Mathematics of CCC: Mathematical Physics with Positive Lambda

This workshop will bring together experts in the fields of relativity, geometry, partial differential equations, observational cosmology, and particle physics to explore in depth aspects of conformal cyclic cosmology (CCC).

CCC proposes that the Big Bang was not the universe's origin, but a conformal continuation of an earlier aeon, where aeons occur sequentially, each starting with a big bang and ending with an exponential expansion driven by positive Λ. There is no early inflation, exponential expansion of the previous aeon serving instead. Emissions from previous-aeon black-hole encounters have observational implications, apparently supported in recent analyses of the CMB. Equations governing the transition from aeon to aeon imply creation of a dark material acquiring mass early in the new aeon, related to Higgs-type conformal symmetry-breaking.

This workshop will explore the many mathematical and astrophysical issues raised by CCC, including

• the extension of Einstein's equations to the crossover between aeons leading to interesting aspects of PDEs
• geometrical aspects of conformal geometry
• galactic dynamics in the very far future
• the nature of gravitational wave emission from black-hole encounters
• conventional cosmology
• energy conservation in general relativity with positive Λ
• particle physics at very high energy, and also at very low energy, in the presence of positive Λ