Confronting the trans-Planckian question of inflationary cosmology with dissipative effects

We provide a class of QFTs which exhibit dissipation above a threshold energy, thereby breaking Lorentz invariance. Unitarity is preserved by coupling the fields to additional degrees of freedom (heavy fields) which introduce the rest frame. Using the Equivalence Principle, we define these theories in arbitrary curved spacetime. We then confront the trans-Planckian question of inflationary cosmology. When dissipation increases with the energy, the quantum field describing adiabatic perturbations is completely damped at the onset of inflation. However it still exists as a composite operator made with the additional fields. And when these are in their ground state, the standard power spectrum obtains if the threshold energy is much larger that the Hubble parameter. In fact, as the energy redshifts below the threshold, the composite operator behaves as if it were a free field endowed with standard vacuum fluctuations. The relationship between our models and the Brane World scenarios studied by Libanov and Rubakov displaying similar effects is discussed. The signatures of dissipation will be studied in a forthcoming paper.Comment: 30 pages, 1 Figure, to appear in CQ

A two-mass expanding exact space-time solution

In order to understand how locally static configurations around gravitationally bound bodies can be embedded in an expanding universe, we investigate the solutions of general relativity describing a space-time whose spatial sections have the topology of a 3-sphere with two identical masses at the poles. We show that Israel junction conditions imply that two spherically symmetric static regions around the masses cannot be glued together. If one is interested in an exterior solution, this prevents the geometry around the masses to be of the Schwarzschild type and leads to the introduction of a cosmological constant. The study of the extension of the Kottler space-time shows that there exists a non-static solution consisting of two static regions surrounding the masses that match a Kantowski-Sachs expanding region on the cosmological horizon. The comparison with a Swiss-Cheese construction is also discussed.Comment: 15 pages, 5 figures. Replaced to match the published versio

Coherent states for the hydrogen atom: discrete and continuous spectra

We construct the systems of generalised coherent states for the discrete and continuous spectra of the hydrogen atom. These systems are expressed in elementary functions and are invariant under the $SO(3, 2)$ (discrete spectrum) and $SO(4, 1)$ (continuous spectrum) subgroups of the dynamical symmetry group $SO(4, 2)$ of the hydrogen atom. Both systems of coherent states are particular cases of the kernel of integral operator which interwines irreducible representations of the $SO(4, 2)$ group.Comment: 15 pages, LATEX, minor sign corrections, to appear in J.Phys.

Null dust in canonical gravity

We present the Lagrangian and Hamiltonian framework which incorporates null dust as a source into canonical gravity. Null dust is a generalized Lagrangian system which is described by six Clebsch potentials of its four-velocity Pfaff form. The Dirac--ADM decomposition splits these into three canonical coordinates (the comoving coordinates of the dust) and their conjugate momenta (appropriate projections of four-velocity). Unlike ordinary dust of massive particles, null dust therefore has three rather than four degrees of freedom per space point. These are evolved by a Hamiltonian which is a linear combination of energy and momentum densities of the dust. The energy density is the norm of the momentum density with respect to the spatial metric. The coupling to geometry is achieved by adding these densities to the gravitational super-Hamiltonian and supermomentum. This leads to appropriate Hamiltonian and momentum constraints in the phase space of the system. The constraints can be rewritten in two alternative forms in which they generate a true Lie algebra. The Dirac constraint quantization of the system is formally accomplished by imposing the new constraints as quantum operator restrictions on state functionals. We compare the canonical schemes for null and ordinary dust and emhasize their differences.Comment: 25 pages, REVTEX, no figure

Desempenho reprodutivo de cabras Alpinas tratadas com hCG cinco dias após o acasalamento.

Objetivou-se com este estudo avaliar o efeito da administração de hCG sobre o desempenho reprodutivo de cabras Alpinas i durante a estação de acasalamento natural. Trinta e duas fêmeas nulíparas e 124lactantes, após a identificação de estro e acasalamento, foram aleatoriamente divididas, de acordo com a categoria, em dois tratamentos. Em TI (n=75) e T2 (n=81), os animais receberam I roL de solução salina ou 250 UI de hCG, respectivamente, por via intramuscular cinco dias após o acasalamento. A gestação foi verificada por ultra-sonografia transabdominal (probe de 3,5 MHz) nos dias 35 e 70 após o acasalamento, para detecção e confirmação da gestação, respectivamente. As taxas de gestação não diferiram entre TI (86,7%) e T2 (70,6%) para nulíparas e TI (78,3 %) e T2 (84,4 %) para lactantes. Não houve diferença entre a taxa de parição (75,0 e 75,7%), o periodo de gestação (150,47 e 150,80 dias) e a prolificidade (1,75 e 1,80 fetos) entre os animais do TI e T2, respectivamente. A prolificidade foi superior em cabras lactantes (I ,90) que em nulíparas (I ,41). A administração de hCG cinco dias após o acasalamento não elevou o desempenho reprodutivo em cabras da raça Alpina. Reproductive performance of Alpine goats treated with hCG five days after breeding. Abstract: The effect of hCG administration on reproductive performance of Alpine goats during the natural breeding season was evaluated. Thirty-two nulliparous and 124 lactating goats, after estrus identification and breeding, were randomly assigned according to the categories to two treatments. In T1 (n=75) and T2 (n=81) the animals received 1 mL of saline solution or 250 IU of hCG intramuscularly, respectively, five days after breeding. Pregnancy was detected and confirmed on days 35 and 70 after breeding by transabdominal ultrasonography (3.5 MHz probe), respectively. Pregnancy rate did not differ between T1 (86.7%) and T2 (70.6%) for nulliparous and T1 (78.3%) and T2 (84.4%) for lactating does. There were no differences for kidding rate (75.0 and 75.7%), gestation period (150.47 and 150.80 days) and prolificacy (1.75 and 1.80 fetuses) between T1 and T2, respectively. Prolificacy was superior in lactating (1.90) than in nulliparous (1.41) goats. The administration of hCG five days after breeding did not increase reproductive performance in Alpine goats

Lorentz breaking Effective Field Theory and observational tests

Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a broad range of constraints on departures from Lorentz invariance. We shall review here the effective field theory approach to Lorentz breaking in the matter sector, present the constraints provided by the available observations and finally discuss the implications of the persisting uncertainty on the composition of the ultra high energy cosmic rays for the constraints on the higher order, analogue gravity inspired, Lorentz violations.Comment: 47 pages, 4 figures. Lecture Notes for the IX SIGRAV School on "Analogue Gravity", Como (Italy), May 2011. V.3. Typo corrected, references adde

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol