Hamiltonian of galileon field theory

We give a detailed calculation for the Hamiltonian of single galileon field theory, keeping track of all the surface terms. We calculate the energy of static, spherically symmetric configuration of the single galileon field at cubic order coupled to a point-source and show that the 2-branches of the solution possess energy of equal magnitude and opposite sign, the sign of which is determined by the coefficient of the kinetic term $\alpha_2$. Moreover the energy is regularized in the short distance (ultra-violet) regime by the dominant cubic term even though the source is divergent at the origin. We argue that the origin of the negativity is due to the ghost-like modes in the corresponding branch in the presence of the point source. This seems to be a non-linear manifestation of the ghost instability.Comment: 13 pages, 1 figur

On p-form theories with gauge invariant second order field equations

We explore field theories of a single p-form with equations of motions of order strictly equal to two and gauge invariance. We give a general method for the classification of such theories which are extensions to the p-forms of the Galileon models for scalars. Our classification scheme allows to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a non trivial Galileon like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no non trivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd p cases.Comment: 29 page

On extended symmetries for the Galileon

We investigate a large class of infinitesimal, but fully nonlinear in the field, transformations of the Galileon and search for extended symmetries. The transformations involve powers of the coordinates $x$ and the field $\pi$ up to any finite order $N$. Up to quadratic order the structure of these symmetry transformations is the unique generalisation of both the infinitesimal version of the standard Galileon shift symmetry as well as a recently discovered infinitesimal extension of this symmetry. The only higher-order extensions of this symmetry we recover are (`Galileon dual' versions of) symmetries of the standard kinetic term.Comment: Latex, 5 pages, conclusions change

Aspects of galileons and generalised scalar-tensor theories

This thesis is devoted to the study of modified gravity theories, especially, the scalar-tensor theories. A theorem due to Weinberg which states, that the equivalence principle is a necessary consequence of Lorentz invariance in a gravitational theory described by spin-2 massless particles is presented in Chapter 2. In view of this theorem modified gravity models either attempt to make \textit{graviton} massive or add other spin degrees of freedom. Scalar tensor theories are a simple and natural choice. An overview of some important scalar-tensor theories such as, Brans-Dicke model, DGP theory (although not a scalar-tensor theory it reduces to one in the so called \textit{decoupling} limit as we would see in chapter 2), Galileon model, Horndeski theory is also given in Chapter 2. The Hamiltonian analysis of the Galileon model is presented in Chapter 3. Chapter 4 presents the boundary terms and junction conditions of the Horndeski theory in the presence of codimension-1 branes. A generalised multiple-scalar-tensor theory analogous to Horndeski theory is developed in Chapter 5. We conclude with the proof of the most general multiple scalar field theory in arbitrary dimensions and flat-space time in Chapter 6. Chapters 3,4,5,6 are original work where the first 3 are based on the following journal articles

Aspects of galileons and generalised scalar-tensor theories

This thesis is devoted to the study of modified gravity theories, especially, the scalar-tensor theories. A theorem due to Weinberg which states, that the equivalence principle is a necessary consequence of Lorentz invariance in a gravitational theory described by spin-2 massless particles is presented in Chapter 2. In view of this theorem modified gravity models either attempt to make \textit{graviton} massive or add other spin degrees of freedom. Scalar tensor theories are a simple and natural choice. An overview of some important scalar-tensor theories such as, Brans-Dicke model, DGP theory (although not a scalar-tensor theory it reduces to one in the so called \textit{decoupling} limit as we would see in chapter 2), Galileon model, Horndeski theory is also given in Chapter 2. The Hamiltonian analysis of the Galileon model is presented in Chapter 3. Chapter 4 presents the boundary terms and junction conditions of the Horndeski theory in the presence of codimension-1 branes. A generalised multiple-scalar-tensor theory analogous to Horndeski theory is developed in Chapter 5. We conclude with the proof of the most general multiple scalar field theory in arbitrary dimensions and flat-space time in Chapter 6. Chapters 3,4,5,6 are original work where the first 3 are based on the following journal articles

Classifying Galileon pp-form theories

We provide a complete classification of all abelian gauge invariant $p$-form theories with equations of motion depending only on the second derivative of the field---the $p$-form analogues of the Galileon scalar field theory. We construct explicitly the nontrivial actions that exist for spacetime dimension $D\leq11$, but our methods are general enough and can be extended to arbitrary $D$. We uncover in particular a new $4$-form Galileon cubic theory in $D\geq8$ dimensions. As a by-product we give a simple proof of the fact that the equations of motion depend on the $p$-form gauge fields only through their field strengths, and show this explicitly for the recently discovered $3$-form Galileon quartic theory.Comment: 17 pages; v2: references adde

Boundary Terms and Junction Conditions for Generalized Scalar-Tensor Theories

We compute the boundary terms and junction conditions for Horndeski's panoptic class of scalar-tensor theories, and write the bulk and boundary equations of motion in explicitly second order form. We consider a number of special subclasses, including galileon theories, and present the corresponding formulae. Our analysis opens up of the possibility of studying tunnelling between vacua in generalized scalar-tensor theories, and braneworld dynamics. The latter follows because our results are independent of spacetime dimension.Comment: 13 pages, Equation corrected. Thanks to Tsutomu Kobayashi for informing us of the typ