Related papers: A Galileon Primer
We explore the possibility for generalized electromagnetism on flat spacetime. For a single copy of $U(1)$ gauge theory, we show that the Galileon-type generalization of electromagnetism is forbidden. Given that the equations of motion for…
The two-dimensional theory of gravity describing a graviton-dilaton system is considered. The graviton-dilaton coupling can be fixed such that the quantum theory remains free of the conformal anomaly for any conformal dimension of the…
A simple way to construct models with early cosmological Genesis epoch is to employ bosonic fields whose Lagrangians transform homogeneously under scaling transformation. We show that in these theories, for a range of parameters defining…
It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the so--called ``Palatini formalism'', i.e., treating the metric and the connection as…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
`Global' symmetries, such as the boost invariance of classical mechanics and special relativity, can give rise to direct empirical counterparts such as the Galileo-ship phenomenon. However, a widely accepted line of thought holds that…
This paper gives a summary of the author's works concerning the emergent general relativity in a particular class of tensor models, which possess Gaussian classical solutions. In general, a classical solution in a tensor model may be…
It has been pointed out that non-singular cosmological solutions in second-order scalar-tensor theories generically suffer from gradient instabilities. We extend this no-go result to second-order gravitational theories with an arbitrary…
All the classes of static massless scalar field models available currently in the Einstein theory of gravity necessarily contain a strong curvature naked singularity. We obtain here a family of solutions for static massless scalar fields…
Suppose a Lagrangian is constructed from its fields and their derivatives. When the field configuration is a distribution, it is unambiguously defined as the limit of a sequence of smooth fields. The Lagrangian may or may not be a…
We perform a detailed dynamical analysis of generalized Galileon cosmology, incorporating also the requirements of ghost and instabilities absence. We find that there are not any new stable late-time solutions apart from those of standard…
In the framework of Galilei classical mechanics (i.e., general relativistic classical mechanics on a spacetime with absolute time) developed by Jadczyk and Modugno, we analyse systematically the relations between symmetries of the geometric…
These notes grew out of a lecture course on mathematical methods of classical physics for students of mathematics and mathematical physics at the master's level. Also, physicists with a strong interest in mathematics may find this text…
Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial…
We study whether it is possible to design a "classical" spatially flat bouncing cosmology or a static, spherically symmetric asymptotically flat Lorentzian wormhole in cubic Galileon theories interacting with an extra scalar field. We show…
We introduce a version of the Hamiltonian formalism based on the Clairaut equation theory, which allows us a self-consistent description of systems with degenerate (or singular) Lagrangian. A generalization of the Legendre transform to the…
It is shown that any singular Lagrangian theory: 1) can be formulated without the use of constraints by introducing a Clairaut-type version of the Hamiltonian formalism; 2) leads to a special kind of nonabelian gauge theory which is similar…
Galileon fields arise naturally from the decoupling limit of massive gravities, and possess special self-interactions which are protected by a spacetime generalization of Galilean symmetry. We briefly revisit the inflationary phenomenology…
We study steady-state spherically symmetric accretion of a galileon field onto a Schwarzschild black hole in the test fluid approximation. The galileon is assumed to undergo a stage of cosmological evolution, thus setting a non-trivial…
The evidence of the acceleration of universe at present time has lead to investigate modified theories of gravity and alternative theories of gravity, which are able to explain acceleration from a theoretical viewpoint without the need of…