Abstract
In this document, we introduce a novel formalism for any field theory and apply it to the effective field theories of large-scale structure. The new formalism is based on functors of actions composing those theories. This new formalism predicts the actionic fields. We discuss our findings in a cosmological gravitology framework. We present these results with a cosmological inference approach and give guidelines on how we can choose the best candidate between those models with some latest understanding of model selection using Bayesian inference.
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Data Availability
The data that support the findings of this study are openly available in AofEFT.
Notes
As the term suggests, it is the study of different gravitational theories within the framework of cosmology. On the other hand, we could also see the perspective in which we develop cosmology using gravitational theories. In that case we could use the terms gravitological cosmology or gravitational cosmology. These terms depend on what one is inspired from.
Note that the name functors of actions can be also replaced by relations of actions or any other name that best describes these novel theories. We give this name as we currently understand this best describes these mathematical entities.
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Acknowledgements
PN acknowledges financial support from “Centre National d’Études Spatiales” (CNES). PN would like to thank F. Piazza for his inspirational phrase: “Here, we are trying to open new possibilities!”. PN is grateful for comments on the draft from L. Amendola, J.P. Solovej, and discussion from A. Blanchard, F.H. Couannier, E.N. Saridakis, Y.Dalianis which improved the presentation of this work. We acknowledge open libraries support IPython [47], Matplotlib [36], NUMPY [58] SciPy 1.0 [57], https://github.com/lontelis/cosmopitCOSMOPIT [42, 43].
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Pierros Ntelis. The first draft of the manuscript was written by Pierros Ntelis and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Appendix A: The Higgs Matter Field
Appendix A: The Higgs Matter Field
As [26, 31, 32] have shown, the matter fields have one main component, the Higgs field, which gives mass to the other fields of the standard model of particle physics. In particular the action for the Higgs field is the following:
where \(\eta\) is the determinant of the Minkowski metric, \(\eta _{\mu \nu }\), which is taken as, \(-+++\), \(\overrightarrow {\phi }(\eta )\) is a vector of real scalar fields and \(A_{\mu }\) is a real vector field used for the interactions. The Lagrangian density is composed as:
where \(\phi _i\equiv \phi _i(\eta _{\mu \nu }),\ i = 1,2\) are the two real scalar fields which interact with the \(A_{\mu }\) field and \(\left( \nabla \phi _i \right) ^2 \equiv \nabla _{\mu }\phi _i \nabla ^{\mu } \phi _i \equiv \eta _{\mu \nu } \nabla ^{\mu }\phi _i \nabla ^{\nu } \phi _i\) . Note that this \(\nabla ^{\mu }\) is different than the \(\nabla ^{\mu }\) in Sect. 2.1. Here this \(\nabla ^{\mu }\) is defined as:
where e is a dimensionless coupling constant. Note that \({\mathcal {L}}_\mathrm{Higgs}\left[ \eta _{\mu \nu },\overrightarrow{\mathbf{\phi}}(\eta ),A_{\mu } \right]\) is invariant under simultaneous gauge transformation of the first kind on \(\phi _1\pm i \phi _2\) and of the second kind on \(A_{\mu }\) . In the case where \(V'(\phi _0^2) = 0\) and \(V'' ( \phi ^2_0 ) > 0\), where \(\phi _0\) is the ground state of either \(\phi _i\), then spontaneous breakdown of U(1) symmetry occurs. Note that we present a generic description of the Higgs field, which can be applied to more specific interactions which constitute the standard model.
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Ntelis, P., Morris, A. Functors of Actions. Found Phys 53, 29 (2023). https://doi.org/10.1007/s10701-022-00628-z
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DOI: https://doi.org/10.1007/s10701-022-00628-z