A computational framework bridging gravitational thermodynamics and baryogenesis — quantifying how the universe's initial geometric low entropy drives the matter-antimatter asymmetry through inflation and reheating.
Two fundamental unanswered questions about the thermodynamic arrow of time in cosmology.
The early universe was remarkably smooth and homogeneous, corresponding to very low gravitational entropy. But unlike matter systems where entropy is computed from phase-space volumes, gravitational entropy lacks a universally accepted definition beyond the black hole case (Bekenstein-Hawking).
How does the gravitational sector's low entropy get transferred to or influence the matter sector, driving processes such as baryogenesis that require departure from thermal equilibrium? This connects gravitational thermodynamics, nonequilibrium statistical mechanics, and early-universe cosmology.
"But we do not really know what we mean by low-entropy geometry, nor how low entropy gets transferred to (or influences) matter degrees of freedom, e.g. in the problem of baryogenesis." — Maes (arXiv:2601.16716, 2026)
A coupled computational pipeline from inflation through reheating into the radiation era.
A coarse-grained entropy functional based on the Weyl-to-Ricci curvature ratio in cosmological perturbation theory. Vanishes for exact FLRW spacetime and grows with gravitational clustering.
Two channels model the transfer: semiclassical particle production (Parker mechanism) from time-varying geometry, and gravitational baryogenesis via a dimension-6 Ricci-scalar/baryon-current coupling.
Integration of the coupled ODE system through Starobinsky R^2 inflation, reheating, and the radiation era using fourth-order Runge-Kutta (RK45) with adaptive step size.
Evolution of the Hubble parameter, inflaton field, and entropy through inflation and reheating (Starobinsky model, M = 1.3 x 10^-5 M_Pl).
H vs. e-folds showing the slow roll plateau during inflation followed by the drop at reheating.
Inflaton field value showing slow roll, rapid descent, and damped oscillations during reheating.
Log-scale entropy evolution showing the transition from geometry-dominated to matter-dominated entropy. The vertical region near N~63 marks reheating.
Systematic variation of the inflaton mass, initial field value, and baryogenesis cutoff scale.
Final matter entropy and baryon asymmetry vs. inflaton mass M (in units of M_Pl).
Number of e-folds and log10(S_total) vs. initial inflaton field value phi_i.
Baryon asymmetry |eta_B| vs. cutoff scale M_* showing the M_*^(-2) scaling. The observed value eta_B ~ 6.1 x 10^-10 is marked in red.
Spanning over 100 orders of magnitude from early inflation to the late matter era.
Geometric entropy computed from the Planck-normalized power spectrum across inflationary, radiation, and matter-dominated epochs.
Verification of the expected ordering from the low-entropy initial state to the cosmological horizon entropy.
Each component of the entropy hierarchy consistent with Egan and Lineweaver (2010).
Quantitative values for each entropy component in the observable universe.
Hierarchy Check: PASSED
S_grav^init << S_matter^today << S_BH << S_dS^horizon
30 randomized trials confirming the second law of thermodynamics at every time step.
Each trial plotted by its number of e-folds and final log10(S_total). All 30 trials pass the second law (zero violations).
Distribution of |eta_B| across Monte Carlo trials. The observed value 6.1 x 10^-10 is achievable for appropriate M_*.
The Weyl entropy functional vanishes for exact FLRW spacetime and grows monotonically with gravitational clustering, realizing the Weyl Curvature Hypothesis computationally.
Total entropy S_total = S_grav + S_matter is monotonically non-decreasing in all 30 Monte Carlo trials across 2000 time steps each, with zero violations detected.
From the initial near-zero geometric entropy (10^-20) to the final total entropy (~ 8.2 x 10^72), spanning 92 orders of magnitude through inflation and reheating.
The gravitational baryogenesis mechanism achieves the observed eta_B ~ 6.1 x 10^-10 for a cutoff scale between the GUT and Planck scales, a physically reasonable range.
The Starobinsky R^2 model produces N ~ 67 e-folds, consistent with solving the horizon and flatness problems, and matching Planck CMB observations.
Full cosmological entropy ordering confirmed: S_grav^init (10^12) << S_matter (10^90) << S_BH (10^106) << S_dS (10^124), consistent with Egan and Lineweaver.