Landauer-Compensated Information Erasure in Cyclic Cosmology

Abstract

A thermodynamically consistent mechanism for cross-cycle information transfer is proposed, combining holographic boundary encoding, de Sitter horizon thermodynamics, and a Cyclic Cascading Dark Energy (CCDE) model in which the Hubble parameter $H(t)$ tends asymptotically to zero, driving the de Sitter horizon temperature $T_{\ddS}\to 0$. Penrose's Conformal Cyclic Cosmology (CCC) is constructed on a de Sitter-like exponentially expanding future ($\Lambda>0$), whose future conformal boundary $\IdS$ is spacelike; this spacelike character is matched conformally to the spacelike Big Bang of the next aeon, and is therefore a precondition of CCC rather than an obstruction. The genuine bottleneck in $\Lambda$CDM is thermodynamic, not topological: with $H\to H_{\infty}>0$ eternally, $T_{\ddS}^{\infty}>0$ eternally and the Landauer cost of bulk erasure never vanishes. We propose the CCDE model as a thermodynamic resolution: a Ratra--Peebles quintessence potential $V(\phi)=M^{4+\alpha}\phi^{-\alpha}$ combined with the Loop Quantum Cosmology holonomy correction $H^{2}\propto\rho(1-\rho/\rcrit)$ drives $H(t)\to 0$ asymptotically, so that $T_{\ddS}(t)\to 0$ and the Landauer cost per bit $k_{B}T_{\ddS}\ln 2$ vanishes in the asymptotic future. A finite-time endpoint $H(t_{*})=0$ is not achieved by canonical quintessence plus standard LQC alone; the quiet-bounce scenario is identified as an additional hypothesis requiring either phantom kinetic energy (quantum-mechanically unstable) or modified gravity. The de Sitter modular Hamiltonian $K_{\ddS}=(2\pi/H)\Hmod+\log Z$ has a c-number part ($\log Z\sim\SdS\sim 1/H^{2}$) that diverges as $H\to 0$ but contributes only a global phase to the bulk-to-horizon transfer map $U(t)$; the operator part $(2\pi/H)\Hmod$ remains bounded on the typical thermal sector. The cross-cycle information channel is formulated using the asymptotic symmetry of spacelike $\IdS$ (the de Sitter group $SO(1,4)$ and its Poincar\'e contraction), without invoking the BMS group, which is the asymptotic symmetry of null infinity and is not the relevant structure for a spacelike $\IdS$. The framework is falsifiable: if $\Lambda$CDM is confirmed with $w=-1$ to high precision, the asymptotic-thermodynamic channel collapses. Falsifiable predictions include a dark-energy equation of state $w(a)\neq -1$ at the percent level (testable by DESI/Euclid 2024--2030, with current DESI 2024 values $w_{0}=-0.827\pm 0.063$, $w_{a}=-0.75^{+0.29}_{-0.25}$ preferring $w\neq -1$ at $\sim 2.5\sigma$ for the PantheonPlus combination; other supernova compilations give $3.5$--$3.9\sigma$), a primordial tensor-to-scalar ratio $r\sim 10^{-4}$--$10^{-3}$ from LQC holonomy corrections, and a characteristic cross-correlation between low-$\ell$ and high-$\ell$ CMB modes seeded by the previous-cycle horizon state. If $\Lambda$CDM is confirmed with $w=-1$ to high precision, the entire cyclic framework collapses; this all-or-nothing dependence is treated as a high-risk, high-reward feature of the framework.