Entropic Origin of the Cosmological Constant Λ(t): Analytical Derivation of 10122 Bits and Validation via Planck Data

Abstract

Friedhelm Manfred Joge

The discrepancy of 10¹²⁰ between the observed cosmological constant and quantum field theory (QFT) predictions remains one of the greatest enigmas in modern physics. This study provides a novel analytical derivation of this value by treating gravity as an entropic force arising from bits on a holographic screen. By establishing a direct link between the bit density of the universe and the dynamic nature of dark energy, the study offers a potential resolution to the cosmological constant problem. These findings bridge the gap between quantum information theory (QIT) and general relativity theory (GRT), suggesting that the accelerated expansion of the universe is a emergent phenomenon driven by the evolution of cosmic entropy.

Since dark energy is not simply given as a number, but is derived from the age of the universe (13.82 billion years), the “naturalness problem” - one of the biggest problems in physics – can be solved.

It is shown that all the information of the universe is encoded on the PLANCK-scale and is “unrolled” into spacetime by factor t_u → Holographic Principle. The fact that the theoretically derived value of the HUBBLE constant (H₀) lies well within the range of astronomical measurements is the strongest indication that the connection between the PLANCK- scale and the age of the universe (tu) is not mere numerology, but a physical principle.

Significance Statement

This study presents an analytical derivation of the cosmological constant problem, resolving the 10120 discrepancy through a novel Energy-Time Equivalence. By defining the universe as an open thermodynamic system, it is demonstated that Dark Energy is not a statistic constant but a dynamic manifestation of a continuous information flow within the Hilbert space. The derived value of the Hubble's constant (H₀ = 1.956 · 10^-18 s^-1) shows unprecedented agreement (within 0.1σ) with precision data from the Max Planck Institute for Radio Astronomy and DESI. This framework unifies Bekenstein-Hawking entropy with quantum action, providing a first principle solution to the Hubble Tension and the Naturalness Problem without empirical fine-tuning.

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