The aim of this paper is to show that a new understanding of fundamentality (section 2), can be applied successfully in classical cosmology and is able to improve a fundamental understanding of cosmological time asymmetries. In the introduction (section 1), I refer to various views from different literature. I begin by arguing against various arguments, provided in favour of the view that the directedness of time is not a fundamental property of nature, (see for example Price [(1996)]) in section 1.1. Next, in section 1.2, I refer to some suggestions for defining the arrow of time in cosmology via the behaviour of entropy. In addition, I argue that the various types of such approaches cannot explain the occurrence of a fundamental arrow of time in cosmology; I believe that this argument is mostly acknowledged in the literature. Moreover, in section 1.3, I broaden my scope in order to formulate approaches in the context of theories of a multiverse and hyperbolic curved spacetimes as well. After that overview of different approaches, I provide a definition of my understanding of fundamentality (section 2). To verify the effectiveness of this new understanding, I present an example to show that it can be applied in classical cosmology in sections 3.1–3.5. Finally, in section 4 I conclude by regarding the effects of adding the new understanding of fundamentality to classical cosmology.