A Thousand Problems in Cosmology: Horizons

TL;DR

This chapter provides a comprehensive collection of problems and solutions related to horizons in cosmology, covering concepts from basic to advanced, including models, causal structures, black holes, and topics like inflation and holography.

Contribution

It compiles and formalizes a wide range of problems on cosmological horizons, serving as a resource for education and research in the field.

Findings

Explains horizons in simple and complex cosmological models.

Analyzes causal structures using conformal diagrams.

Addresses problems related to black holes, inflation, and holography.

Abstract

This is one chapter of the collection of problems in cosmology, in which we assemble the problems, with solutions, that concern one of the most distinctive features of general relativity and cosmology---the horizons. The first part gives an elementary introduction into the concept in the cosmological context, then we move to more formal exposition of the subject and consider first simple, and then composite models, such as $\Lambda$CDM. The fourth section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes. The consequent parts focus on more specific topics, such as the various problems regarding the Hubble sphere, inflation and holography. The full collection is available in the form of a wiki-based resource at universeinproblems.com. The cosmological community is welcome to contribute to its development.