Gravitational scalar–tensor theory

Abstract

We consider a new form of theories of gravity in which the action is written in terms of the Ricci scalar and its first and second derivatives. Despite the higher derivative nature of the action, the theory is free from ghost under an appropriate choice of the functional form of the Lagrangian. This model possesses 2 + 2 physical degrees of freedom, namely 2 scalar degrees and 2 tensor degrees. We exhaust all such theories with the Lagrangian of the form f (R, (∇R) 2 , ✷R), where R is the Ricci scalar, and then show some examples beyond this ansatz. In course of analysis, we prove the equivalence between these examples and generalized bi-Galileon theories.

Cosmological models in modified gravity theories with extended nonminimal derivative couplings

“…It would be interesting to examine whether there are any issues related to the fifth force, as it has been done previously on the original Horndeski theory [78,79]. Finally, it could be interesting to apply extended nonminimal derivative couplings to bi-scalar theories, such as those proposed recently in [80][81][82][83]. These investigations lie beyond the scope of the present work, and are left for future projects.…”

Observational constraints on f(T) gravity from varying fundamental constants

“…Thus, one can obtain f (R) gravity [5], Gauss-Bonnet a e-mail: nunes@ecm.ub.edu b e-mail: abonillar@udistrital.edu.com c e-mail: span@iiserkol.ac.in d e-mail: Emmanuel_Saridakis@baylor.edu and f (G) gravity [6,7], gravity with higher-order curvature invariants [8,9], massive gravity [10] etc. Nevertheless, one could start from the equivalent, torsional formulation of gravity, namely from the Teleparallel Equivalent of General Relativity (TEGR) [11][12][13], in which the gravitational Lagrangian is the torsion scalar T , and construct various modifications, such as f (T ) gravity [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] (see [30] for a review), teleparallel Gauss-Bonnet gravity [31,32], gravity with higher-order torsion invariants [33], etc.…”

Cosmology in new gravitational scalar-tensor theories

“…In this section we briefly review the construction of gravitational scalar-tensor theories following [37], starting from the modified gravitational action and resulting in the corresponding specific bi-scalar action. Then we derive the general equations of motion for both metric and scalar degrees of freedom, in a general background.…”

“…The starting point for the construction of new gravitational scalar-tensor theories is the idea to (re-)formulate generalized scalar-tensor theories only in terms of the metric and its derivatives, without the use of a scalar field [37]. Hence, one starts by extending the f (R) action to include derivatives of the Ricci scalar, namely…”

“…Indeed, in [37] the authors managed to construct a modified gravity using the Ricci scalar and its first and second derivatives, which under a specific Lagrangian choice is free of ghosts, possessing 2 + 2 degrees of freedom, namely 2 scalar degrees and 2 tensor ones. These constructions, named gravitational scalar-tensor theories, are equivalent with specific cases of generalized bi-Galileon theories, however whether there is a complete one-to-one correspondence between them is an open question.…”