Metric Phase Transition Theory: Three Phases of the Sine-Gordon Metric Field as the Unified Origin of Matter, Dark Matter, and Dark Energy
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2026
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| _version_ | 1866901858086289408 |
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| author | Rogers, Gary Howard |
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| contents | <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Metric Phase Transition Theory (MPT) proposes that the three components of the observable universe -- ordinary matter (5%), dark matter (27%), and dark energy (68%) -- are not separate substances but three phases of a single scalar metric field governed by the sine-Gordon equation. Their ratio follows from the kink spectrum without free parameters.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The three fundamental solution classes of this equation correspond directly to the three observed components: topological kinks (baryons/ordinary matter), breathers (dark matter), and radiation (dark energy). No new particles or fields are introduced.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">From the single stability condition that the kink supports exactly one bound state, the golden ratio phi = (1+sqrt(5))/2 emerges as the unique eigenvalue. From phi, through an exact algebraic cascade verified by symbolic mathematics (SymPy), MPT derives:</p> <ul class="[li_&]:mb-0 [li_&]:mt-1 [li_&]:gap-1 [&:not(:last-child)_ul]:pb-1 [&:not(:last-child)_ol]:pb-1 list-disc flex flex-col gap-1 pl-8 mb-3"> <li class="whitespace-normal break-words pl-2">The Standard Model gauge group SU(3) x SU(2) x U(1) [exact]</li> <li class="whitespace-normal break-words pl-2">The effective SM degrees of freedom g*(SM) = 106.75 [exact]</li> <li class="whitespace-normal break-words pl-2">The fine structure constant 1/alpha = 137.037 (error +0.001%)</li> <li class="whitespace-normal break-words pl-2">All three lepton masses via the Koide formula (errors < 0.10%)</li> <li class="whitespace-normal break-words pl-2">The proton mass (error 0.000%)</li> <li class="whitespace-normal break-words pl-2">The CMB temperature (error +0.020%, within FIRAS 1-sigma)</li> <li class="whitespace-normal break-words pl-2">The Hubble constant (error -0.48%, within Planck 1-sigma)</li> <li class="whitespace-normal break-words pl-2">An algebraically exact dark energy density formula: rho_Lambda = m_pi^4 * (1/kappa_23)^kappa_23</li> <li class="whitespace-normal break-words pl-2">The cosmic energy budget from the kink spectrum</li> </ul> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">In total, 45 physical quantities are derived from one postulate (every particle is a metric kink) and one external measurement (the baryon fraction Omega_b = 0.0493). All exact results are verified using SymPy. The cosmological constant problem is resolved dynamically: dark energy is exponentially suppressed by the kink spectrum, not by fine-tuning.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Three falsifiable predictions are stated:</p> <ol class="[li_&]:mb-0 [li_&]:mt-1 [li_&]:gap-1 [&:not(:last-child)_ul]:pb-1 [&:not(:last-child)_ol]:pb-1 list-decimal flex flex-col gap-1 pl-8 mb-3"> <li class="whitespace-normal break-words pl-2">A dark matter particle at 93 MeV/c^2 with self-interaction cross-section sigma/m = 0.21 cm^2/g</li> <li class="whitespace-normal break-words pl-2">H_0 ~ 67 km/s/Mpc (Planck-consistent, Hubble tension prediction)</li> <li class="whitespace-normal break-words pl-2">w = -1 exactly for dark energy</li> </ol> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The paper includes complete step-by-step derivations with units, SymPy verification code for all exact results, full error analysis tracing every discrepancy to a single identified source, and a complete reference section.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19538655 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Metric Phase Transition Theory: Three Phases of the Sine-Gordon Metric Field as the Unified Origin of Matter, Dark Matter, and Dark Energy Rogers, Gary Howard sine-Gordon, dark matter, dark energy, metric field, topological soliton, Skyrme model, cosmological constant, Koide formula, golden ratio, Hubble constant <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Metric Phase Transition Theory (MPT) proposes that the three components of the observable universe -- ordinary matter (5%), dark matter (27%), and dark energy (68%) -- are not separate substances but three phases of a single scalar metric field governed by the sine-Gordon equation. Their ratio follows from the kink spectrum without free parameters.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The three fundamental solution classes of this equation correspond directly to the three observed components: topological kinks (baryons/ordinary matter), breathers (dark matter), and radiation (dark energy). No new particles or fields are introduced.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">From the single stability condition that the kink supports exactly one bound state, the golden ratio phi = (1+sqrt(5))/2 emerges as the unique eigenvalue. From phi, through an exact algebraic cascade verified by symbolic mathematics (SymPy), MPT derives:</p> <ul class="[li_&]:mb-0 [li_&]:mt-1 [li_&]:gap-1 [&:not(:last-child)_ul]:pb-1 [&:not(:last-child)_ol]:pb-1 list-disc flex flex-col gap-1 pl-8 mb-3"> <li class="whitespace-normal break-words pl-2">The Standard Model gauge group SU(3) x SU(2) x U(1) [exact]</li> <li class="whitespace-normal break-words pl-2">The effective SM degrees of freedom g*(SM) = 106.75 [exact]</li> <li class="whitespace-normal break-words pl-2">The fine structure constant 1/alpha = 137.037 (error +0.001%)</li> <li class="whitespace-normal break-words pl-2">All three lepton masses via the Koide formula (errors < 0.10%)</li> <li class="whitespace-normal break-words pl-2">The proton mass (error 0.000%)</li> <li class="whitespace-normal break-words pl-2">The CMB temperature (error +0.020%, within FIRAS 1-sigma)</li> <li class="whitespace-normal break-words pl-2">The Hubble constant (error -0.48%, within Planck 1-sigma)</li> <li class="whitespace-normal break-words pl-2">An algebraically exact dark energy density formula: rho_Lambda = m_pi^4 * (1/kappa_23)^kappa_23</li> <li class="whitespace-normal break-words pl-2">The cosmic energy budget from the kink spectrum</li> </ul> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">In total, 45 physical quantities are derived from one postulate (every particle is a metric kink) and one external measurement (the baryon fraction Omega_b = 0.0493). All exact results are verified using SymPy. The cosmological constant problem is resolved dynamically: dark energy is exponentially suppressed by the kink spectrum, not by fine-tuning.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Three falsifiable predictions are stated:</p> <ol class="[li_&]:mb-0 [li_&]:mt-1 [li_&]:gap-1 [&:not(:last-child)_ul]:pb-1 [&:not(:last-child)_ol]:pb-1 list-decimal flex flex-col gap-1 pl-8 mb-3"> <li class="whitespace-normal break-words pl-2">A dark matter particle at 93 MeV/c^2 with self-interaction cross-section sigma/m = 0.21 cm^2/g</li> <li class="whitespace-normal break-words pl-2">H_0 ~ 67 km/s/Mpc (Planck-consistent, Hubble tension prediction)</li> <li class="whitespace-normal break-words pl-2">w = -1 exactly for dark energy</li> </ol> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The paper includes complete step-by-step derivations with units, SymPy verification code for all exact results, full error analysis tracing every discrepancy to a single identified source, and a complete reference section.</p> |
| title | Metric Phase Transition Theory: Three Phases of the Sine-Gordon Metric Field as the Unified Origin of Matter, Dark Matter, and Dark Energy |
| topic | sine-Gordon, dark matter, dark energy, metric field, topological soliton, Skyrme model, cosmological constant, Koide formula, golden ratio, Hubble constant |
| url | https://doi.org/10.5281/zenodo.19538655 |