Dragoljub D. Dimitrijevic

About non standard Lagrangians in cosmology

A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.

Tachyon inflation in an AdS braneworld with backreaction

We analyze the inflationary scenario based on the tachyon field coupled with the radion of the second Randall–Sundrum model (RSII). The tachyon Lagrangian is derived from the dynamics of a 3-brane moving in the five-dimensional bulk. The AdS5 geometry of the bulk is extended to include the radion. Using the Hamiltonian formalism we find four nonlinear field equations supplemented by the modified Friedmann equations of the RSII braneworld cosmology. After a suitable rescaling we reduce the parameters of our model to only one free parameter related to the brane tension and the AdS5 curvature. We solve the equations numerically assuming a reasonably wide range of initial conditions determined by physical considerations. Varying the free parameter and initial conditions we confront our results with the Planck 2015 data.

Quantum cosmology and tachyons

We discuss the relevance of the classical and quantum rolling tachyons inflation in the frame of the standard, p-adic and adelic minisuperspace quantum cosmology. The field theory of tachyon matter proposed by Sen in a zero-dimensional version suggested by Kar leads to a model of a particle moving in a constant external field with quadratic damping. We calculate the exact quantum propagator of the model, as well as, the vacuum states and conditions necessary to construct an adelic generalization.

On classical and quantum dynamics of tachyon-like fields and their cosmological implications

We consider a class of tachyon-like potentials, motivated by string theory, D-brane dynamics and inflation theory in the context of classical and quantum mechanics. A formalism for describing dynamics of tachyon fields in spatially homogenous and one-dimensional - classical and quantum mechanical limit is proposed. A few models with concrete potentials are considered. Additionally, possibilities for p-adic and adelic generalization of these models are discussed. Classical actions and corresponding quantum propagators, in the Feynman path integral approach, are calculated in a form invariant on a change of the background number fields, i.e. on both archimedean and nonarchimedean spaces. Looking for a quantum origin of inflation, relevance of p-adic and adelic generalizations are briefly discussed.