determined by the logarithmic growth rate of horizon entropy:
w_{\mathrm{eff}}(a) = -1 + \dfrac{1}{3}\,\dfrac{d \ln S}{d \ln a}.This is the central relation: the way information (entropy) on the cosmic horizon grows with the scale factor directly fixes how the Universe expands. No explicit dark-energy density is introduced; any “DE-like” behaviour arises as a consequence of the chosen S(a).
4. Example: Saturating Horizon Entropy
As a minimal example, consider a saturating form for S(a):
S(a) = \dfrac{S_\infty}{1 + \left(\dfrac{a_c}{a}\right)^3},where:
- S_\infty is the asymptotic maximum entropy (informational capacity) of the horizon;
- a_c is a characteristic scale factor marking the transition between a “matter-like” phase and a “dark-energy-like” phase.
For a \ll a_c we have:
\left(\dfrac{a_c}{a}\right)^3 \gg 1 \;\Rightarrow\; S(a) \approx S_\infty \left(\dfrac{a}{a_c}\right)^3 \propto a^3.For a \gg a_c we obtain:
S(a) \to S_\infty = \text{const}.The logarithmic derivative is then:
\dfrac{d \ln S}{d \ln a} = \dfrac{3}{1 + \left(\dfrac{a}{a_c}\right)^3}.Substituting into the main relation for w_{\mathrm{eff}}(a),
w_{\mathrm{eff}}(a) = -1 + \dfrac{1}{3}\,\dfrac{d \ln S}{d \ln a} = -1 + \dfrac{1}{1 + \left(\dfrac{a}{a_c}\right)^3}.The limiting regimes are:
- Early times (a \ll a_c): (a/a_c)^3 \to 0 and w_{\mathrm{eff}} \approx -1 + 1 = 0, i.e. the Universe behaves like pressureless matter, with no explicit dark energy.
- Late times (a \gg a_c): (a/a_c)^3 \to \infty and w_{\mathrm{eff}} \to -1, i.e. the Universe asymptotically approaches a de Sitter–like accelerated expansion.
Thus, a single informational law S(a) reproduces both a decelerating, matter-dominated phase at early times and a late-time accelerated expansion, with asymptotic w \to -1, without introducing dark energy as a separate fluid. In this picture, the effective “cosmological constant” is determined by the saturation value S_\infty, since S \propto H^{-2} implies:
H^2 \to H_\infty^2 \propto 1 / S_\infty.5. Interpretation in the GIEST Framework
In GIEST language:
- The informational boundary (cosmological horizon) stores the effective description of all accessible states of the Universe.
- The internal volume (geometry and matter fields) is a materialization or projection of this informational layer.
- The growth law S(a) is primary: it encodes how many configurations the Universe is “allowed” to explore as it evolves.
The standard ΛCDM approach effectively says: there exists a dark-energy component with w \approx -1, and the Universe expands accordingly. The GIEST perspective replaces this by:
There exists a law of growth and saturation of horizon information S(a). The effective equation of state w_{\mathrm{eff}}(a) — and hence the expansion history — is a derived quantity: w_{\mathrm{eff}}(a) = -1 + \dfrac{1}{3}\,\dfrac{d \ln S}{d \ln a}. Late-time acceleration is not driven by a separate substance, but by the fact that the informational capacity of the horizon approaches its maximum S_\infty.
In this sense, the present construction does not “prove” the primacy of information in an absolute way, but it shows explicitly, in mathematical form, how one can take information on the Boundary as fundamental and treat both geometry and effective dark-energy behaviour as emergent from its evolution.