Physics & Meteorology

Particle creation in spacetimes with a warped extra dimension is studied. In particular, we investigate the dynamics of a conformally coupled, massless scalar field in a five dimensional warped geometry where the induced metric on the 3-branes is that of a spatially flat cosmological model. We look at situations where the scale of the extra dimension is assumed (i) to be time independent or (ii) to have specific functional forms for time dependence. The warp factor is chosen to be that of the Randall-Sundrum model. With particular choices for the functional form of the scale factor (and also the function characterising the time evolution of the extra dimension) we obtain the |β k | 2 , the particle number and energy densities after solving (wherever possible, analytically but, otherwise, numerically) the conformal scalar field equations. The behaviour of these quantities for the massless and massive Kaluza-Klein modes are examined. Our results show the effect of a warped extra dimension on particle creation and illustrate how the nature of particle production on the brane depends on the nature of warping, type of cosmological evolution as well as the temporal evolution of the extra dimension.

This work focuses on an unexplored aspect of non-symmetric geometry where only the off-diagonal metric components along the extra dimension, in a 5-dimensional spacetime, are non-symmetric. We show that the energy densities of the stationary non-symmetric models are similar to that of brane models thereby mimicking the thick-brane scenario. We find that the massive test particles are confined near the location of the brane for both growing and decaying warp factors. This feature is unique to the non-symmetric nature of our model. We have also studied the dynamical models where standard 4D FLRW brane is embedded. Our analysis shows that the non-symmetric terms deconfine energy density at the early universe while automatically confine at late times.

Quantum systems described by linear, higher order spatial derivatives of the field exhibit a new kind of phase transition as the coupling strength of the higher order terms varies. This essentially happens because a fundamental change in the ratio of ground state energy eigenvalues, between linear and non-linear regime, takes place which leads to excitation of higher modes. The new phase has inverse relation with area.

We explore the possibilities of constructing bulk spacetimes in five dimensions for warped braneworld models with a spatially flat Friedmann-Robertson-Walker (FRW) line element on the 3-brane and with a time-dependent extra dimension. Our first step in this direction involves looking at the status of energy conditions when such a bulk line element is assumed. We check these conditions by analysing the relevant inequalities, for specific functional forms (chosen to satisfy certain desirable features) of the warp factor, the cosmological scale factor and the extra-dimensional scale factor. Subsequently, we aim at obtaining solutions with different types of bulk matter sources. We begin with a general analysis of the solution space of non-singular Randall-Sundrum type bulk models with an exponential warp factor and a chosen equation of state. Thereafter, we focus on three specific bulk sources-the ordinary scalar field, the Brans-Dicke scalar and the dilaton. In each case, we are able to solve the field equations and obtain desirable solutions for which, we once again check the viability of the energy conditions. We also show how one can place branes in the bulk using the junction conditions. The issue of resolution of the bulk singularities which appear in our solutions, using standard methods, is also presented briefly. In summary, we are able to demonstrate, that it is indeed possible to construct viable bulk spacetimes for warped cosmological braneworlds with a time-varying extra dimension and with bulk matter satisfying the energy conditions.

In this article, we explore the kinematics of timelike geodesic congruences in warped five dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall-Sundrum AdS (Anti de Sitter) geometry without and with branes we find analytical expressions for the expansion scalar and comment on the effects of including thin branes on its evolution. Later, we move on to congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using analytical expressions for the velocity field, we interpret the expansion, shear and rotation (ESR) along the flows, as functions of the extra dimensional coordinate. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer's point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in backgrounds with a thick brane are solved numerically in order to figure out the role of initial conditions (prescribed on the ESR) and spacetime curvature on the evolution of the ESR.

We investigate test particle trajectories in warped spacetimes with a thick brane warp factor, a cosmological on-brane line element and a time dependent extra dimension. The geodesic equations are reduced to a first order autonomous dynamical system. Using analytical methods, we arrive at some useful general conclusions regarding possible trajectories. Oscillatory motion, suggesting confinement about the location of the thick brane, arises for a growing warp factor. On the other hand, we find runaway trajectories (exponential-like) for a decaying warp factor. Variations of the extra dimensional scale factor yield certain quantitative differences. Results obtained from explicit numerical evaluations match well with the qualitative conclusions obtained from the dynamical systems analysis.

Over the last three decades entanglement entropy has been obtained for quantum fields propagating in Genus-0 topologies (spheres). For scalar fields propagating in these topologies, it has been shown that the entanglement entropy scales as area. In the last few years nontrivial topologies are increasingly relevant for different areas. For instance, in describing quantum phases, it has been realized that long-range entangled states are described by topological order. If quantum entanglement can plausibly provide explanation for these, it is then imperative to obtain entanglement entropy in these topologies. In this work, using two different methods, we explicitly show that the entanglement entropy scales as area of the Genus-1 geometry.

We show that the variation of the ground state entanglement in linear, higher spatial derivatives field theories at zero-temperature have signatures of phase transition. Around the critical point, when the dispersion relation changes from linear to non-linear, there is a fundamental change in the reduced density matrix leading to a change in the scaling of entanglement entropy. We suggest possible explanations involving both kinematical and dynamical effects. We discuss the implication of our work for 2-D condensed matter systems, black-hole entropy and models of quantum gravity.