It is commonly argued that an undesirable feature of a theoretical or phenomenological model is that salient observables are sensitive to values of parameters in the model. But in what sense is it undesirable to have such ‘fine-tuning’ of observables? In this paper, we argue that the fine-tuning can be interpreted as a shortcoming of the explanatory capacity of the model: in particular it signals a lack of a particular type of explanatory depth. The aspect of depth that we probe (...) relates most closely to a lack of sensitivity to changes in parameters associated with such models. In support of this argument, we develop a schema—for models that arise broadly in physical settings—that quantitatively relates fine-tuning of observables to a lack of depth of explanations based on these models. We apply our schema in two different settings in which, within each setting, we compare the depth of two competing explanations. The first setting involves explanations for the Euclidean nature of spatial slices of the universe today: in particular, we compare an explanation provided by the big-bang model of the early 1970s with an explanation provided by a general model of cosmic inflation. The second setting has a more phenomenological character, where the goal is to infer from a limited sequence of data points, using maximum entropy techniques, the underlying probability distribution from which these data are drawn. In both of these settings we find that our analysis favors the model that intuitively provides the deeper explanation of the observable of interest. We thus provide an account that relates two ‘theoretical virtues’ of models used broadly in physical settings—namely, a lack of fine-tuning and explanatory depth—and argue that finely tuned models sacrifice explanatory depth. (shrink)

We introduce a mathematical framework for quantifying fine-tuning in general physical settings. In particular, we identify two distinct perspectives on fine-tuning, namely, a local and a global perspective --- and develop corresponding measures. These measures apply broadly to settings characterized by an arbitrary number of observables whose values are dependent on an arbitrary number of parameters. We illustrate our formalism by quantifying fine-tuning as it arises in two pertinent astrophysical settings: in models where a significant fraction of the dark matter (...) in the universe is in the form of primordial black holes, and in scenarios that derive the fraction of protons in habitable dark-matter halos from underlying models of cosmic inflation. (shrink)

Though astrophysicists have developed a theoretical framework for understanding how the first stars and galaxies formed, only now are we able to begin testing those theories with actual observations of the very distant, early universe. We are entering a new and exciting era of discovery that will advance the frontiers of knowledge, and this book couldn't be more timely. It covers all the basic concepts in cosmology, drawing on insights from an astronomer who has pioneered much of this research over (...) the past two decades. Abraham Loeb starts from first principles, tracing the theoretical foundations of cosmology and carefully explaining the physics behind them. Topics include the gravitational growth of perturbations in an expanding universe, the abundance and properties of dark matter halos and galaxies, reionization, the observational methods used to detect the earliest galaxies and probe the diffuse gas between them--and much more. Cosmology seeks to solve the fundamental mystery of our cosmic origins. This book offers a succinct and accessible primer at a time when breathtaking technological advances promise a wealth of new observational data on the first stars and galaxies. Provides a concise introduction to cosmology Covers all the basic concepts Gives an overview of the gravitational growth of perturbations in an expanding universe Explains the process of reionization Describes the observational methods used to detect the earliest galaxies. (shrink)