Narrow Results

We study whether the approach of Deffayet et al. (DPSV) can be adopted for obtaining a derivative part of quadratic action for scalar perturbations in beyond Horndeski theories about homogeneous and isotropic backgrounds. We find that even though the method does remove the second and higher derivatives of metric perturbations from the linearized Galileon equation, in the same manner as in the general Horndeski theory, it gives incorrect result for the quadratic action. We analyze the reasons behind this property and suggest the way of modifying the approach, so that it gives valid results.

We consider scalar field theories invariant under extended shift symmetries consisting of higher order polynomials in the spacetime coordinates. These generalize ordinary shift symmetries and the linear shift symmetries of the galileons. We find Wess–Zumino Lagrangians which transform up to total derivatives under these symmetries, and which possess fewer derivatives per field and lower order equations of motion than the strictly invariant terms. In the nonrelativistic context, where the extended shifts are purely spatial, these theories may describe multi-critical Goldstone bosons. In the relativistic case, where the shifts involve the full spacetime coordinate, these theories generally propagate extra ghostly degrees of freedom.

We show how the flat spacetime Galileon field theories (FSGFT) in arbitrary dimensions can be obtained through a Born–Infeld (BI) type structure. This construction involves a brane metric and nonlinear combinations of derivatives of a scalar field. Our setup gives rise to some Galileon tensors and vectors useful for the variational analysis which are related to the momentum density of the probe Lovelock branes floating in a N-dimensional flat bulk. We find further that the Noether currents associated to these Galileon theories may be written in terms of such tensors.

We modify the Galileon theory minimally coupled to general relativity by breaking the Lorentz invariance of the theory. To break the Lorentz invariance, we use the Lagrange multiplier method. The new term in the action implies that the gradient of the Galileon field is time-like, with unit norm. The theory can also be considered as an extension of the mimetic dark matter theory, by adding some derivative self interactions to the action, which keeps the equation of motion at most second order in time derivatives. Also the theory is similar to scalar Einstein-aether theory with healthy scalar aether self interactions. For pressure-less baryonic matter, we show that the universe experiences a decelerated expanding phase followed by a late time acceleration. The cosmological implications of a special coupling between the scalar field and the trace of the energy-momentum tensor are also explored.

The cosmology has made enormous progress after the construction of General Relativity (GR) in 1915. The theoretical predictions of GR — such as the existence of black holes and gravitational waves — have been directly/indirectly confirmed by observations. Now, we know that GR is sufficiently dependable to describe the gravitational law in the solar system.