B Is the Galileon theory an alternative to GR

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The Galileon theory presents a potential alternative to General Relativity (GR) by suggesting that gravitational effects attributed to dark matter could be explained through modified gravity with a screening mechanism. Recent studies indicate that this theory can account for observations in galaxy clusters without requiring dark matter, utilizing data from gravitational lensing and X-ray observations. However, the theory faces criticism for being complex, speculative, and not fully testable in laboratory settings, raising concerns about its viability. While it shows promise in matching observational data and producing statistically significant results, it must also address all the explanatory power of GR to be considered a legitimate alternative. The ongoing debate highlights the need for further research to validate or refute the Galileon theory's claims.
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We have been searching for Dark Matter a long time, is it time to look at theories like this Galileon one?
What draw backs does it have? arXiv:1607.02606 [pdf, ps, other]
No need for dark matter in galaxy clusters within Galileon theory
Vincenzo Salzano, David F. Mota, Mariusz P. Dabrowski, Salvatore Capozziello
Comments: 14 pages, 4 figures
Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO)

Modified gravity theories with a screening mechanism have acquired much interest recently in the quest for a viable alternative to General Relativity on cosmological scales, given their intrinsic property of being able to pass Solar System scale tests and, at the same time, to possibly drive universe acceleration on much larger scales. Here, we explore the possibility that the same screening mechanism, or its partial breaking at a certain astrophysical scale, might be responsible of those gravitational effects which, in the context of general relativity, are generally attributed to Dark Matter. We consider a recently proposed extension of covariant Galileon models in the so-called "beyond Horndeski" scenario, where a breaking of the Vainshtein mechanism is possible and, thus, some peculiar observational signatures should be detectable and make it distinguishable from general relativity. We apply this model to a sample of clusters of galaxies observed under the CLASH survey, using both new data from gravitational lensing events and archival data from X-ray intra-cluster hot gas observations. In particular, we use the latter to model the gas density, and then use it as the only ingredient in the matter clusters' budget to calculate the expected lensing convergence map. Results show that, in the context of this extended Galileon, the assumption of having only gas and no Dark Matter at all in the clusters is able to match observations. We also obtain narrow and very interesting bounds on the parameters which characterize this model. In particular, we find that, at least for one of them, the general relativity limit is excluded at 2σ confidence level, thus making this model clearly statistically different and competitive with respect to general relativity.
 
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Its been around since the 70's, see:
arXiv:1508.00046v2

I found a set of notes as slides... galileon theory is a subset of massive gravity theory.
https://clareburrage.files.wordpress.com/2013/04/helsinki_2013.pdf

Afaict...
Its very complicated, not testable in the lab, and introduces more problems than it solves.
Basically it is still at the status of speculation... it is not good enough for a new theory to explain something the current theory has trouble with, it also has to explain everything the current theory does.
 
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