# The Degree of Fine-Tuning in our Universe -- and Others

## TL;DR

This paper reviews the constraints on fundamental constants and cosmological parameters necessary for universe development and habitability, highlighting the range of viable fine-tuned conditions and exploring alternative astrophysical processes.

## Contribution

It provides a comprehensive analysis of the parameter ranges allowing universe formation and habitability, including new insights into fine-tuning and alternative astrophysical processes.

## Key findings

- Viable universes exist over a range of parameter space.
- Constraints on constants ensure galaxy and star formation.
- Alternative processes can support habitability in different universes.

## Abstract

(abridged) Both fundamental constants that describe the laws of physics and cosmological parameters that determine the cosmic properties must fall within a range of values in order for the universe to develop astrophysical structures and ultimately support life. This paper reviews current constraints on these quantities. The standard model of particle physics contains both coupling constants and particle masses, and the allowed ranges of these parameters are discussed first. We then consider cosmological parameters, including the total energy density, the vacuum energy density, the baryon-to-photon ratio, the dark matter contribution, and the amplitude of primordial density fluctuations. These quantities are constrained by the requirements that the universe lives for a long time, emerges from the BBN epoch with an acceptable chemical composition, and can successfully produce galaxies. On smaller scales, stars and planets must be able to form and function. The stars must have sufficiently long lifetimes and hot surface temperatures. The planets must be massive enough to maintain an atmosphere, small enough to remain non-degenerate, and contain enough particles to support a complex biosphere. These requirements place constraints on the gravitational constant, the fine structure constant, and composite parameters that specify nuclear reaction rates. We consider specific instances of possible fine-tuning in stars, including the triple alpha reaction that produces carbon, as well as the effects of unstable deuterium and stable diprotons. For all of these issues, viable universes exist over a range of parameter space, which is delineated herein. Finally, for universes with significantly different parameters, new types of astrophysical processes can generate energy and support habitability.