We derive the effective four-dimensional gravity action in the RandallSundrum scenario in which two 3-branes of opposite tension reside in a fivedimensional spacetime. The dimensional reduction with the Ansatz for the radion field by Charmousis et al., which solves five-dimensional linearized field equations, results in a class of scalar-tensor gravity theories. In the limit of vanishing radion...

Using the influence functional formalism we show how to derive a generalized Einstein equation in the form of a Langevin equation for the description of the backreaction of quantum fields and their fluctuations on the dynamics of curved spacetimes. We show how a functional expansion on the influence functional gives the cumulants of the stochastic source, and how these cumulants enter in the eq...

Using s-wave and large N approximation the one-loop effective action for 2d dilaton coupled scalars and spinors which are obtained by spherical reduction of 4d minimal matter is found. Quantum effective equations for reduced Einstein gravity are written. Their analytical solutions corresponding to 4d Kantowski-Sachs (KS) Universe are presented. For quantum-corrected Einstein gravity we get non-...

where Lm is the matter part Lagrangian. The gravitational field equation is presented in Eq. (2) of [1]. In contrast with the situation with generalized f(φ,R) gravity in Eq. (27), the gravity with Ricci-curvature square term in the action does not have the conformal symmetry to Einstein gravity [2]. In [1] we analysed the gravitational wave and derived a fourth order differential equation. How...

We study spherically symmetric solutions in f(R) theories and its compatibility with local tests of gravity. We start by clarifying the range of validity of the weak field expansion and show that for many models proposed to address the Dark Energy problem this expansion breaks down in realistic situations. This invalidates the conclusions of several papers that make inappropriate use of this ex...

The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting spacelike Killing vector fields, may be written as the equations of the SL(2, R) principal chiral model with certain ‘source’ terms. Using this formulation, we give a procedure for generating an infinite number of non-local constants of motion for this sector of the Einstein equations. The constants of motion arise as exp...

The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting spacelike Killing vector fields, may be written as the equations of the SL(2, R) principal chiral model with certain ‘source’ terms. Using this formulation, we give a procedure for generating an infinite number of non-local constants of motion for this sector of the Einstein equations. The constants of motion arise as exp...

The finiteness requirement for Euclidean Einstein gravity is shown to be so stringent that only the flat metric is allowed. We examine counterterms in 4D and 6D Ricci-flat manifolds from general invari-ance arguments.

This paper reviews the theory, phenomenology, and observational constraints on the coupling parameters of Einstein-aether gravity, i.e. General Relativity coupled to a dynamical unit timelike vector field. Several new remarks and a discussion of open issues are included.

It is proved that classical BRS-invariance of the Lagrangian implies perturbative gauge invariance for tree diagrams to all orders. The proof applies in particular to the Einstein Hilbert Largrangian of gravity.