Is the Cosmological Coincidence a Problem?

TL;DR

This paper argues that the apparent coincidence of dark energy and dark matter densities is not a fine-tuning problem but an artifact of anthropic selection, explained by the epoch's observational bias.

Contribution

It introduces a model showing that the cosmological coincidence arises from observational bias, not fine-tuning, by linking measurement likelihood to epoch-dependent linear modes.

Findings

Probability of observing the current ratio r is high due to measurement bias.

Most measurements occur during epochs with abundant linear modes.

The coincidence is explained as an observational artifact rather than fine-tuning.

Abstract

The matching of our epoch of existence with the approximate equality of dark energy and dark matter energy densities is an apparent further fine-tuning, beyond the already troubling 120 orders of magnitude that separate dark energy from the Planck scale. In this paper I will argue that the coincidence is not a fine-tuning problem, but instead an artifact of anthropic selection. Rather than assuming measurements are equally likely in all epochs, one should insist that measurements of a quantity be typical amongst all such measurements. As a consequence, particular observations will reflect the epoch in which they are most easily made. In the specific case of cosmology, most measurements of dark energy and dark matter will done during an epoch when large numbers of linear modes are available to observers, so we should not be surprised at living at such a time. This is made precise in a particular model for the probability distribution for r=min(Omega_m/Omega_L,Omega_L/Omega_m), where it is shown that if p(r) \sim [N(r)]^b (where N(r) is the number of linear modes, and bis some arbitrary positive power), the probability that r is greater than its observed value of 0.4, is close to 1. Thus the cosmological coincidence is no longer problematic.