This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

/pdf/the-electronic-properties-of-graphene-2siyzsnf5w.pdf

The electronic properties of graphene

Modified Gravity and Cosmology

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

f(R) theories

We compute the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models We obtain explicit expressions in the slow roll limit where the answer is given terms of the two usual slow roll parameters In a particular limit the three point functions are determined completely by the tilt of the spectrum of the two point functions We also make some remarks on the relation of this computation to dS/CFT and AdS/CFT We emphasize that (A)dS/CFT can be viewed as a statement about the wavefunction of the universe

https://iopscience.iop.org/article/10.1088/1126-6708/2003/05/013/pdf

Non-Gaussian features of primordial fluctuations in single field inflationary models

https://www.physics.rutgers.edu/grad/690/Padmanabhan-2003.pdf

Cosmological constant—the weight of the vacuum

This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.

Quantum Fields in Curved Space

AMONG the exact solutions to Einstein's field equations of general relativity are those describing black holes which rotate and/or carry electric charge. These solutions are novel in that they may be analytically continued through the black hole interior in a time-like direction into a succession of asymptotically flat spacetime regions that are inaccessible in the spacetime region in which the black hole first formed. There has been speculation about whether matter could travel through such black holes into these ‘other universes’. As real black holes will never be precisely non-rotating and electrically neutral, it is of interest to determine whether such a transfer of matter from one universe to another is possible. If it were, it might imply the possibility of matter appearing explosively in our region of spacetime through white holes. The exact solutions of interest are suspect because they are idealised. For example, they exclude the effects of matter surrounding the hole, and quantum processes. It has been suggested1,2 that the interior of the idealised black hole might be smashed in a more realistic model by unbounded blue shift effects associated with classical matter falling along the so-called inner horizon. In this way the space bridge would be destroyed by back reaction of the gravitational field due to the energetic matter. Here we demonstrate that quantum vacuum effects, similar in origin to the attraction energy between two electrically neutral conducting plates (Casimir effect), also cause an unbounded back-reaction which would smash the idealised interior geometry, even if no actual matter were falling into the hole. We do not speculate whether other analytically extendible spactimes exist which these quantum processes leave topologically unmodified, but demonstrate that the models which have been explicitly advanced to date cannot be taken seriously as space bridges.

N. D. Birrell

Papers

Quantum Fields in Curved Space

Quantum Fields in Curved Space

On falling through a black hole into another universe