Gauging fine-tuning

Azhar, Feraz; Loeb, Abraham

doi:10.1103/physrevd.98.103018

Cited by 13 publications

(14 citation statements)

References 59 publications

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“…To complete our investigation, we consider an alternative to calculating PBH abundances using Peak Theory, which postulates that PBHs result from peaks in the primordial overdensity field exceeding a threshold value (see Bardeen et al (1986); Green et al (2004) for reviews). It is well known that the PS and Peak Theory do not agree, although previous authors have suggested that Peak Theory is grounded on a firmer theoretical footing, and is more sensitive to the shape of the inflationary power spectrum (Germani & Musco 2019;Kalaja et al 2019;.…”

Section: Peak Theorymentioning

confidence: 99%

“…If we now assume that PBHs are formed across a spectrum of masses, the monochromatic upper bounds, denoted

f_{\max}^{italicmono} false(M false)

, must be corrected using procedures such as those previously presented in Azhar & Loeb (2018); Carr et al (2017); Kühnel & Freese (2017); Lehmann et al (2018). These studies have only relatively recently gained traction, but are nevertheless indispensable if PBHs were to be taken as a serious candidate for dark matter and GW sources.…”

Section: Pbh Formation: a Case Studymentioning

confidence: 99%

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Extreme primordial black holes

2021

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We present a formalism for calculating the probability distribution of the most massive primordial black holes (PBHs) expected within an observational volume. We show how current observational upper bounds on the fraction of PBHs in dark matter translate to constraints on extreme masses of primordial black holes. We demonstrate the power of our formalism via a case study, and argue that our formalism can be used to produce extreme-value distributions for a wide range of PBH formation theories.

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Section: Peak Theorymentioning

confidence: 99%

“…If we now assume that PBHs are formed across a spectrum of masses, the monochromatic upper bounds, denoted

f_{\max}^{italicmono} false(M false)

Section: Pbh Formation: a Case Studymentioning

confidence: 99%

Extreme primordial black holes

2021

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“…If we now assume that PBHs are formed across a spectrum of masses, the monochromatic upper bounds, denoted f mono max (M ), must be corrected using procedures such as those previously presented in [27][28][29][30]. These studies have only relatively recently gained traction, but are nevertheless indispensable if PBHs were to be taken as a serious candidate for dark matter and GW sources.…”

Section: Observational Constraintsmentioning

confidence: 99%

“…The upshot from these studies is that the corrected upper bound for the total PBH fraction in CDM, f PBH,max , is given by [29]…”

Section: Observational Constraintsmentioning

confidence: 99%

Extreme Primordial Black Holes

Chongchitnan,

Chantavat,

Zunder

2019

Preprint

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“…II, we describe our schema for an explanation. We introduce a (quantitative) notion of fine-tuning of observables, adapting previous work of ours [in Azhar and Loeb (2018)], and describe how this notion relates to the depth of an explanation. We provide a measure for depth that depends on our description of fine-tuning that can, in principle, be used to compare the depth of explanations across a broad class of physical settings.…”

Section: Introductionmentioning

confidence: 99%

Finely tuned models sacrifice explanatory depth

Azhar¹,

Loeb²

2019

Preprint

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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 (and hence of the underlying model)? 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 explanatory depth. In support of this argument, we develop a scheme-for models that arise broadly in the sciences-that quantitatively relates fine-tuning of observables described by these models to a lack of depth of explanations based on these models. A significant aspect of our scheme is that, broadly speaking, the inclusion of larger numbers of parameters in a model will decrease the depth of the corresponding explanation. To illustrate our scheme, we apply it 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 (namely, a cosmological model that traces the evolution of the universe back to a singularity without encountering an inflationary period) 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(s) of interest. We thus provide an account that unifies two 'theoretical virtues' of models used broadly in the sciences-namely, a lack of fine-tuning and explanatory depth-to show that, indeed, finely tuned models sacrifice explanatory depth. ContentsI. Introduction II. Explanatory depth from a lack of fine-tuning III. Applications of our approach A. The flatness problem in cosmology B. Model selection in maximum-entropy modeling IV. Discussion

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Gauging fine-tuning

Cited by 13 publications

References 59 publications

Extreme primordial black holes

Extreme primordial black holes

Extreme Primordial Black Holes

Finely tuned models sacrifice explanatory depth

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