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Anthropic tuning of the weak scale and of mu/md in two-Higgs-doublet models
Abstract
It is shown that, in a model in which up-type and down-type fermions acquire mass from different Higgs doublets, the anthropic tuning of the Higgs mass parameters can explain the fact that the observed masses of the d and u quarks are nearly the same with d slightly heavier. If Yukawa couplings are assumed not to scan (vary among domains), this would also help explain why t is much heavier than b. It is also pointed out that the existence of dark matter invalidates some earlier anthropic arguments against the viability of domains where the standard model Higgs has positive mu2, but makes other even stronger arguments possible.
... A large body of previous work has placed constraints on the allowed range of particle masses, including quark masses [54,69,73,162,184,280,296], the Higgs mass [185], the proton mass [415], and the Standard Model in general [261,262]. This section reviews and reconsiders the conventional arguments for the allowed range of light quark masses. ...
... If the mass difference between up quarks and down quarks is too large, then the heavier quark can decay into the lighter one within a hadron (such as a proton or neutron). In order to prevent such decays, and allow for long-lived particles of interest, there exists an upper limit to the mass difference between the quarks, as outlined below [280,54]. ...
... This constraint requires that the binding energy of deuterium is positive. One model [54] writes the modified binding energy B D in the form ...
(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.
... On the Higgs side, it has been noticed that light quark and lepton masses m e , m u , m d are anthropically restricted in a significant way: a nontrivial nuclear physics with more nuclei than just H and/or He (and thereby chemistry, and life) exists because m e =Λ QCD , m u =Λ QCD , m d =Λ QCD have appropriate values which allow for the existence of a hundred of nuclear species [9][10][11][12]. Such anthropic boundaries in m e , m u , m d give extra indicative support to the possibility that physics is described by a theory where fundamental constants have different values in different local minima. ...
... We do not explore the possibility that O, rather than Fe, might be the most stable nucleus in vacua with different values of m u;d or α em .2 Light fermion masses are independently anthropically constrained[9][10][11][12]. For v < v SM a top Yukawa coupling larger than one would be needed to keep the top quark mass fixed; anyhow, the top quark plays no anthropic role. ...
Core-collapse supernovæ presumably explode because trapped neutrinos push the material out of the stellar envelope. This process is directly controlled by the weak scale v: we argue that supernova explosions happen only if fundamental constants are tuned within a factor of few as v∼ΛQCD3/4MPl1/4, such that neutrinos are trapped in supernovæ for a time comparable to the gravitational timescale. We provide analytic arguments and simulations in spherical approximation, that need to be validated by more comprehensive simulations. The above result can be important for fundamental physics, because core-collapse supernova explosions seem anthropically needed, as they spread intermediate-mass nuclei presumably necessary for “life.” We also study stellar burning, finding that it does not provide anthropic boundaries on v.
... On the Higgs side, it has been noticed that light quark and lepton masses m e , m u , m d are anthropically restricted in a significant way: a non-trivial nuclear physics with more nuclei than just H and/or He (and thereby chemistry, and 'life') exists because m e /Λ QCD , m u /Λ QCD , m d /Λ QCD have appropriate values which allow for the existence of a hundred of nuclear species [9][10][11][12]. Such anthropic boundaries in m e , m u , m d give extra indicative support to the possibility that physics is described by a theory where fundamental constants have different values in different local minima. ...
... We do not explore the possibility that O, rather than Fe, might be the most stable nucleus in vacua with different values of m u,d or α em .2 Light fermion masses are independently anthropically constrained[9][10][11][12]. For v < v SM a top Yukawa coupling larger than one would be needed to keep the top quark mass fixed; anyhow, the top quark plays no anthropic role. ...
Core-collapse supernovae presumably explode because trapped neutrinos push the material out of the stellar envelope. This process is directly controlled by the weak scale v: we argue that supernova explosions happen only if fundamental constants are tuned within a factor of few as , such that neutrinos are trapped in supernovae for a time comparable to the gravitational time-scale. We provide analytic arguments and simulations in spherical approximation, that need to be validated by more comprehensive simulations. The above result can be important for fundamental physics, because core-collapse supernova explosions seem anthropically needed, as they spread intermediate-mass nuclei presumably necessary for `life'. We also study stellar burning, finding that it does not provide anthropic boundaries on v.
... Real plots of this kind can be found in many papers, e.g. Agrawal et al. (1998b); Tegmark (1998);Hogan (2000); Tegmark et al. (2006); Hellerman and Walcher (2005); Graesser and Salem (2007); Hall and Nomura (2008); Barr and Khan (2007); Jaffe et al. (2009);Elor et al. (2010); and Barnes (2012). ...
... An updated discussion of bounds on quark masses can be found in Barr and Khan (2007). They also consider the possibility of having separate up and down quark Higgs bosons, each with variable scales, while the Yukawa couplings are kept fixed. ...
If the results of the first LHC run are not betraying us, many decades of
particle physics are culminating in a complete and consistent theory for all
non-gravitational physics: the Standard Model. But despite this monumental
achievement there is a clear sense of disappointment: many questions remain
unanswered. Remarkably, most unanswered questions could just be environmental,
and disturbingly (to some) the existence of life may depend on that
environment. Meanwhile there has been increasing evidence that the seemingly
ideal candidate for answering these questions, String Theory, gives an answer
few people initially expected: a huge "landscape" of possibilities, that can be
realized in a multiverse and populated by eternal inflation. At the interface
of "bottom-up" and "top-down" physics, a discussion of anthropic arguments
becomes unavoidable. We review developments in this area, focusing especially
on the last decade.
... Now, it is possible that certain values are a priori disallowed, because, for instance, they would make physics internally inconsistent. For instance, the masses of particles are typically assumed to be smaller than the Planck scale at which gravity and quantum mechanics inevitably converge (e.g., Barr and Khan 2007; see also Barnes 2019Barnes , 1234. While this restriction of parameter space still allows for a huge range of values, it is at least finite. ...
The apparent fine-tuning of several fundamental parameters that determine the properties of our Universe and make it hospitable to life is sometimes used as an argument for God from design. I review the concept of cosmic fine-tuning and critically examine the claim that God is its most probable cause. While not definitively repudiating this claim, I argue that it is potentially in tension with the more apophatic approach to God found in the Abrahamic traditions. I then offer a metaphysical analysis of the contingency of fine-tuning that situates it within the classical analogy of being that points to the Divinity.
... In some cases, atoms and nuclei no longer exist, and the universe would be sterile. Various aspects of this conclusion are discussed in [6,7,15,16,17,18,19,20,21,22,23,24]. Cosmology provides another constraint, with the well-known argument that if the cosmological constant were much different, matter would not clump into stars and planets [25,26,27,28,29,30,31,32,33,34]. ...
The possibility of fundamental theories with very many ground states, each with different physical parameters, changes the way that we approach the major questions of particle physics. Most importantly, it raises the possibility that these different parameters could be realised in different domains in the larger universe. In this review, we survey the motivations for the multiverse and impact of the idea of the multiverse on the search for new physics beyond the Standard Model.
... This, in turn, places observational limits on possible variations of these quantities in the early universe [21][22][23][24]. The dependence of the deuteron binding energy (B D ) on the sum of the light quark masses varies between these papers; following Barr & Khan [25], a typical conservative parameterization of this relationship is, ...
Stellar nucleosynthesis proceeds via the deuteron (D), but only a small change in the fundamental constants of nature is required to unbind it. Here, we investigate the effect of altering the binding energy of the deuteron on proton burning in stars. We find that the most definitive boundary in parameter space that divides probably life-permitting universes from probably life-prohibiting ones is between a bound and unbound deuteron. Due to neutrino losses, a ball of gas will undergo rapid cooling or stabilization by electron degeneracy pressure before it can form a stable, nuclear reaction-sustaining star. We also consider a less-bound deuteron, which changes the energetics of the pp and pep reactions. The transition to endothermic pp and pep reactions, and the resulting beta-decay instability of the deuteron, do not seem to present catastrophic problems for life.
... (The exact number depends on the version of the Standard Model.) Writing Θ for this parameter space, it appears (see for example [1,4,37]) that only a small subset Θ L of Θ gives rise to universes with complex chemistry. For the sake of our illustration, let us make the simplifying assumptions that complex chemistry is necessary for observers, that there is a natural probability measure µ on Θ, and that µ(Θ L ) ≪ 1. ...
We consider models for inference which involve observers which may have multiple copies, such as in the Sleeping Beauty problem. We establish a framework for describing these problems on a probability space satisfying Kolmogorov's axioms, and this enables the main competing solutions to be compared precisely.
... The anthropic boundaries we include are those found in [100]. Stated briefly, they are as follows: (i) the proton and neutron should be the most stable nuclei, rather than the ∆``or ∆´, (ii) heavy elements are stable, (iii) the proton is stable in nuclei, (iv) hydrogen is stable, both to positron emission and electron capture, (v) proton-proton fusion is exothermic, (vi) the deuteron is stable both to strong and weak decays, and (vii) the diproton is unstable. ...
We investigate the dependence of elemental abundances on physical constants, and the implications this has for the distribution of complex life for various proposed habitability criteria. We consider three main sources of abundance variation: differing supernova rates, alpha burning in massive stars, and isotopic stability, and how each affects the metal-to-rock ratio and the abundances of carbon, oxygen, nitrogen, phosphorus, sulfur, silicon, magnesium, and iron. Our analysis leads to several predictions for which habitability criteria are correct by determining which ones make our observations of the physical constants, as well as a few other observed features of our universe, most likely. Our results indicate that carbon-rich or carbon-poor planets are uninhabitable, slightly magnesium-rich planets are habitable, and life does not depend on nitrogen abundance too sensitively. We also find suggestive but inconclusive evidence that metal-rich planets and phosphorus-poor planets are habitable. These predictions can then be checked by probing regions of our universe that closely resemble normal environments in other universes. If any of these predictions are found to be wrong, the multiverse scenario would predict that the majority of observers are born in universes differing substantially from ours, and so can be ruled out, to varying degrees of statistical significance.
... The anthropic boundaries we include are those found in [100]. Stated briefly, they are as follows: (i) the proton and neutron should be the most stable nuclei, rather than the ∆``or ∆´, (ii) heavy elements are stable, (iii) the proton is stable in nuclei, (iv) hydrogen is stable, both to positron emission and electron capture, (v) proton-proton fusion is exothermic, (vi) the deuteron is stable, both to strong and weak decays, and (vii) the diproton is unstable. ...
We investigate the dependence of elemental abundances on physical constants, and the implications this has for the distribution of complex life for various proposed habitability criteria. We consider three main sources of abundance variation: differing supernova rates, alpha burning in massive stars, and isotopic stability, and how each affects the metal-to-rock ratio and the abundances of carbon, oxygen, nitrogen, phosphorus, sulfur, silicon, magnesium, and iron. Our analysis leads to several predictions for which habitability criteria are correct by determining which ones make our observations of the physical constants, as well as a few other observed features of our universe, most likely. Our results indicate that carbon-rich or carbon-poor planets are uninhabitable, slightly magnesium-rich planets are habitable, and life does not depend on nitrogen abundance too sensitively. We also find suggestive but inconclusive evidence that metal-rich planets and phosphorus-poor planets are habitable. These predictions can then be checked by probing regions of our universe that closely resemble normal environments in other universes. If any of these predictions are found to be wrong, the multiverse scenario would predict that the majority of observers are born in universes differing substantially from ours, and so can be ruled out, to varying degrees of statistical significance.
... Planck units [139] is within a single order-of-magnitude from the theoretical life-permitting upper bound. [140,141] Can similar arguments be made for tolerance with respect to fine-tuning in biology? ...
Cell membranes are now emerging as finely tuned molecular systems, signifying that re‐evaluation of our understanding of their structure is essential. Although the idea that cell membrane lipid bilayers do little more than give shape and form to cells and limit diffusion between cells and their environment is totally passé, the structural, compositional, and functional complexity of lipid bilayers often catches cell and molecular biologists by surprise. Models of lipid bilayer structure have developed considerably since the heyday of the fluid mosaic model, principally by the discovery of the restricted diffusion of membrane proteins and lipids within the plane of the bilayer. In reviewing this field, we now suggest that further refinement of current models is necessary and propose that describing lipid bilayers as “finely‐tuned molecular assemblies” best portrays their complexity and function. Lipid bilayers are surprisingly complex, containing a wide variety of lipids and proteins. Their composition, asymmetry, and internal molecular interactions operate with a range of tolerances, some as fine as a single mole percent. This essay presents cell membranes as finely tuned molecular assemblies.
... The more interesting issue is the significance and accuracy of approximate global symmetries. Consider the following: while it would have been technically natural for all the fermions in the Standard Model to be extremely light, as the theory would acquire an approximate chiral symmetry in this regime, it did not do this; the top quark's Yukawa coupling is O(1), while the up and down quark masses may be light due to environmental effects [29]. In summary, there is no current evidence of nature choosing even approximate global symmetries as a principle. ...
A bstract
The Standard Model of particle physics is governed by Poincaré symmetry, while all other symmetries, exact or approximate, are essentially dictated by theoretical consistency with the particle spectrum. On the other hand, many models of dark matter exist that rely upon the addition of new added global symmetries in order to stabilize the dark matter particle and/or achieve the correct abundance. In this work we begin a systematic exploration into truly natural models of dark matter, organized by only relativity and quantum mechanics, without the appeal to any additional global symmetries, no fine-tuning, and no small parameters. We begin by reviewing how singlet dark sectors based on spin 0 or spin 1 2 should readily decay, while pure strongly coupled spin 1 models have an overabun-dance problem. This inevitably leads us to construct chiral models with spin 1 2 particles charged under confining spin 1 particles. This leads to stable dark matter candidates that are analogs of baryons, with a confinement scale that can be naturally 𝒪(100)TeV. This leads to the right freeze-out abundance by annihilating into massless unconfined dark fermions. The minimal model involves a dark copy of SU(3) × SU(2) with 1 generation of chiral dark quarks and leptons. The presence of massless dark leptons can potentially give rise to a somewhat large value of ∆ N eff during BBN. In order to not upset BBN one may either appeal to a large number of heavy degrees of freedom beyond the Standard Model, or to assume the dark sector has a lower reheat temperature than the visible sector, which is also natural in this framework. This reasoning provides a robust set of dark matter models that are entirely natural. Some are concrete realizations of the nightmare scenario in which dark matter may be very difficult to detect, which may impact future search techniques.
... The more interesting issue is the significance and accuracy of approximate global symmetries. Consider the following: while it would have been technically natural for all the fermions in the Standard Model to be extremely light, as the theory would acquire an approximate chiral symmetry in this regime, it did not do this; the top quark's Yukawa coupling is O(1), while the up and down quark masses may be light due to environmental effects [28]. In summary, there is no current evidence of nature choosing even approximate global symmetries as a principle. ...
The Standard Model of particle physics is governed by Poincar\'e symmetry, while all other symmetries, exact or approximate, are essentially dictated by theoretical consistency with the particle spectrum. On the other hand, many models of dark matter exist that rely upon the addition of new added global symmetries in order to stabilize the dark matter particle and/or achieve the correct abundance. In this work we begin a systematic exploration into truly natural models of dark matter, organized by only relativity and quantum mechanics, without the appeal to any additional global symmetries, no fine-tuning, and no small parameters. We begin by reviewing how singlet dark sectors based on spin 0 or spin should readily decay, while pure strongly coupled spin 1 models have an overabundance problem. This inevitably leads us to construct chiral models with spin particles charged under confining spin 1 particles. This leads to stable dark matter candidates that are analogs of baryons, with a confinement scale that can be naturally TeV. This leads to the right freeze-out abundance by annihilating into massless unconfined dark fermions. The minimal model involves a dark copy of with 1 generation of chiral dark quarks and leptons. The presence of massless dark leptons can potentially give rise to a somewhat large value of during BBN. In order to not upset BBN one may either appeal to a large number of heavy degrees of freedom beyond the Standard Model, or to assume the dark sector has a lower reheat temperature than the visible sector, which is also natural in this framework. This reasoning provides a robust set of dark matter models that are entirely natural. Some are concrete realizations of the nightmare scenario in which dark matter may be very difficult to detect, which may impact future search techniques.
... respect to the strength of the weak force has been found as well (Barr and Khan 2007). Further suggested instances of fine-tuning concern the strength of gravity, the strength of the strong and weak nuclear forces (when measured against that of electromagnetism as a reference), the vacuum energy density, the overall energy density of the universe in its very early stages, the relative amplitude of energy density fluctuations in the very early universe, the initial entropy of the universe, and the form of the known laws of nature itself. 1 The finding that life requires finely tuned parameters has been cited as support for the idea of divine creation (e.g. ...
The idea that there might be multiple universes with different parameters of nature is often considered an attractive response to the finding that various parameters appear to be delicately fine-tuned for life. The present paper investigates whether the appeal to fine-tuning can legitimately be combined with an appeal to independent empirical evidence for other universes or whether, as suggested by Cory Juhl, combining such appeals inevitably results in illegitimate double counting of the finding that the parameters are right for life. In doing so, the paper takes into account the fact that the parameters' life-friendliness is old evidence for us, which makes Bayesianism's problem of old evidence relevant to Bayesian analysis of its evidential impact. Ultimately, the verdict reached is that the warning of double counting is helpful, but that double counting can in principle be avoided. The paper highlights remaining independent challenges against the fine-tuning argument for the multiverse.
... Life would apparently also have been impossible if the mass of the electron, which is roughly ten times smaller than the mass difference between the down-and the up-quark, had been somewhat larger in relation to that difference. Fine-tuning of the lightest quark masses with respect to the strength of the weak nuclear force has been found as well [4]. Further suggested instances of fine-tuning concern the strength of gravity, the strengths of the strong and weak nuclear forces, the mass of the Higgs B Simon Friederich s.m.friederich@rug.nl 1 University of Groningen, Hoendiepskade 23/24, 9718 BG Groningen, The Netherlands given the competing theories. ...
This paper has two aims. First, it points out a crucial difference between the standard argument from fine-tuning for the multiverse and paradigmatic instances of anthropic reasoning. The former treats the life-friendliness of our universe as the evidence whose impact is assessed, whereas the latter treat the life-friendliness of our universe as background information. Second, the paper develops a new fine-tuning argument for the multiverse which, unlike the old one, parallels the structure of paradigmatic instances of anthropic reasoning. The main advantage of the new argument is that it is not susceptible to the inverse gambler’s fallacy charge.
... This, in turn, places observational limits on possible variations of these quantities in the early universe [18,19,21,22]. The dependence of the deuteron binding energy (B D ) on the sum of the light quark masses varies between these papers; following Barr & Khan [12], a typical conservative parameterization of this relationship is, ...
Stellar nucleosynthesis proceeds via the deuteron (D), but only a small change in the fundamental constants of nature is required to unbind it. Here, we investigate the effect of altering the binding energy of the deuteron on proton burning in stars. We find that the most definitive boundary in parameter space that divides probably life-permitting universes from probably life-prohibiting ones is between a bound and unbound deuteron. Due to neutrino losses, a ball of gas will undergo rapid cooling or stabilization by electron degeneracy pressure before it can form a stable, nuclear reaction-sustaining star. We also consider a less-bound deuteron, which changes the energetics of the pp and pep reactions. The transition to endothermic pp and pep reactions, and the resulting beta-decay instability of the deuteron, do not seem to represent catastrophic problems for life.
... In some cases, atoms and nuclei no longer exist, and the universe would be sterile. Various aspects of this conclusion are discussed in [6,7,15,16,17,18,19,20,21,22,23,24]. Cosmology provides another constraint, with the well-known argument that if the cosmological constant were much different, matter would not clump into stars and planets [25,26,27,28,29,30,31,32,33,34]. ...
The possibility of fundamental theories with very many ground states, each with different physical parameters, changes the way that we approach the major questions of particle physics. Most importantly, it raises the possibility that these different parameters could be realized in different domains in the larger universe. In this review, I survey the motivations for the multiverse and the impact of the idea of the multiverse on the search for new physics beyond the Standard Model. Expected final online publication date for the Annual Review of Nuclear and Particle Science Volume 66 is October 19, 2016. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.
... • The existence of any atomic species and chemical processes whatsoever places tight constraints on the masses of the fundamental particles and the strengths of the fundamental forces. For example, figure 4 of [4] shows the effect of varying the masses of the up and down quark, finding that chemistry-permitting universes are huddled in a small shard of parameter space which has area ∆m up ∆m down / m 2 Planck ≈ 10 −40 , where m up (m down ) is the mass of the up (down) quark, and m Planck = c/G is the Planck mass, which combines the (reduced) Planck's constant ( ), the speed of light (c) and Newton's gravitational constant (G). Similarly, the stability of free protons requires α (m down − m up )/141 MeV ≈ 1/50 [23,24], where α = e 2 / c is the fine structure constant. ...
We calculate the properties and investigate the stability of stars that burn
via strong (and electromagnetic) interactions, and compare their properties
with those that, as in our Universe, include a rate-limiting weak interaction.
It has been suggested that, if the diproton were bound, stars would burn
~10^{18} times brighter and faster via strong interactions, resulting in a
universe that would fail to support life. By considering the representative
case of a star in our Universe with initially equal numbers of protons and
deuterons, we find that stable, "strong-burning" stars adjust their central
densities and temperatures to have familiar surface temperatures, luminosities
and lifetimes. There is no "diproton disaster". In addition, strong-burning
stars are stable in a much larger region of the parameter space of fundamental
constants, specifically the strength of electromagnetism and gravity. The
strongest anthropic bound on stars in such universes is not their stability, as
is the case for stars limited by the weak interaction, but rather their
lifetime. Regardless of the strength of electromagnetism, all stars burn out in
mere millions of years unless the gravitational coupling constant is extremely
small, \alpha_G < 10^{-30}.
The cross sections of proton-capture reactions are extremely important to model explosive nucleosynthesis, in particular for the poorly understood production of the rare p-nuclei. Taking advantage of the unique possibilities at the Experimental Storage Ring (ESR) at GSI, the so-called proton-capture campaign has been started in 2009 focusing on the study of (p,γ) reactions for hot, explosive stellar scenarios. In this thesis, the recent experiment of the campaign, performed in March 2020, is analyzed and discussed in detail. The (p,γ) and (p,n) reaction cross-sections have been successfully measured at 10 MeV/u using a stable 124Xe ion beam and for the first time also using a radioactive ion beam, namely 118Te with 6 days half-life. In addition, a novel experimental scheme to improve the sensitivity of the method has been developed. Using the stable 124Xe beam it is demonstrated that the application of this new technique enables measurement at maximum sensitivity for proton-induced reactions in inverse kinematics.
If the laws of nature are fine-tuned for life, can we infer other universes with different laws? How could we even test such a theory without empirical access to those distant places? Can we believe in the multiverse of the Everett interpretation of quantum theory or in the reality of other possible worlds, as advocated by philosopher David Lewis? At the intersection of physics and philosophy of science, this book outlines the philosophical challenge to theoretical physics in a measured, well-grounded manner. The origin of multiverse theories are explored within the context of the fine-tuning problem and a systematic comparison between the various different multiverse models are included. Cosmologists, high energy physicists, and philosophers including graduate students and researchers will find a systematic exploration of such questions in this important book.
Este artículo distingue en primer lugar entre el dato del ajuste fino del universo y sus posibles interpretaciones. Mientras que el tema de las posibles interpretaciones sigue siendo muy controvertido, el dato en sí es ampliamente aceptado. El autor más destacado entre los que rechazan el dato del ajuste fino del universo es Victor Stenger. El artículo resume la discusión entre Stenger y Barnes sobre el tema del ajuste fino y apunta varias conclusiones derivables de dicha discusión.
We consider a scalar field with a bottom-less potential, such as , finding that cosmologies unavoidably end up with a crunch, late enough to be compatible with observations if . If rebounces avoid singularities, the multiverse acquires new features; in particular probabilities avoid some of the usual ambiguities. If rebounces change the vacuum energy by a small enough amount, this dynamics selects a small vacuum energy and becomes the most likely source of universes with anthropically small cosmological constant. Its probability distribution could avoid the gap by 2 orders of magnitude that seems left by standard anthropic selection.
Both the fundamental constants that describe the laws of physics and the cosmological parameters that determine the properties of our universe must fall within a range of values in order for the cosmos to develop astrophysical structures and ultimately support life. This paper reviews the current constraints on these quantities. The discussion starts with an assessment of the parameters that are allowed to vary. The standard model of particle physics contains both coupling constants (α,α s ,α w ) and particle masses (m u ,m d ,m e ), and the allowed ranges of these parameters are discussed first. We then consider cosmological parameters, including the total energy density of the universe (Ω), the contribution from vacuum energy (ρ Λ ), the baryon-to-photon ratio (η), the dark matter contribution (δ), and the amplitude of primordial density fluctuations (Q). These quantities are constrained by the requirements that the universe lives for a sufficiently long time, emerges from the epoch of Big Bang Nucleosynthesis with an acceptable chemical composition, and can successfully produce large scale structures such as galaxies. On smaller scales, stars and planets must be able to form and function. The stars must be sufficiently long-lived, have high enough surface temperatures, and have smaller masses than their host galaxies. The planets must be massive enough to hold onto an atmosphere, yet small enough to remain non-degenerate, and contain enough particles to support a biosphere of sufficient complexity. These requirements place constraints on the gravitational structure constant (α G ), the fine structure constant (α), and composite parameters (C ⋆ ) that specify nuclear reaction rates. We then consider specific instances of possible fine-tuning in stellar nucleosynthesis, including the triple alpha reaction that produces carbon, the case of unstable deuterium, and the possibility of stable diprotons. For all of the issues outlined above, 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 thereby support habitability.
Following a long-term international collaboration between leaders in cosmology and the philosophy of science, this volume addresses foundational questions at the limit of science across these disciplines, questions raised by observational and theoretical progress in modern cosmology. Space missions have mapped the Universe up to its early instants, opening up questions on what came before the Big Bang, the nature of space and time, and the quantum origin of the Universe. As the foundational volume of an emerging academic discipline, experts from relevant fields lay out the fundamental problems of contemporary cosmology and explore the routes toward finding possible solutions. Written for graduates and researchers in physics and philosophy, particular efforts are made to inform academics from other fields, as well as the educated public, who wish to understand our modern vision of the Universe, related philosophical questions, and the significant impacts on scientific methodology.
Our everyday macroscopic experience of being in the world is saturated with asymmetries – thermodynamic asymmetries, and radiative asymmetries, and epistemic asymmetries, and phenomenological asymmetries, and asymmetries of over-determination, and asymmetries of influence, and what have you – between the past and the future.
And there is a long-cherished hope – something that has its origins in the work of Boltzmann, and which has been pursued, by any number of other investigators, through any number of fits and starts and revelations and wrong turns, ever since – that all of those asymmetries can ultimately be traced back to some relatively simple characteristic of the initial macrocondition of the universe. The thought (as people put it now) is that all we need to do, in order to account for these asymmetries, is to add to the fundamental time-reversalsymmetric dynamical laws, and to the standard statistical-mechanical probability-measure over the space of possible fundamental physical states, a simple postulate – a so-called past-hypothesis – to the effect that the world first came into being in whatever particular low-entropy macrocondition it is that the normal inferential procedures of cosmology are eventually going to present to us.
The business of working this thought out in detail is a large undertaking, which is still very much in its infancy, and which is still very much under debate – and I do not want to attempt anything along the lines of an overview of that project here. All I want to talk about in this chapter is a widespread and fundamental and perennial sort of puzzlement about how such a project could even seriously be entertained – a puzzlement (that is) about how it is that the macrocondition of the universe 14 billion years ago – all by itself – could even imaginably be up to the job of explaining so much about the feel, now and on earth, of the passing of time.
This puzzlement takes a number of different forms, and arises in a number of different contexts.
On the most trivial level, there is a question of how the lowness of the entropy of the world 14 billion years ago can impose any genuinely profound and vivid constraints whatever on what the world is doing now.
In nonsupersymmetric grand unified models a “radiative fermion mass hierarchy” can be achieved in which the spectrum of quark and lepton masses is determined entirely by physics at the unification scale, with many relations following from the unified gauge symmetry, and with the masses of the lightest family arising from loops. A simple, realistic, and predictive model of this kind is presented. A “doubly lopsided” structure, known to lead to bilarge neutrino mixing, plays a crucial role in the radiative hierarchy.
A class of nonsupersymmetric extensions of the standard model is proposed in which there is a multiplicity of light scalar doublets in a multiplet of a nonabelian family group with the standard model Higgs doublet. Anthropic tuning makes the latter light, and consequently the other scalar doublets remain light because of the family symmetry. The family symmetry greatly constrains the pattern of flavor-changing neutral-current interactions (FCNC) and p decay operators coming from scalar-exchange. Such models show that useful constraints on model-building can come from an extended naturalness principle when the electroweak scale is anthropically tuned.
A nonsupersymmetric grand unified theory can exhibit a “radiative fermion mass hierarchy”, in which the heavier quarks and leptons get mass at tree level and the lighter ones get mass from loop diagrams. Recently the first predictive model of this type was proposed. Here it is analyzed numerically and it is shown to give an excellent fit to the quark and lepton masses and mixings, including the CP violating phase δCKM. A relation between the neutrino angle θ13 and the atmospheric neutrino angle is obtained.
We summarize our work on the O'Raifeartaigh uplifted KKLT model at finite temperature. We study the system for parameter values for which the zero temperature potential for the volume modulus has a dS minimum. The temperature-dependent part of the effective potential has a runaway behaviour for one exponent in the superpotential, whereas it can have local minima at finite field vevs for two exponents in the superpotential. However, it turns out that, despite the presence of those minima, the zero temperature dS vacuum is not destabilized by thermal corrections within the whole range of validity of our approximations.
We study whether finite temperature corrections decompactify the internal space in KKLT compactifications with an uplifting sector given by a system that exhibits metastable dynamical supersymmetry breaking. More precisely, we calculate the one-loop temperature corrections to the effective potential of the volume modulus in the KKLT model coupled to the quantum corrected O'Raifeartaigh model. We prove that for the original KKLT model, namely with one exponent in the non-perturbative superpotential, the finite temperature potential is runaway when at zero temperature there is a dS minimum. On the other hand, for a non-perturbative superpotential of the race-track type with two exponents, we demonstrate that the temperature-dependent part of the effective potential can have local minima at finite field vevs. However, rather unexpectedly, it turns out that these minima do not affect the structure of the full effective potential and so the volume modulus is stabilized at the local minimum of the zero temperature potential for the whole range of validity of the supergravity approximation.
The fine-tuning of the universe for intelligent life has received a great
deal of attention in recent years, both in the philosophical and scientific
literature. The claim is that in the space of possible physical laws,
parameters and initial conditions, the set that permits the evolution of
intelligent life is very small. I present here a review of the scientific
literature, outlining cases of fine-tuning in the classic works of Carter, Carr
and Rees, and Barrow and Tipler, as well as more recent work. To sharpen the
discussion, the role of the antagonist will be played by Victor Stenger's
recent book The Fallacy of Fine-Tuning: Why the Universe is Not Designed for
Us. Stenger claims that all known fine-tuning cases can be explained without
the need for a multiverse. Many of Stenger's claims will be found to be highly
problematic. We will touch on such issues as the logical necessity of the laws
of nature; objectivity, invariance and symmetry; theoretical physics and
possible universes; entropy in cosmology; cosmic inflation and initial
conditions; galaxy formation; the cosmological constant; stars and their
formation; the properties of elementary particles and their effect on chemistry
and the macroscopic world; the origin of mass; grand unified theories; and the
dimensionality of space and time. I also provide an assessment of the
multiverse, noting the significant challenges that it must face. I do not
attempt to defend any conclusion based on the fine-tuning of the universe for
intelligent life. This paper can be viewed as a critique of Stenger's book, or
read independently.
A classification is given of Higgs-flavor models. In these models, there are
several Higgs doublets in an irreducible multiplet R_{Phi} of a non-abelian
symmetry G_{Phi}, under which the quarks and leptons do not transform (thus
giving minimal flavor-changing for the fermions). It is found that different
G_{Phi} and R_{Phi} lead to very distinctive spectra of the extra Higgs
doublets, including different numbers of "sequential Higgs" and of "inert
Higgs" that could play the role of dark matter, different mass relations, and
different patterns of SU(2)_L-breaking splittings within the Higgs doublets.
It is shown that realistic models can be constructed in which the Standard
Model Higgs field is in a non-trivial multiplet of a non-abelian family group
of the quarks and leptons. It is shown that the observed quark and lepton
masses and mixing angles can be fit, while the coefficients of flavor-changing
four-fermion operators mediated by the extra Higgs doublets are determined in
terms of only a few unknown parameters.
In the absence of low-energy supersymmetry, a multiplicity of weak-scale
Higgs doublets would require additional fine-tunings unless they formed an
irreducible multiplet of a non-abelian symmetry. Remnants of such symmetry
typically render some Higgs fields stable, giving several dark matter particles
of various masses. The non-abelian symmetry also typically gives simple,
testable mass relations.
In any theory it is unnatural if the observed parameters lie very close to special values that determine the existence of complex structures necessary for observers. A naturalness probability, P, is introduced to numerically evaluate the unnaturalness. If P is small in all known theories, there is an observer naturalness problem. In addition to the well-known case of the cosmological constant, we argue that nuclear stability and electroweak symmetry breaking (EWSB) represent significant observer naturalness problems. The naturalness probability associated with nuclear stability is conservatively estimated as P_nuc < 10^{-(3-2)}, and for simple EWSB theories P_EWSB < 10^{-(2-1)}. This pattern of unnaturalness in three different arenas, cosmology, nuclear physics, and EWSB, provides evidence for the multiverse. In the nuclear case the problem is largely solved even with a flat multiverse distribution, and with nontrivial distributions it is possible to understand both the proximity to neutron stability and the values of m_e and m_d - m_u in terms of the electromagnetic contribution to the proton mass. It is reasonable that multiverse distributions are strong functions of Lagrangian parameters due to their dependence on various factors. In any EWSB theory, strongly varying distributions typically lead to a little or large hierarchy, and in certain multiverses the size of the little hierarchy is enhanced by a loop factor. Since the correct theory of EWSB is unknown, our estimate for P_EWSB is theoretical. The LHC will determine P_EWSB more robustly, which may remove or strengthen the observer naturalness problem of EWSB. For each of the three arenas, the discovery of a natural theory would eliminate the evidence for the multiverse; but in the absence of such a theory, the multiverse provides a provisional understanding of the data.
It is shown that in supersymmetric SU(N) models with N>5 the so-called doubly lopsided mass matrix structure can emerge in a natural way. The non-trivial flavor structure is entirely accounted for by the SU(N) gauge symmetry and supersymmetry, without any flavor symmetry. The hierarchy among the families results directly from a hierarchy of scales in the chain of breaking from SU(N)to the Standard Model group. A simple SU(7) example is presented.
We give an explanation of the CP conservation of strong interactions which includes the effects of pseudoparticles. We find it is a natural result for any theory where at least one flavor of fermion acquires its mass through a Yukawa coupling to a scalar field which has nonvanishing vacuum expectation value.
We explore the consequences of the assumption that the direct and induced weak neutral currents in an SU(2)⊗U(1) gauge theory conserve all quark flavors naturally, i.e., for all values of the parameters of the theory. This requires that all quarks of a given charge and helicity must have the same values of weak T3 and T⃗2. If all quarks have charge +2/3 or -1/3 the only acceptable theories are the "standard" and "pure vector" models, or their generalizations to six or more quarks. In addition, there are severe constraints on the couplings of Higgs bosons, which apparently cannot be satisfied in pure vector models. We also consider the possibility that neutral currents conserve strangeness but not charm. A natural seven-quark model of this sort is described. The experimental consequences of charm nonconservation in direct or induced neutral currents are found to be quite dramatic.
In theories in which different regions of the universe can have different values of certain physical parameters, we would naturally find ourselves in a region where they take values favorable for life. We explore the range of such viable values of the mass parameter in the Higgs potential, μ2. For μ2<0, the requirement that complex elements be formed suggests that the Higgs vacuum expectation value v must have a magnitude less than 5 times its observed value. For μ2>0, baryon stability requires that |μ|≪MP, the Planck mass. Smaller values of |μ2| may or may not be allowed depending on issues of element synthesis and stellar evolution. We conclude that the observed value of μ2 appears reasonably typical of the viable range, and a multiple-domain scenario may provide a plausible explanation for the closeness of the QCD scale and the weak scale.
One of the puzzles of the Standard Model is why the mass parameter which
determines the scale of the Weak interactions is closer to the scale of QCD
than to the Grand Unification or Planck scales. We discuss a novel approach to
this problem which is possible in theories in which different regions of the
universe can have different values of the physical parameters. In such a
situation, we would naturally find ourselves in a region which has parameters
favorable for life. We explore the whole range of values of the mass parameter
in the Higgs potential, , from to and find that there
is only a narrow window, overlapping with the observed value, in which life is
likely to be possible. The observed value of is fairly typical of the
values in this range. Thus multiple domain theories in which varies
among domains may give a promising approach to solving the fine tunign problem
and explaining the closeness of the QCD scale and the Weak scale.
An approach is suggested for modeling quark and lepton masses and mixing in
the context of grand unified theories that explains the curious fact that m_u ~
m_d even though m_t >> m_b. The structure of the quark mass matrices is such as
to allow a non-Peccei-Quinn solution of the Strong CP Problem.
Energy flows in the universe are described and the genesis of the various kinds of energy is discussed. The process by which energy is channeled in the cosmos are discussed with implications for the earth highlighted.
We show, by explicit construction of a highly convergent superweak theory of CP nonconservation, that the problem of natural suppression of strong P and T noninvariances: in the presence of instantons: may be resolved without invoking symmetries which imply massless quarks or nearly massless bosons.
In gauge theories with spontaneously broken left-right symmetry, strong P and T non-invariant effects can also be made to vanish naturally in the tree approximation without introducing massless quarks or axions. In a four-flavor SU(2)L × SU(2)R × U(1)L+R model with manifest left-right symmetry, we show that strong CP noninvariance is absent up to the one-loop level and weak CP-violation is of superweak type. Extension to the case of six quarks gives a left-right symmetric generalization of the Kobayashi-Maskawa model without axions.
In recent cosmological models, there is an "anthropic" upper bound on the cosmological constant Lambda. It is argued here that in universes that do not recollapse, the only such bound on Lambda is that it should not be so large as to prevent the formation of gravitationally bound states. It turns out that the bound is quite large. A cosmological constant that is within 1 or 2 orders of magnitude of its upper bound would help with the missing-mass and age problems, but may be ruled out by galaxy number counts. If so, one may conclude that anthropic considerations do not explain the smallness of the cosmological constant.
Typically in unified theories the neutrino mixing angles, like the
Cabibbo-Kobayashi-Maskawa (CKM) angles of the quarks, are related to the small
mass ratios between fermions of different generations and are therefore quite
small. A new approach for explaining the intergenerational mass hierarchies is
proposed here which, while giving small CKM angles, naturally leads to neutrino
angles of order unity. Such large mixing angles may be required for a
resolution of the atmospheric neutrino anomaly and may also be relevant for the
solar neutrino puzzle. The mechanism presented here provides a framework in
which novel approaches to the fermion mass question can arise. In particular,
within this framework a variant of the texture idea allows highly predictive
models to be constructed, an illustrative example of which is given. It is
shown how the neutrino mixing angles may be completely determined in such
schemes.
Motivated by landscape models in string theory, cosmic nuclear evolution is analyzed allowing the Standard Model Higgs expectation value w to take values different from that in our world (w=1), while holding the Yukawa couplings fixed. Thresholds are estimated, and astrophysical consequences are described, for several sensitive dependences of nuclear behavior on w. The dependence of the neutron-proton mass difference on w is estimated based on recent calculations of strong isospin symmetry breaking, and is used to derive the threshold of neutron-stable worlds, w ~ 0.6+/- 0.2. The effect of a stable neutron on nuclear evolution in the Big Bang and stars is shown to lead to radical differences from our world, such as a predominance of heavy r-process and s-process nuclei and a lack of normal galaxies, stars and planets. Rough estimates are reviewed of w thresholds for deuteron stability and the pp and pep reactions dominant in many stars. A simple model of nuclear resonances is used to estimate the w dependence of overall carbon and oxygen production during normal stellar nucleosynthesis; carbon production is estimated to change by a fraction ~15(1-w). Radical changes in astrophysical behavior seem to require changes in w of more than a few percent, even for the most sensitive phenomena. Comment: 11 pages, Latex, to appear in Phys. Rev. D
Some properties of the world are fixed by physics derived from mathematical symmetries, while others are selected from an ensemble of possibilities. Several successes and failures of ``anthropic'' reasoning in this context are reviewed in the light of recent developments in astrobiology, cosmology and unification physics. Specific issues raised include our spacetime location (including the reason for the present age of the universe), the timescale of biological evolution, the tuning of global cosmological parameters, and the origin of the Large Numbers of astrophysics and the parameters of the Standard Model. Out of the twenty parameters of the Standard Model, the basic behavior and structures of the world (nucleons, nuclei, atoms, molecules, planets, stars, galaxies) depend mainly on five of them: and (where and are taken as defined quantities). Three of these appear to be independent in the context of Grand Unified Theories (that is, not fixed by any known symmetry) and at the same time have values within a very narrow window which provides for stable nucleons and nuclei and abundant carbon. The conjecture is made that the two light quark masses and one coupling constant are ultimately determined even in the ``Final Theory'' by a choice from a large or continuous ensemble, and the prediction is offered that the correct unification scheme will not allow calculation of from first principles alone.
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