f(R) brane cosmology

Despite the nice features of the Dvali, Gabadadze and Porrati (DGP) model to explain the late-time acceleration of the universe, it suffers from some theoretical problems like the ghost issue. We present a way to self-accelerate the normal DGP branch, which is known to be free of the ghost problem, by means of an f(R) term on the brane action. We obtain the de Sitter self-accelerating solutions of the model and study their stability under homogeneous perturbations.Comment: 4 pages, 2 figures. Contribution to the proceedings of Spanish Relativity Meeting 2009, Bilbao, Spain, 7-11 September 200

QCD uncertainties at the LHC and the implications of HERA

Strong interaction physics will be ubiquitous at the Large Hadron Collider since the colliding beams consist of confined quarks and gluons. Although the main purpose of the LHC is to study the mechanism of electroweak symmetry breaking and to search for physics beyond the Standard Model, to maximise the precision and sensitivity of such anaylses it is necessary to understand in detail various perturbative, semi-perturbative and non-perturbative QCD effects. Many of these effects have been extensively studied at HERA and will be studied further at HERA II. We discuss the impact of the knowledge thus gained on physics at the LHC.Comment: Contributed to the Proceedings of DIS04, Strbske Pleso, Slovaki

On the generalised Chaplygin gas: worse than a big rip or quieter than a sudden singularity?

Although it has been believed that the models with generalised Chaplygin gas do not contain singularities, in a previous work we have studied how a big freeze could take place in some kinds of phantom generalised Chaplygin gas. In the present work, we study some types of generalised Chaplygin gas in order to show how different sorts of singularities could appears in such models, in the future or in the past. We point out that: (i) singularities may not be originated from the phantom nature of the fluid, and (ii) if initially the tension of the brane in a brane-world Chaplygin model is large enough then an infrared cut off appears in the past.Comment: 19 pages, 6 figures. Discussion expanded and references added. Version to appear in the International Journal of Modern Physics

Crossing the cosmological constant line in a dilatonic brane-world model with and without curvature corrections

We construct a new brane-world model composed of a bulk -with a dilatonic field-, plus a brane -with brane tension coupled to the dilaton-, cold dark matter and an induced gravity term. It is possible to show that depending on the nature of the coupling between the brane tension and the dilaton this model can describe the late-time acceleration of the brane expansion (for the normal branch) as it moves within the bulk. The acceleration is produced together with a mimicry of the crossing of the cosmological constant line (w=-1) on the brane, although this crossing of the phantom divide is obtained without invoking any phantom matter neither on the brane nor in the bulk. The role of dark energy is played by the brane tension, which reaches a maximum positive value along the cosmological expansion of the brane. It is precisely at that maximum that the crossing of the phantom divide takes place. We also show that these results remain valid when the induced gravity term on the brane is switched off.Comment: 12 pages, 2 figures, RevTeX

Resonant structure of space-time of early universe

A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes of wave function, penetrability $T_{\rm bar}$ and reflection $R_{\rm bar}$ relatively the barrier (accuracy of the method: $|T_{\rm bar}+R_{\rm bar}-1| < 1 \cdot 10^{-15}$), coefficient of penetration (i.e. probability of the packet to penetrate from the internal well outside with its tunneling), coefficient of oscillations (describing oscillating behavior of the packet inside the internal well). Using the method, evolution of universe in the closed Friedmann--Robertson--Walker model with quantization in presence of positive cosmological constant, radiation and component of generalize Chaplygin gas is studied. It is established (for the first time): (1) oscillating dependence of the penetrability on localization of start of the packet; (2) presence of resonant values of energy of radiation $E_{\rm rad}$, at which the coefficient of penetration increases strongly. From analysis of these results it follows: (1) necessity to introduce initial condition into both non-stationary, and stationary quantum models; (2) presence of some definite values for the scale factor $a$, where start of expansion of universe is the most probable; (3) during expansion of universe in the initial stage its radius is changed not continuously, but passes consequently through definite discrete values and tends to continuous spectrum in latter time.Comment: 18 pages, 14 figures, 4 table

Tensorial perturbations in the bulk of inflating brane worlds

In this paper we consider the stability of some inflating brane-world models in quantum cosmology. It is shown that whereas the singular model based on the construction of inflating branes from Euclidean five-dimensional anti-de Sitter space is unstable to tensorial cosmological perturbations in the bulk, the nonsingular model which uses a five-dimensional asymptotically anti-de Sitter wormhole to construct the inflating branes is stable to these perturbations.Comment: 4 pages, RevTex, to appear in Phys. Rev.

Classical and semi-classical energy conditions

The standard energy conditions of classical general relativity are (mostly) linear in the stress-energy tensor, and have clear physical interpretations in terms of geodesic focussing, but suffer the significant drawback that they are often violated by semi-classical quantum effects. In contrast, it is possible to develop non-standard energy conditions that are intrinsically non-linear in the stress-energy tensor, and which exhibit much better well-controlled behaviour when semi-classical quantum effects are introduced, at the cost of a less direct applicability to geodesic focussing. In this article we will first review the standard energy conditions and their various limitations. (Including the connection to the Hawking--Ellis type I, II, III, and IV classification of stress-energy tensors). We shall then turn to the averaged, nonlinear, and semi-classical energy conditions, and see how much can be done once semi-classical quantum effects are included.Comment: V1: 25 pages. Draft chapter, on which the related chapter of the book "Wormholes, Warp Drives and Energy Conditions" (to be published by Springer), will be based. V2: typos fixed. V3: small typo fixe

FRW Quantum Cosmology with a Generalized Chaplygin Gas

Cosmologies with a Chaplygin gas have recently been explored with the objective of explaining the transition from a dust dominated epoch towards an accelerating expansion stage. We consider the hypothesis that the transition to the accelerated period involves a quantum mechanical process. Three physically admissible cases are possible. In particular, we identify a minisuperspace configuration with two Lorentzian sectors, separated by a classically forbidden region. The Hartle-Hawking and Vilenkin wave functions are computed, together with the transition amplitudes towards the accelerating epoch. Furthermore, it is found that for specific initial conditions, the parameters characterizing the generalized Chaplygin gas become related through an expression involving an integer $n$. We also introduce a phenomenological association between some brane-world scenarios and a FRW minisuperspace cosmology with a generalized Chaplygin gas. The aim is to promote a discussion and subsequent research on the quantum creation of brane cosmologies from such a perspective. Results suggest that the brane tension would become related with generalized Chaplygin gas parameters through another expression involving an integer.Comment: 13 pages, 3 figures, RevTeX

Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism

We obtain the band edge eigenfunctions and the eigenvalues of solvable periodic potentials using the quantum Hamilton - Jacobi formalism. The potentials studied here are the Lam{\'e} and the associated Lam{\'e} which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function $p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $p^{2} -i \hbar \frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential use is made of suitable conformal transformations, which leads to the eigenvalues and the eigenfunctions corresponding to the band edges in a simple and straightforward manner. Our study reveals interesting features about the singularity structure of $p$, responsible in yielding the band edge eigenfunctions and eigenvalues.Comment: 21 pages, 5 table