So, going then back to the underdetermination problem, we may ask what is the available evidence for the concordance model? And here we will find replicated Pierre Duhem's story about how a piece of negative evidence may not necessarily speak against the main theoretical hypothesis, but may instead indicate the need of introducing an auxiliary hypothesis. If that's the case, then the problem of underdetermination of theory by evidence looms on the horizon as the following table shows. So if the underdetermination argument is correct, then the choice between the concordance model and some of its rivals must seem to be not on rational ground. And one might be tempted to bring in a sociological explanation of why scientists gather their consensus around the concordance model and the hypothesis of dark energy and dark matter. For example, one might argue that it's easier to hold on to a well established and well accepted theory such as general relativity plus the auxiliary hypothesis of dark energy than trying to modify the theory. And even in those cases where we do have a very well worked out alternative such as MOND, people may prefer to hold on to traditional Newtonian dynamics because of the ad-hoc nature of the modification of the Newtonian dynamics required by MOND. Are scientists following their good sense in taking those decisions, and what counts as good sense? For example, a MOND supporter would argue that they have a very successful theory to explain galaxy rotation curves without resorting to dark matter. From their point of view, good sense would recommend accepting relativistic MOND over the concordance model. To give an answer to these pressing questions at the forefront of contemporary research in cosmology, we should go back to one of the premises of the underdetermination argument, the premise about empirical equivalence, and ask whether we do have genuine empirically equivalent competitors for dark energy and dark matter. For example, one rival dark energy-free model is the so-called Inhomogeneous Lemaitre-Tolman-Bondi, or LTB model, rather than the FLRW models of the concordance model, which assumes, with the Cosmological Principle, that our universe is roughly homogenous and isotropic. Namely, it assumes that our universe has the same uniform structure in all spatial positions and in all spatial directions. So if we deny homogeneity but retain isotropy, we might be assuming that there are variations, spatial variations in the distribution of matter in our universe. And we may want to assume that we occupy an underdense, or void region in our universe, what cosmologists call the Hubble Bubble, that is accelerating at a rate faster than the average. So the argument goes that our inference to dark energy is flawed because it's based on a flawed homogeneous FLRW model. Critics of dark energy argue that an LTB model is a genuine empirically equivalent rival to FLRW model, because it can account for, for example, fluctuations in cosmic microwave background, as well as accounting for the same evidence that dark energy typically explains, namely supernova 1a data. Although with an important caveat. Supernova 1a data, which is a typical evidence for an accelerating expansion of the universe for which dark energy is usually introduced, is now interpreted without acceleration. Dark energy critics argue that light traveling through an inhomogeneous universe doesn't see the Hubble expansion, and we make inferences about an accelerating expansion using red shift and light intensity, neither of which can track any eventual inhomogeneities in the universe through which the light travels. However, many cosmologists find LTB models unattractive because of the need to place ourselves in a very special position in our universe, a so-called Hubble Bubble. And this violates what is called the Copernican principle, namely, the view named after Copernicus that we don't occupy any special or privileged position in our universe. Moreover, one may retort that the charge of being ad hoc affects the interpretation of supernova 1a data here as implying no acceleration no less that it affects the assumption of dark energy, the assumption of a known zero vacuum energy density to interpret the very same data as data for an accelerating expansion of the universe. What if instead of modifying FLRW models, we try to modify general relativity instead, and go with dark energy? Well, some physicists appeal to string theory to speculate that there might be many vacua with different energy of the vacuum density, and we might just be occupying a very special vacuum with a tiny positive value of the vacuum energy density. But it's fair to say, that as of today, we don't really have a genuine contender to general relativity. Shifting to rivals of dark matter, the best candidate we currently have is Modified Newtonian Dynamics, or MOND, first proposed by Milgrom in the 1980's and in its relativistic form by Bekenstein. As we mentioned before, MOND was introduced to explain the anomaly of galaxy flat rotation curves without introducing the auxiliary hypothesis of dark matter, but by modifying Newton's law instead. MOND supporters appeal to arguments from simplicity and mathematical elegance. For example, Bekenstein argues that for disk galaxies MOND provides a more economical and more falsifiable theory than the dark matter paradigm. It's interesting that appeals should be made here to Popper's falsifiability and simplicity as arguments for preferring MOND over dark matter, which brings us back to the philosophical topic of today's class. Do we have genuine empirically equivalent rivals to dark energy and dark matter? Or is the theory choice between dark energy and dark matter on one hand and rivals really underdetermined by evidence. Was Thomas Kuhn right in thinking that neither simplicity nor any other criteria will ever be sufficient to explain how scientists go about making decisions about which theory to support? As a philosophical reply to those questions, one might stress that there is a lot more to theory choice than just the ability of two rival theories to imply or to entail the same piece of evidence. It is within this context that philosophers of science appeal to the notion of empirical support as a way forward in the debate about underdetermination of theory by evidence and the rationality of theory choice. For example, the concordance model is not just empirically supported by direct empirical evidence that we may be able to find one day about dark energy and dark matter. But the model is embedded into a larger theoretical framework, general relativity. And in so doing, the model receives indirect empirical support from any other piece of evidence that is a consequence of the larger theoretical framework within which the model is embedded. Along similar lines, although none of the phenomena of terrestrial mechanics is directly relevant to galaxy flat rotation curves, one may appeal to the success of Newtonian dynamics across this wide range spectrum of phenomena as an argument for Newtonian dynamics being empirically very well supported, and not in need of any ad-hoc modification, such as those required by MOND, to explain anomalous phenomena in cosmology.
