Cosmology from Two Axioms 11; The Discrete Automorphism Interpretation of the Information Twistor and the Fine-Tuning Problem of the Cosmological Constant

Starting from the two fundamental principles of ”information conservation”and ”computability of physical laws,” this paper proposes that the fine-tuningproblem of the cosmological constant is essentially a natural consequence of thefiniteness of orbits of a discrete automorphism group. By introducing the ”information twistor”—defined as the remainder of the information potential differencemodulo the minimum information unit ln2—we demonstrate that the accumulation of information twistors is closely related to the orbit structure of a class ofdiscrete automorphism groups. When the cumulative information twistor reaches83ln2, the automorphism group’s orbit space develops a unique fixed-point orbit,which uniquely determines the effective cosmological constant. The theoreticalcalculation of this value is in excellent agreement with observations. Furthermore,this framework predicts that the early-universe automorphism structure will leavecharacteristic dipole–quadrupole mixed modulation signals in the primordial gravitational wave power spectrum, with an amplitude of approximately 0.83% and acharacteristic scale around k∗ ≈ 0.83×10−3 Mpc−1. These predictions can be testedby future space-based gravitational wave detectors (e.g., LISA) and next-generationcosmic microwave background experiments (e.g., CMB-S4).