Hugo A. Morales-Técotl

Quantum gravity corrections to neutrino propagation

Massive spin-1/2 fields are studied in the framework of loop quantum gravity by considering a state approximating, at a length scale L much greater than Planck length l(P), a spin-1/2 field in flat spacetime. The discrete structure of spacetime at l(P) yields corrections to the field propagation at scale L. Neutrino bursts ( &pmacr; approximately 10(5) GeV) accompanying gamma ray bursts that have traveled cosmological distances L are considered. The dominant correction is helicity independent and leads to a time delay of order (&pmacr;l(P))L/c approximately 10(4) s. To next order in &pmacr;l(P), the correction has the form of the Gambini and Pullin effect for photons. A dependence L(-1)(os) approximately &pmacr;(2)l(P) is found for a two-flavor neutrino oscillation length.

Cosmological applications of loop quantum gravity

An introductory review of the Randall-Sundrum type II braneworld scenario is presented, with emphasis on the relationship between the density and gravitational wave perturbations that are generated during inflation. The implications of relaxing the reflection symmetry in the fifth dimension are considered. The effects of including a Gauss-Bonnet combination of higher-order curvature invariants in the bulk action are briefly discussed.The origin of the matter-antimatter asymmetry of the universe remains one of the outstanding questions yet to be answered by modern cosmology and also one of only a handful of problems where the need of a larger number of degrees of freedom than those contained in the standard model (SM) is better illustrated. An appealing scenario for the generation of baryon number is the electroweak phase transition that took place when the temperature of the universe was about 100 GeV. Though in the minimal version of the SM, and without considering the interaction of the SM particles with additional degrees of freedom, this scenario has been ruled out given the current bounds for the Higgs mass, this still remains an open possibility in supersymmetric extensions of the SM. In recent years it has also been realized that large scale magnetic fields could be of primordial origin. A natural question is what effect, if any, these fields could have played during the electroweak phase transition in connection to the generation of baryon number. Prior to the electroweak symmetry breaking, the magnetic modes able to propagate for large distances belonged to the U(1) group of hypercharge and hence receive the name of hypermagnetic fields. In this contribution, we summarize recent work aimed to explore the effects that these fields could have introduced during a first order electroweak phase transition. In particular, we show how these fields induce a CP asymmetric scattering of fermions off the true vacuum bubbles nucleated during the phase transition. The segregated axial charge acts as a seed for the generation of baryon number. We conclude by mentioning possible research venues to further explore the effects of large scale magnetic fields for the generation of the baryon asymmetry.The measured luminosity distances of Type Ia supernovae (SNe Ia) as a function of redshift have shown that the expansion of the Universe is currently accelerating, probably due to the presence of repulsive dark energy such as Einsteins cosmological constant (Lambda). From about 200 SNe Ia, we find that H_0t_0 = 0.96 +/ 0.04, and Omega_Lambda - 1.4 Omega_M = 0.35 +/- 0.14. Combining our data with the results of large-scale structure surveys, we find a best fit for Omega_M and Omega_Lambda of 0.28 and 0.72, respectively -- essentially identical to the recent WMAP results (and having comparable precision). The sum of the densities, ~1.0, agrees with extensive measurements of the cosmic microwave background radiation, including WMAP, and coincides with the value predicted by most inflationary models for the early Universe. A number of possible systematic effects (dust, SN evolution) thus far do not seem to eliminate the need for Omega_Lambda > 0. Recently, analyses of SNe Ia at z = 1.0-1.7 provide further support for current acceleration, and give tentative evidence for an early epoch of deceleration. The dynamical age of the Universe is 13.1 +/- 1.5 Gyr, consistent with the ages of globular star clusters and with the WMAP result of 13.7 +/- 0.2 Gyr. Current projects include the search for additional SNe Ia at z > 1 to confirm the early deceleration, and the measurement of a few hundred SNe Ia at z = 0.2-0.8 to determine the equation of state of the dark energy, w = P/(rho c^2).After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of modified dispersion relations for quantum gravity phenomenology. The presentation is held at a level which does not require much background knowledge in general relativity or mathematical techniques such as functional analysis, so as to make the article accessible to graduate students and researchers from other fields.Space is not a boring static stage on which events unfold over time, but a dynamic entity with curvature, fluctuations, and a rich life of its own. Spectacular measurements of the cosmic microwave background, gravitational lensing, type Ia supernovae, large-scale structure, spectra of the Lyman alpha forest, stellar dynamics, and x-ray binaries are probing the properties of spacetime over 22 orders of magnitude in scale. Current measurements are consistent with an infinite flat everlasting universe containing about 30% cold dark matter, 65% dark energy, and at least two distinct populations of black holes.Conditions for accelerated expansion of Friedmann-Robertson-Walker space-time are analyzed. Connection of this scenario with present-day observations are reviewed. It is explained how a scalar field could be responsible for cosmic acceleration observed in present times and predicted for the very early Universe. Ideas aimed at answering whether is that the actual case for our Universe are described.

On Loop Quantum Gravity Phenomenology and the Issue of Lorentz Invariance

A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A comparison with more involved semiclassical techniques shows that there is agreement even at a quantitative level. Furthermore, by contrasting Hamiltonian and Lagrangian descriptions we show that possible Lorentz symmetry violations may be blurred as an artifact of the approximation scheme. Whether this is the case in a purely Hamiltonian analysis can be resolved by an improvement in the effective semiclassical analysis.

Loop space representation of quantum fermions and gravity

Abstract We study the quantum fermions + gravity system, that is, the gravitational counterpart of QED. We start from the standard Einstein-Weyl theory, reformulated in terms of Ashtekar variables; and we construct its non-perturbative quantum theory by extending the loop representation of general relativity. To this aim, we construct the fermion equivalent of the loop variables, and we define the quantum theory as a representation of their Poisson algebra. Not surprisingly, fermions can be accounted for in the loop representation simply by including open curves into loop space, as expected from lattice Yang-Mills theory. We explicitly construct the diffeomorphism and Hamiltonian operators. The first can be fully solved as in pure gravity. The second is constructed by using a background independent regularization technique. The theory retains the clean geometrical features of pure quantum gravity. In particular, the Hamiltonian constraint admits the same simple geometrical interpretation as its pure gravity counterpart: it is the operator that shifts curves along themselves (shift operator). Quite surprisingly, we believe, this simple action codes the full dynamics of the interacting fermion-gravity theory. To unravel the dynamics of the theory we study the evolution of the fermion-gravity system in the physical time defined by an additional coupled (clock-) scalar field. We explicitly construct the Hamiltonian operator that evolves the system in this physical time. We show that this Hamiltonian is finite, diffeomorphism invariant, and has a simple geometrical action confined to the intersections and the end points of the “loops”. The quantum theory of fermions + gravity evolving in the clock time is finally given by the combinatorial and geometrical action of this Hamiltonian on a set of graphs with a finite number of end points. This geometrical action defines the topological Feynman rules of the theory.

High-order quantum back-reaction and quantum cosmology with a positive cosmological constant

When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods to derive the dynamical equations including all quantum corrections to high order in the moments are introduced, together with a (deparameterized) quantum cosmological example to illustrate some implications. The results show, for instance, that the Gaussian form of an initial state is maintained only briefly, but that the evolving state settles down to a new characteristic shape afterwards. Remarkably, even in the regime of large high-order moments, we observe a strong convergence within all considered orders that supports the use of this effective approach.

Casimir force for a scalar field in warped brane worlds

In looking for imprints of extra dimensions in braneworld models one usually builds these so that they are compatible with known low energy physics and thus focuses on high energy effects. Nevertheless, just as submillimeter Newtons law tests probe the mode structure of gravity other low energy tests might apply to matter. As a model example, in this work we determine the 4D Casimir force corresponding to a scalar field subject to Dirichlet boundary conditions on two parallel planes lying within the single brane of a Randall-Sundrum scenario extended by one compact extra dimension. Using the Greens function method such a force picks the contribution of each field mode as if it acted individually but with a weight given by the square of the mode wave functions on the brane. In the low energy regime one regains the standard 4D Casimir force that is associated to a zero mode in the massless case or to a quasilocalized or resonant mode in the massive one while the effect of the extra dimensions gets encoded as an additional term.

Reality conditions for Ashtekar variables as Dirac constraints

We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity can be implemented as second-class constraints following Dirac. Thus, counting gravitational degrees of freedom follows accordingly. Some constraints of the real theory turn out to be non-polynomial, regardless of the form, polynomial or non-polynomial, taken for the reality conditions. We comment upon the compatibility of our approach with the recently proposed Wick transform point of view, as well as on some alternatives for dealing with such second-class constraints.

Chiral fermions coupled to chiral gravity

Abstract Using a purely imaginary translational Chern-Simons term as a generating function , a chiral reformulation of gravity a la Ashtekar is achieved. It is a crucial advantage of our Clifford algebra approach that the coupling to the chiral Dirac and the Rarita-Schwinger fields arises from the same translational Chern-Simons term, now evaluated “on shell”.

Manifestly covariant Jüttner distribution and equipartition theorem

The relativistic equilibrium velocity distribution plays a key role in describing several high-energy and astrophysical effects. Recently, computer simulations favored Jüttners as the relativistic generalization of Maxwells distribution for d=1,2,3 spatial dimensions and pointed to an invariant temperature. In this work, we argue an invariant temperature naturally follows from manifest covariance. We present a derivation of the manifestly covariant Jüttners distribution and equipartition theorem. The standard procedure to get the equilibrium distribution as a solution of the relativistic Boltzmanns equation, which holds for dilute gases, is here adopted. However, contrary to previous analysis, we use Cartesian coordinates in d+1 momentum space, with d spatial components. The use of the multiplication theorem of Bessel functions turns crucial to regain the known invariant form of Jüttners distribution. Since equilibrium kinetic-theory results should agree with thermodynamics in the comoving frame to the gas the covariant pseudonorm of a vector entering the distribution can be identified with the reciprocal of temperature in such comoving frame. Then by combining the covariant statistical moments of Jüttners distribution a form of the equipartition theorem is advanced which also accommodates the invariant comoving temperature and it contains, as a particular case, a previous not manifestly covariant form.

Alternative approaches to Lorentz violation invariance in loop quantum gravity inspired models

Recent claims point out that possible violations of Lorentz symmetry appearing in some semiclassical models of extended matter dynamics motivated by loop quantum gravity can be removed by a different choice of phase-space variables. In this note we show that such alternative is inconsistent with (i) the choice of variables in the regularized underlying quantum theory from which the effective theories are derived and (ii) the application of the correspondence principle. A consistent choice will violate standard Lorentz invariance, with the exception of trivial zero Planck scale corrections which are allowed by the analysis. Thus, for nontrivial corrections, to preserve a relativity principle in these models, the linear realization of Lorentz symmetry should be extended or superseded.