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How do ontology and cosmology relate to metaphysics?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — metaphysics Detail of a Roman copy (2nd century bce) of a Greek alabaster portrait bust of Aristotle (c. 325 bce); in the collection of the Museo Nazionale Romano, Rome.

In the context of metaphysics, both ontology and cosmology function as core components or specialized branches of the discipline.

Ontology

Ontology is the philosophical study of being in general, often referred to as "first philosophy." It focuses on fundamental questions regarding what exists, the nature of reality, and the categories of objects—such as properties, relations, and substances—that populate the world. Historically, philosophers have used ontology to categorize reality, ranging from "rich" ontologies that include abstract forms to "sparse" ontologies that prioritize material bodies and sets.1

Cosmology

Cosmology, in a metaphysical sense, is historically linked to the study of the origin and nature of the physical world. Early Greek philosophers, often termed cosmologists, sought to identify the ultimate substances or "first causes" of the universe. While ontology addresses the nature of being itself, cosmology focuses on the structure and origins of the physical universe, often overlapping with the metaphysics of matter.32

Together, these fields allow metaphysicians to explore both the abstract requirements for existence and the concrete nature of the cosmos we inhabit.