Higher-order gravity theories and scalar?tensor theories

By E. Flanagan. 2003

203 citations recorded by the source corpus.

We generalize the known equivalence between higher-order gravity theories and scalar–tensor theories to a new class of theories. Specifically, in the context of a first-order or Palatini variational principle where the metric and connection are treated as independent variables, we consider theories for which the Lagrangian density is a function f of (i) the Ricci scalar computed from the metric, and (ii) a second Ricci scalar computed from the connection. We show that such theories can be written as tensor–multi-scalar theories with two scalar fields with the following features: (i) the two-dimensional σ-model metric that defines the kinetic energy terms for the scalar fields has constant, negative curvature; (ii) the coupling function determining the coupling to matter of the scalar fields is universal, independent of the choice of function f; and (iii) if both mass eigenstates are long range, then the Eddington post-Newtonian parameter γ has value 1/2. Therefore, in order to be compatible with solar system experiments at least one of the mass eigenstates must be short range.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/22129a467cfc8a7f4cf5c6b316d1e9ccc1206566

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Citations in the corpus

f(R) Theories Of Gravity (2008, methodology): “…this frame is equivalent to the Jordan frame and both are perfectly suitable for 26 Note that in the case of (Flanagan, 2004b) in which fermions are used as the matter fields, one could decide to couple the indepen- performing calculations (Flanagan, 2004a) [see also the relevant discussion in Sec.”
The Conformal frame freedom in theories of gravitation (2004, background): “Our papers [9, 11] implicitly adopted this point of view, and this definition of “physically equivalent.”
Hybrid Metric-Palatini Gravity (2015, unknown): “The generalized hybrid Ricci scalar theories were introduced in [74,75] and found to have qualitatively different properties compared to the more restricted class of f(X) models described above.”
f(R) Theories (2010, methodology): “While the above analysis is based on the calculation in the Jordan frame in which test particles follow geodesics [55], the same result was also obtained by the analysis in the Einstein frame [261, 262, 260, 318].”