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Studies in History and Philosophy of Modern Physics 64 (2018) 26e38 Contents lists available at ScienceDirect Studies in History and Philosophy of Modern Physics journal homepage: www.elsevier.com/locate/shpsb Three problems about multi-scale modelling in cosmology Michela Massimi* School of Philosophy, Psychology and Language Sciences, The University of Edinburgh, Dugald Stewart Building 3 Charles Street, Edinburgh EH8 9AD, UK article info Article history: problem by looking at the role of the renormalization group in Received 25 September 2017 modelling what he calls the “in between scales” point of view. Received in revised form Batterman has explored methodological ways of modelling “in 18 April 2018 between” scales as a way of counteracting the tyranny of scales and Accepted 19 April 2018 Available online 18 May 2018 the apparent choice it forces upon us between pure top-down or pure bottom-up modelling techniques.1 Batterman’s message is that “mesoscopic structures cannot be ignored and, in fact, provide the bridges that allow us to model across scales” because they are the scale at which top-down modelling strategies and bottom-up modelling strategies typically meet: 1. Introduction bottom-up modelling of systems that exist across a large range of scales is not sufficient to yield observed properties of those fi In the vast literature on scienti c models and simulations, systems at higher scale. Neither is complete top-down model- increasing attention has been paid to the sensitivity of modelling to ling. After all, we know that the parameters appearing in con- scales. Models and simulations are tied to particular scales, with tinuum models must depend upon details at lower scale levels. far-reaching consequences for the ontological inferences that can The interplay between the two strategiesda kind of mutual fl be drawn about the target system. For example, uid dynamics adjustment in which lower scale physics informs upper scale fl typically offers scale-based models for the behavior of uids. It is models and upper scale physics corrects lower scale modelsdis fl possible to model a uid at the macro-scale (e.g. its viscosity) complex, fascinating and unavoidable (Batterman (2013), p. without having to model what happens at the micro-scale (and the 283). Navier-Stokes equations typically take care of this modelling task at the macro-scale). On the other hand, if the goal is to model and understand the statistical behavior of molecules composing the The overarching goal of the present paper is to contribute to this fluid, then modelling at the macro-scale does not help with the literature of modelling across scales by looking not at hydrody- task. Batterman (2013) has called this well-known feature of namics, or condensed matter physics, but instead at contemporary modelling practices the “tyranny of scales”; and has addressed the cosmology. This paper explores the distinctive ways in which the “tyranny of scales” affects modelling dark matter at the meso-scale as I am going to call the scale of individual galaxies in contemporary * Corresponding author. cosmology. Three scale-related problems about modelling dark E-mail address: [email protected]. matter are presented and discussed. These problems are interesting 1 e In Batterman’s (2013, p. 256 257) own words, a reductionist view might as- because they lie at the very heart of cutting-edge research in cos- sume for example that “whatever the fundamental theory is at the smallest, basic scale, it will be sufficient in principle to tell us about the behavior of the system at mology; and, they touch upon pressing methodological aspects on all scales. Continuum modelling on this view represents an idealizationdas Feyn- which the debate in cosmology between the standard model man has said, ‘a smoothed-out imitation of a really much more complicated (LCDM) vs. Modified Newtonian Dynamics (MOND) has been microscopic world’ (Feynman, Leighton and Sands 1964, p. 12) … Many believe that revolving. I am going to call them the “downscaling problem”; the a reductionist/eliminativist picture is the correct one. I maintain that even if we can “upscaling problem”; and the “in between” scales problem. Before explain the safety and robustness of continuum modeling (how this can be done is fl the focus of this essay), the reductionist picture is mistaken. It is a mistaken picture presenting each of them, it is necessary to esh out both the phil- of how science works. My focus here is on a philosophical investigation that is true osophical and scientific context behind the problem of multiscale to the actual modeling practices of scientists (…). The fact of the matter is that modelling in contemporary cosmology. scientists do not model the macroscale behaviors of materials using pure bottom- What Batterman calls the “tyranny of scales” affects modelling up techniques. I suggest that much philosophical confusion about reduction, emergence, atomism, and antirealism follows from the absolute choice between in cosmology in interesting and novel ways, I am going to argue. For bottom-up and top-down modeling that the tyranny of scales apparently forces it affects the very nature of the debate between the LCDM model upon us”. https://doi.org/10.1016/j.shpsb.2018.04.002 1355-2198/© 2018 The Author. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). M. Massimi / Studies in History and Philosophy of Modern Physics 64 (2018) 26e38 27 and MOND as well as some novel hybrid proposals that have (v) Ultimately, I suggest, a successful multi-scale cosmology emerged to go beyond the LCDM e MOND dichotomy. The LCDM ought to address these problems of scales that different e MOND debate has been ongoing since the 1980s when the work models respectively face. Even if dark matter particles were of Milgrom (1983) challenged the standard LCDM model, which detected tomorrow, the LCDM would still need to come up postulates the existence of cold dark matter, and suggested instead with an explanation of the BTF relation for galaxies. Even if the need for amending the laws of Newtonian dynamics at large MOND were able to retrieve clusters’ behavior, the problem scale. While the majority of the cosmology community has gath- of consistency with large scale phenomena (CMB angular ered consensus around the LCDM model dbecause of its remark- power spectrum, the matter spectrum, gravitational lensing) able success at explaining structure formation at large scale, among would still have to be addressed. many other phenomena (as explained in Section 2)d as of today, no dark matter particles have been detected yet. The paper is structured as follows. Section 2 introduces the There is more. In the past two decades increasingly more ac- standard LCDM cosmological model, and very briefly reviews the curate astrophysical data and measurements concerning galaxies evidence for it at large scale and ongoing searches for dark matter have been made. These data have highlighted some phenomen- particles. The emphasis in this Section is on the meso-scale of indi- adfor example, the so-called Baryonic Tully-Fisher relation, (BTF vidual galaxies (rather than the micro scale of dark matter particle hereafter) among othersdthat naturally fit MOND but are more candidates, or the large scale of structure formation in the universe). problematic to explain within the LCDM model. Most within the This is the scale at which most of the contemporary debates and cosmology community would not be swayed by BTF evidence at controversy takes place. Three problems about multiscale modelling galactic scale, while MOND supporters have increasingly pointed at are presented. Section 3 illustrates what I refer to as the “down- this evidence to keep the debate open. It is fair to say that many in scaling problem”, faced by the current cosmological model, with a the cosmology community feel that this debate will be settled if and focus on some very recent developments on the front of computer when either dark matter is detected in the laboratory; or when simulations and their ability to tackle this problem. Section 4 dis- MOND can be generalized from the status of a successful phe- cusses the “upscaling problem” faced by modified Newtonian Dy- nomenology at the galaxy scale onto a general theory at large scale. namics (MOND), as a rival of the current cosmological model. I From a philosophical point of view, however, this debate goes review in particular two recent attempts at expanding upon MOND deeper than the dichotomy between finding the smoking gun of (the so-called EMOND and Verlinde’s emergent gravity). Section 5 dark matter particles; or elaborating a suitable relativistic MOND briefly illustrates a recent proposal that has been put forward with for large-scale structure. What is philosophically at stake in this an eye to overcoming the stand-off between the downscaling and debate is yet another manifestation of the “tyranny of scales”; or the upscaling problem. This hybrid proposal (by Berezhiani and better, how challenging multi-scale modelling proves when the Khoury) while exciting and promising, faces its own problem, scales in question are of the order of cosmological scales. My namely what I call the “in between” scale problem, in the creative overarching philosophical goal is to lay out the nature, problems, attempt at devising modelling solutions for dark matter across and prospects of multi-scale modelling in contemporary cosmology different scales. In the final Section 6, I draw some qualified and by advancing and substantiating five main claims: tentative conclusions on the philosophical and physical challenges still open for multiscale modelling in contemporary cosmology. (i) LCDM and MOND, respectively, work best at a specific scale (large scale for LCDM, meso or galactic scale for MOND); 2.

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