Conformal Methods in Mathematical Cosmology

TL;DR

This paper reviews the application of conformal boundary methods in mathematical cosmology, focusing on the case of positive cosmological constant relevant to our universe, and discusses how these methods vary with different values of b3.

Contribution

It provides a comprehensive review of conformal boundary techniques in cosmology, emphasizing the positive b3 case and its implications for understanding the universe's structure.

Findings

Conformal boundary methods are effective in analyzing cosmological models with positive b3.

The nature of the conformal boundary varies with the sign of b3, affecting cosmological interpretations.

The review highlights the importance of these methods in current cosmological research.

Abstract

When he first introduced the notion of a conformal boundary into the study of asymptotically empty space-times, Penrose noted that that the boundary would be null, space-like or time-like according as the cosmological constant $\Lambda$ was zero, positive or negative. While most applications of the idea of a conformal boundary have been to the zero-$\Lambda$, asymptotically-Minkowskian case, there also has been work on the nonzero cases. Here we review work with a positive $\Lambda$, which is the appropriate case for cosmology of the universe in which we live.