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Gravity and Scalar Fields

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Modifications of Einstein's Theory of Gravity at Large Distances

Part of the book series: Lecture Notes in Physics ((LNP,volume 892))

Abstract

Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes can be seen as an illustration of features, concepts and subtleties that are present in most types of alternative theories, but they also provide a brief review of generalised scalar-tensor theories.

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Notes

  1. 1.

    However, one can infer certain properties of gravity indirectly. Matter couples to gravity and we understand and probe the structure and behaviour of particles and fields at scales much smaller than the micron, so if one is given a model that describes how gravity interacts with matter then one could in principle gain insight into some aspects of gravity through the behaviour of matter. Applying this logic to the quantum aspects of gravity has given rise to what is called Quantum Gravity Phenomenology [1, 2]. The fact that the gravitational coupling is very weak poses a particular challenge in such an approach, but smoking gun signals can still exist in certain models.

  2. 2.

    Erich Kretschmann argued in 1917 that any theory can be put in a generally covariant form, which led to a famous debate with Einstein. A covariant version of Newtonian gravity can be found in [10].

  3. 3.

    If there is a potential ϕ = ϕ 0 solutions are only admissible if U ′(ϕ 0) = 0 as well.

  4. 4.

    The numbering of the terms in the Lagrangian, L 2 to L 5, is also a remnant of the original flat space Galileons [27]. The index indicates there the number of copies of the field in each term. In the Generalised Galileons the L i term contains i − 2 second derivatives of the scalar.

  5. 5.

    The Einstein–Hilbert action also contains second derivatives of the metric and is degenerate, thus avoiding Ostrogradski’s instability.

  6. 6.

    Hořava gravity exhibits instantaneous propagation even at low energies [50], and on general grounds one would expect the UV completion of any Lorentz violating theory to generically introduce higher order dispersion relations.

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Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant Agreement n. 306425 “Challenging General Relativity”.

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Authors and Affiliations

  1. School of Mathematical Sciences & School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Thomas P. Sotiriou

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  1. Thomas P. Sotiriou
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Correspondence to Thomas P. Sotiriou .

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Editors and Affiliations

  1. Department of Physics, National Technical University of Athens, Athens, Greece

    Eleftherios Papantonopoulos

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Sotiriou, T.P. (2015). Gravity and Scalar Fields. In: Papantonopoulos, E. (eds) Modifications of Einstein's Theory of Gravity at Large Distances. Lecture Notes in Physics, vol 892. Springer, Cham. https://doi.org/10.1007/978-3-319-10070-8_1

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