  (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.
