Search

The detection of gravitational waves from a binary neutron star merger by Advanced LIGO and Advanced Virgo (GW170817), along with the discovery of the electromagnetic counterparts of this gravitational wave event, ushered in a new era of multimessenger astronomy, providing the first direct evidence that BNS mergers are progenitors of short gamma-ray bursts (GRBs). Such events may also produce very-high-energy (VHE, > 100GeV) photons which have yet to be detected in coincidence with a gravitational wave signal. The Cherenkov Telescope Array (CTA) is a next-generation VHE observatory which aims to be indispensable in this search, with an unparalleled sensitivity and ability to slew anywhere on the sky within a few tens of seconds. New observing modes and follow-up strategies are being developed for CTA to rapidly cover localization areas of gravitational wave events that are typically larger than the CTA field of view. This work will evaluate and provide estimations on the expected number of of gravitational wave events that will be observable with CTA, considering both on- and off-axis emission. In addition, we will present and discuss the prospects of potential follow-up strategies with CTA., Comment: Presented at the 38th International Cosmic Ray Conference (ICRC 2023), 2023 (arXiv:2309.08219)

In this work we study the gravitational radiation produced by a keplerian binary system within the context of Very Special Linear Gravity (VSLG), a novel theory of linearized gravity in the framework of Very Special Relativity (VSR) allowing for a gauge-invariant mass $m_g$ of the graviton. For this task, we exploit Effective Field Theory's techniques, which require, among others, the calculation of the squared amplitude of the emission process and therefore the polarization sum for VSLG gravitons. Working in the radiation zone and using the standard energy momentum tensor's expression for keplerian binaries, we derive and study the properties of the VSLG energy loss and period decrease rates, also verifying they reduce to the correct General Relativity limit when sending $m_g\to0$. Finally, using astronomical data from the Hulse-Taylor binary and the Double Pulsar J0737-3039, we obtain an upperbound on the VSLG graviton mass of $m_g\sim 10^{-21}eV$ that, while being comparable to bounds obtained in this same way for other massive gravity models, is still weaker than the kinematical bound $\sim 10^{-22}eV$ obtained from the combined observation of the astronomical events GW170817 and GRB170817A, which should still hold in VSLG.

Mandelstam-Leibbrandt(ML) regularization of Very Special Relativity (VSR) amplitudes in momentum space depends on two fixed null vectors $n_\mu,\bar{n}_\mu$ besides external momenta. ML is known to preserve gauge invariance and naive power counting. The second null vector $\bar{n}_\mu$ destroys the $Sim(2)$ symmetry of the VSR model. We devise a systematic procedure to take the $\bar{n}_\mu->0$ limit to recover the lost $Sim(2)$ symmetry. The procedure produces $Sim(2)$ and gauge invariant loop amplitudes. We show how to use this method to remove unphysical terms from the Non Relativistic Potential of Very Special Relativity Quantum Electrodynamics(VSR QED) with a massive photon. Then we compute the one loop renormalization of VSR QED. Finally we derive the anomalous magnetic moment of the electron, modified by neutrino and photon mass; and comments on the phenomenological implications., Comment: 25 pages, 13 figures, latex

Linearized gravity in the Very Special Relativity (VSR) framework is considered. We prove that this theory allows for a non-zero graviton mass $m_g$ without breaking gauge invariance nor modifying the relativistic dispersion relation. We find the analytic solution for the new equations of motion in our gauge choice, verifying as expected the existence of only two physical degrees of freedom. Finally, through the geodesic deviation equation, we confront some results for classic gravitational waves (GW) with the VSR ones: we see that the ratios between VSR effects and classical ones are proportional to $(m_g/E)^2$, $E$ being the energy of a graviton in the GW. For GW detectable by the interferometers LIGO and VIRGO this ratio is at most $10^{-20}$. However, for GW in the lower frequency range of future detectors, like LISA, the ratio increases significantly to $ 10^{-10}$, that combined with the anisotropic nature of VSR phenomena may lead to observable effects., Comment: Latex,6 pages

In this paper we study the axial anomaly in Very Special Relativity Electrodynamics using Pauli-Villars and dimensional regularization of ultraviolet divergences and Mandelstam-Leibbrandt regularization of infrared divergences. We compute the anomaly in 2 and 4 dimensional space-time. We find that this procedure preserves the vector Ward identity(charge conservation) and reproduce the standard axial anomaly in 2 and 4 dimensions without corrections from VSR. Finally, we show how to obtain the anomaly in the path integral approach., Comment: latex, 13 pages

In this work, we present the thermodynamic study of a model that considers the black hole as a condensate of gravitons. In this model, the spacetime is not asymptotically flat because of a topological defect that introduces an angle deficit in the spacetime like in Global Monopole solutions. We have obtained a correction to the Hawking temperature plus a negative pressure associated with the black hole of mass $M$. In this way, the graviton condensate, which is assumed to be at the critical point defined by the condition $\mu_{ch}$=0, has well-defined thermodynamic quantities $P$, $V$, $T_{h}$, $S$, and $U$ as any other Bose-Einstein condensate (BEC). In addition, we present a formal equivalence between the Letelier spacetime and the line element that describes the graviton condensate. We also discuss the Kiselev black hole, which can parametrize the most well-known spherically symmetric black holes. Finally, we present a new metric, which we will call the BEC-Kiselev solution, that allows us to extend the graviton condensate to the case of solutions with different matter contents., Comment: 17 pages, 2 figures; Section III reconstructed, Added 2 Appendices, Added 2 references, typos corrected

Delta Gravity is a gravitational model based on an extension of General Relativity given by a new symmetry called $\tilde{\delta}$. In this model, new matter fields are added to the original matter fields, motivated by the additional symmetry. We call them $\tilde{\delta}$ matter fields. This model predicts an accelerating Universe without the need to introduce a cosmological constant. In this work, we study the Delta Gravity prediction about the scalar CMB TT power spectrum using an analytical hydrodynamical approach. To fit the Planck satellite's data with the DG model, we used a Markov Chain Monte Carlo analysis. We also include a study about the compatibility between SNe-Ia and CMB observations in the Delta Gravity Context. Finally, we obtain the scalar CMB TT power spectrum and the fitted parameters needed to explain both SNe-Ia Data and CMB measurements. The results are in a reasonable agreement with both observations considering the analytical approximation. We also discuss if the Hubble Constant and the Accelerating Universe are in concordance with the observational evidence in the Delta Gravity context.

Starting from the Mandelstam-Leibbrandt prescription, we introduce a general rule for the null vector $\bar{n}$ to compute any $SIM(2)$ integral and diagram with an arbitrary number of external legs. Using the new prescription, the computation of the low energy limit of photon-photon scattering under the Very Special Relativity (VSR) framework is presented. The prescription preserves automatically the Ward identities corresponding to the gauge symmetry. Within the low momentum approximation we get the standard unpolarized differential cross section for photon-photon scattering. The result suggests that loops with any external photon legs on-shell will be zero in VSR., Comment: 9 pages, 2 figures

About 70\% of the Universe is Dark Energy, but the physics community still does not know what it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. Previously, we studied the Universe's accelerated expansion, where DG was able to explain the SNe-Ia data successfully. In this work, we explore the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculate the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve in a semi-analytical way the scalar TT Power Spectrum. These equations will be useful for comparing the DG theory with astronomical observations and thus being able to constraint the DG cosmology, testing, in the future, the compatibility with the CMB Planck data, which are currently in controversy with SNe-Ia., Comment: 39 pages, latex

Recently it has been shown that in two dimensions is possible to add new Lorentz invariant terms built with fractions containing the null vector $n= (1, 1)$. In this work, we have computed the meson spectrum following the 't Hooft model in $QCD_2$ incorporating these new kinds of terms. We found these new terms does not affect the meson spectrum. We have computed the 't Hooft model with a new regulator. We have introduced a gluon mass and we have recovered the 't Hooft result when this parameter is set to zero., Comment: 10 pages, 3 figures

In this work, we show that Lorentz invariant theories in $1+1$ dimensions admit new terms inspired by Very Special Relativity (VSR) theories. We have studied the Schwinger model in VSR. We show the axial current is classically conserved in the presence of a mass term coming from the VSR invariant terms but without standard Lorentz invariant mass. Furthermore, it is shown that both the vector current as well as the axial current are modified with respect to the free case when the fermion is coupled to an external electromagnetic field due to the nonlocal operator present in the theory. The axial anomaly is computed, and we found the same standard topological invariant with a modification in the coefficient., Comment: 10 pages, 2 figures. V2: Minor changes, references updated, accepted in PLB

In this work we continue our previous studies concerning the possibility of the existence of a Bose-Einstein condensate in the interior of a static black hole, a possibility first advocated by Dvali and G\'omez. We find that the phenomenon seems to be rather generic and it is associated to the presence of an horizon, acting as a confining potential. We extend the previous considerations to a Reissner-Nordstr\"om black hole and to the de Sitter cosmological horizon. In the latter case the use of static coordinates is essential to understand the physical picture. In order to see whether a BEC is preferred, we use the Brown-York quasilocal energy, finding that a condensate is energetically favourable in all cases in the classically forbidden region. The Brown-York quasilocal energy also allows us to derive a quasilocal potential, whose consequences we explore. Assuming the validity of this quasilocal potential allows us to suggest a possible mechanism to generate a graviton condensate in black holes. However, this mechanism appears not to be feasible in order to generate a quantum condensate behind the cosmological de Sitter horizon., Comment: 25 pages, 6 figures

Recent research show that the cosmological components of the Universe should influence on the propagation of Gravitational Waves (GWs) and even it has been proposed a new way to measure the cosmological constant using Pulsar Timing Arrays (PTAs). However, these results have considered very particular cases (e.g. a de Sitter Universe or a mixing with non-relativistic matter). In this work we propose an extension of these results, using the Hubble constant as the natural parameter that includes all the cosmological information and studying its effect on the propagation of GWs. Using linearized gravity we considered a mixture of perfect fluids permeating the spacetime and studied the propagation of GWs within the context of the LCDM model. We found from numerical simulations that the timing residual of local pulsars should present a distinguishable peak depending on the local value of the Hubble constant. As a consequence, when assuming the standard LCDM model, our result predicts that the region of maximum timing residual is determined by the redshift of the source. This framework represents a new test for the standard cosmological model, and it can be used to facilitate the measurements of gravitational wave by ongoing PTAs projects., Comment: 19 pages, 7 figures, 3 tables. Initially submitted to ApJ on March 5, 2019

In Very Special Relativity (VSR) a gauge invariant photon mass is allowed. We explore some consequences of keeping this parameter not zero. VSR-Maxwell equations are presented. In addition, we show modifications to the Feynman rules keeping the photon mass and we apply it in the computation of the electron self energy, whose result is free from infrared divergences. A computation of the Coulomb scattering is developed and a small signal of the privileged direction predicted in the theory is present at tree level. Radiative corrections are computed and the photon mass cancels due to soft photon emission as in the standard case., Comment: 12 pages, 5 figures. v2: Changes in the section II. References updated. v3: Version accepted in PRD

A gravitational field model based on two symmetric tensors, $g_{\mu \nu}$ and $\tilde{g}_{\mu \nu}$, is studied, using a Markov Chain Monte Carlo (MCMC) analysis with the most updated catalog of SN-Ia. In this model, new matter fields are added to the original matter fields, motivated by an additional symmetry ($\tilde{\delta}$~symmetry). We call them $\tilde{\delta}$ matter fields. This theory predicts an accelerating Universe without the need to introduce a cosmological constant $\Lambda$ by hand in the equations. We obtained a very good fit to the SN-Ia Data, and with this, we found the two free parameters of the theory called $C$ and $L_2$. With these values, we have fixed all the degrees of freedom in the model. The last $H_0$ local value measurement is in tension with the CMB Data from Planck. Based on an absolute magnitude $M_V = -19.23$ for the SN, Delta Gravity finds $H_0$ to be $74.47\pm 1.63$ km/(s Mpc). This value is in concordance with the last measurement of the $H_0$ local value, $73.83\pm 1.48$ km/(s Mpc)., Comment: latex, 27 pages,15 figures

We study here how the presence of non-zero matter density and a cosmological constant could affect the observation of gravitational waves in Pulsar Timing Arrays. Conventionally, the effect of matter and cosmological constant is included by considering the redshift in frequency due to the expansion. However, there is an additional effect due to the change of coordinate systems from the natural ones in the region where waves are produced to the ones used to measure the pulsar timing residuals. This change is unavoidable as the strong gravitational field in a black hole merger distorts clocks and rules. Harmonic waves produced in such a merger become anharmonic when detected by a cosmological observer. The effect is small but appears to be observable for the type of gravitational waves to which PTA are sensitive and for the favoured values of the cosmological parameters., Comment: 18 pages, 2 figures

$\tilde{\delta}$ Gravity is a gravitational field model, where the geometry is governed by two symmetric tensors, $g_{\mu \nu}$ and $\tilde{g}_{\mu \nu}$, and new matter fields ($\tilde{\delta}$ Matter fields) are added to the original matter fields. These new components appear motivated by a new symmetry, called $\tilde{\delta}$ symmetry. In previous works, the model is used to explain the expansion of the Universe without Dark Energy and use $\tilde{\delta}$ Matter as a source of Dark Matter. In this paper, we will developed an initial study of Schwarzschild geometry in $\tilde{\delta}$ Gravity to complement the Dark Matter analysis and introduce other phenomena. We will get a modified deflection of light produced by the sun, the perihelion precession and black hole solution., Comment: latex 21 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1704.02888, arXiv:1711.00361

$\tilde{\delta}$ Gravity is a gravitational field model, where the geometry is governed by two symmetric tensors, $g_{\mu \nu}$ and $\tilde{g}_{\mu \nu}$, and new matter fields ($\tilde{\delta}$ Matter fields) are added to the original matter fields. These new components appear motivated by a new symmetry, called $\tilde{\delta}$ symmetry. In previous works, the model is used to explain the expansion of the Universe without Dark Energy. This result and the additional contribution to the mass by $\tilde{\delta}$ Matter are motivations to study the Dark Matter effect with $\tilde{\delta}$ Gravity. In this work, we will derive the Non-Relativistic limit to obtain a correction to the rotation velocity in a galaxy, then we will analyze the most common galaxy density profiles to describe Dark Matter., Comment: latex 21 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1704.02888, arXiv:1711.00360

A gravitational field model based on two symmetric tensors, $g_{\mu \nu}$ and $\tilde{g}_{\mu \nu}$, is presented. In this model, new matter fields are added to the original matter fields, motivated by an additional symmetry ($\tilde{\delta}$ symmetry). We call them $\tilde{\delta}$ matter fields. We find that massive particles do not follow geodesics, while trajectories of massless particles are null geodesics of an effective metric. Then we study the Cosmological case, where we get an accelerated expansion of the Universe without dark energy., Comment: 24 pages,1 figure, latex. arXiv admin note: text overlap with arXiv:1210.6107

We introduce a $Sim(2)$ invariant dimensional regularization of loop integrals. Then we compute the one loop quantum corrections to the photon self energy, electron self energy and vertex in the Electrodynamics sector of the Very Special Relativity Standard Model(VSRSM)., Comment: 11 pages, latex

We analyze in detail a previous proposal by Dvali and G\'omez that black holes could be treated as consisting of a Bose-Einstein condensate of gravitons. In order to do so we extend the Einstein-Hilbert action with a chemical potential-like term, thus placing ourselves in a grand-canonical ensemble. The form and characteristics of this chemical potential-like piece are discussed in some detail. We argue that the resulting equations of motion derived from the action could be interpreted as the Gross-Pitaevskii equation describing a graviton Bose-Einstein condensate trapped by the black hole gravitational field. After this, we proceed to expand the ensuring equations of motion up to second order around the classical Schwarzschild metric so that some non-linear terms in the metric fluctuation are kept. Next we search for solutions and, modulo some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. Inspired by a linearized approximation around the horizon we are able to find an exact solution for the mean-field wave function describing the graviton Bose-Einstein condensate in the black hole interior. After this, we can rederive some of the relations involving the number of gravitons $N$ and the black hole characteristics along the lines suggested by Dvali and G\'omez., Comment: 18 pages, 1 figure

The light cone gauge is used frequently in string theory as well as gauge theories and gravitation. Loop integrals however have to be infrared regulated to remove spurious poles. The most popular and consistent of these infrared regulators is the Mandelstam-Leibbrandt(ML) prescription. The calculations with ML are rather cumbersome, though. In this work we show that the ML can be replaced by a symmetry of the regulator. This symmetry simplify the calculations, reducing them to conventional dimensional regularization integrals., Comment: Latex 7 pages

The Very Special Relativity Electroweak Standard Model (VSR EW SM) is a theory with $SU(2)_L \times U(1)_R$ symmetry, with the same number of leptons and gauge fields as in the usual Weinberg-Salam (WS) model. No new particles are introduced. The model is renormalizable and unitarity is preserved. However, photons obtain mass and the massive bosons obtain different masses for different polarizations. Besides, neutrino masses are generated. A VSR invariant term will produce neutrino oscillations and new processes are allowed. In particular, we compute the rate of the decays $\mu \rightarrow e + \gamma$. All these processes, which are forbidden in the Electroweak Standard Model, put stringent bounds on the parameters of our model and measure the violation of Lorentz invariance. We investigate the canonical quantization of this non-local model. Second quantization is carried out obtaining a well defined particle concept. Additionally, we do a counting of the degrees of freedom associated to the gauge bosons involved in this work, after Spontaneous Symmetry Breaking has been realized. Violations of Lorentz invariance have been predicted by several theories of Quantum Gravity \cite{amu}. It is a remarkable possibility that the low energy effects of Lorentz violation induced by Quantum Gravity could be contained in the non-local terms of the VSR EW SM., Comment: Latex, 24 pages. Accepted for publication in Phys. Rev. D

We introduce bosonic (p - 1)-form fields that couple to the spin connection of the Einstein-Cartan theory of gravity thus becoming a non-trivial source of space-time torsion. We analyze all the general features of both the matter and the gravitational sectors of the theory. Finally we briefly consider the implications of the existence of such fields in different physical settings., Comment: 14 pages

Very special relativity (VSR) keeps the main features of special relativity but breaks rotational invariance. It can not be regarded as a fundamental symmetry of nature because many observed phenomena depend on the existence of Lorentz boosts. However, within the scope of Lorentz violating theories it can have a role since it is breaking Lorentz symmetry in a very mild way. In this context, when VSR terms are incorporated in a Lorentz invariant theory several possibilities are allowed. In order to generate such terms systematically we start with a formulation for a spinning particle in VSR. It is then coupled minimally to the electromagnetic field and a gyromagnetic factor is added to give rise to a magnetic moment. In order to analyze the effects of VSR in Thomas precession a spin vector is then proposed in terms of the spinning particle variables. It is then found the VSR contributions to the equation which determines the spin precession angular velocity., Comment: Latex, 16 pages. Add references and discussion on the distribution function

We study non-Abelian fields in the context of very special relativity (VSR). For this we define the covariant derivative and the gauge field gauge transformations, both of them involving a fixed null vector $n_{\mu}$, related to the VSR breaking of the Lorentz group to the Hom(2) or Sim(2) subgroups. As in the Abelian case the gauge field becomes massive. Moreover we show that the VSR gauge transformations form a closed algebra. We then write actions coupling the gauge field to various matter fields (bosonic and fermionic). We mention how we can use the spontaneous symmetry breaking mechanism to give a flavor dependent VSR mass to the gauge bosons. Finally, we quantize the model using the BRST formalism to fix the gauge. The model is renormalizable and unitary and for non abelian groups, asymptotically free., Comment: 11 pages, latex

We present a model of the gravitational field based on two symmetric tensors. Gravity is affected by the new field, but outside matter the predictions of the model coincide exactly with general relativity, so all classical tests are satisfied. We find that massive particles do not follow a geodesic while massless particles trajectories are null geodesics of an effective metric. We study the Cosmological case, where we get an accelerated expansion of the universe without dark energy. We also introduce the possibility to explain dark matter with $\tilde{\delta}$ gravity., Comment: latex, 18 pages. arXiv admin note: text overlap with arXiv:1006.5765

We present the extension to 4 dimensions of an euclidean 2-dimensional model that exhibits spontaneous generation of a metric. In this model gravitons emerge as Goldstone bosons of a global SO(D) X GL(D) symmetry broken down to SO(D). The microscopic theory can be formulated without having to appeal to any particular space-time metric and only assumes the pre-existence of a manifold endowed with an affine connection. We emphasize that not even a flat metric needs to be assumed; in this sense the microscopic theory is quasi-topological. The vierbein appears as a condensate of the fundamental fermions. In spite of having non-standard characteristics, the microscopic theory appears to be renormalizable. The effective long-distance theory is obtained perturbatively around a vacuum that, if the background affine connection is set to zero, is (euclidean) de Sitter space-time. If perturbatively small connections are introduced on this background, fluctuations of the metric (i.e. gravitons) appear; they are described by an effective theory at long distances whose more relevant operators correspond to the Einstein-Hilbert action with a cosmological constant. This effective action is derived in the large N limit, N being the number of fermion species in the fundamental theory. The counterterms required by the microscopic theory are directly related to the cosmological constant and Newton constant and their couplings could eventually be adjusted to the physical values of Mp and \Lambda.

Recently the OPERA collaboration {\cite{opera}} has reported the observation of superluminal neutrinos traveling a distance of 730 km from Grand Sasso Laboratory to CERN.These results contradict the basic tenet of the Theory of Special Relativity: No particle can travel faster than light in vacuum. Moreover they seem to be in conflict with the speed of (anti)neutrinos detected from the explosion of the SP1987A Super Nova{\cite{SP1987A}}.Here we show that the relative velocity between neutrino and photon has the following property: It depends weakly on the energy of the particle excepts in certain regions(thresholds) where discrete jumps appear.This explains both Opera and SP1987A Super Nova data., Comment: latex, 4 pages

We discuss the quantization of Delta gravity, a two symmetric tensors model of gravity. This model, in Cosmology, shows accelerated expansion without a cosmological constant. We present the $\tilde{\delta}$ transformation which defines the geometry of the model. Then we show that all delta type models live at one loop only. We apply this to General Relativity and we calculate the one loop divergent part of the Effective Action showing its null contribution in vacuum, implying a finite model. Then we proceed to study the existence of ghosts in the model. Finally, we study the form of the finite quantum corrections to the classical action of the model., Comment: Latex, 33 pages

We review the similarities between the effective chiral lagrangrian, relevant for low-energy strong interactions, and the Einstein-Hilbert action. We use these analogies to suggest a specific mechanism whereby gravitons would emerge as Goldstone bosons of a global SO(D) X GL(D) symmetry broken down to SO(D) by fermion condensation. We propose a two-dimensional toy model where a dynamical zwei-bein is generated from a topological theory without any pre-existing metric structure, the space being endowed only with an affine connection. A metric appears only after the symmetry breaking; thus the notion of distance is an induced effective one. In spite of several non-standard features this simple toy model appears to be renormalizable and at long distances is described by an effective lagrangian that corresponds to that of two-dimensional gravity (Liouville theory). The induced cosmological constant is related to the dynamical mass M acquired by the fermion fields in the breaking, which also acts as an infrared regulator. The low-energy expansion is valid for momenta k >M, i.e. for supra-horizon scales. We briefly discuss a possible implementation of a similar mechanism in four dimensions., Comment: 18 pages

We introduce a new version of non-linear electrodynamics which is produced by a spontaneous symmetry breaking of Lorentz invariance induced by the non-zero expectation value of the electromagnetic field strength. The symmetry breaking potential is argued to effectively arise from the integration of massive gauge bosons and fermions in an underlying fundamental theory. All possible choices of the vacuum lead only to the remaining invariant subgroups T(2) and HOM(2). We explore the plane wave solutions of the linearized sector of the model for an arbitrary vacuum. They present two types of dispersion relations. One corresponds to the case of the usual Maxwell electrodynamics with the standard polarization properties of the fields. The other dispersion relation involves anisotropies determined by the structure of the vacuum. The model is stable in the small Lorentz invariance violation approximation. We have embedded our model in the photon sector of the Standard Model Extension in order to set bounds for our parameters. The one-way anisotropic speed of light is calculated for a general vacuum and its isotropic component is strongly bounded by ${\tilde \delta c}/c < 2 \times 10^{-32}$. The anisotropic violation contribution is estimated by introducing an alternative definition for the difference of the two-way speed of light in perpendicular directions $\Delta c$, which is also strongly bounded by ${\Delta c}/c < 10^{-32}$. Finally, we speculate on the relation of the vacuum energy of the model with the cosmological constant and propose a connection between the vacuum fields and the intergalactic magnetic fields., Comment: 27 pages,1 figure,1 table, revtex4

Recently many studies have considered the possibility of a Lorentz Invariance Violation (LIV), and explored its consequences in a wide range of experiments. If this is true, a LIV could explains some mysteries in Cosmology. In this paper specifically, we will analyze the effects on The Primordial Baryogenesis because it is one of the more important and mysterious phenomena of the Big-Bang, that happened at very high energies, so we have a real chance to obtain an important effect. We will see that this effect could exist, depending directly on the temperature, that is very high at this time in the history of the Universe. So, it is possible to use this result as a test for a LIV and explore the possibility that the boson that started the baryogenesis explains, in part, the dark matter. We will obtain estimates about the beginning time of the baryogenesis and the boson mass too, that come directly from the LIV., Comment: latex, 14 pages

The Cosmic Neutrinos Background (\textbf{CNB}) are Primordial Neutrinos decoupled when the Universe was very young. Its detection is complicated, especially if we take into account neutrino mass and a possible breaking of Lorentz Invariance at high energy, but has a fundamental relevance to study the Big-Bang. In this paper, we will see that a Lorentz Violation does not produce important modification, but the mass does. We will show how the neutrinos current velocity, with respect to comobile system to Universe expansion, is of the order of 1065 $[\frac{km}{s}]$, much less than light velocity. Besides, we will see that the neutrinos distribution is complex due to Planetary motion. This prediction differs totally from the usual massless case, where we would get a correction similar to the Dipolar Moment of the \textbf{CMB}., Comment: 16 pages, latex, 7 figures

A main difficulty in the quantization of the gravitational field is the lack of experiments that discriminate among the theories proposed to quantize gravity. Recently we showed that the Standard Model(SM) itself contains tiny Lorentz invariance violation(LIV) terms coming from QG. All terms depend on one arbitrary parameter $\alpha$ that set the scale of QG effects. In this talk we review the LIV for mesons nucleons and leptons and apply it to study several effects, including the GZK anomaly., Comment: latex, 9 pages, Talk at the VI Silafae, Puerto Vallarta, Mexico, November 1-8,2006. Added references

The most important problem of fundamental Physics is the quantization of the gravitational field. A main difficulty is the lack of available experimental tests that discriminate among the theories proposed to quantize gravity. Recently we showed that the Standard Model(SM) itself contains tiny Lorentz invariance violation(LIV) terms coming from QG. All terms depend on one arbitrary parameter $\alpha$ that set the scale of QG effects. In this paper we obtain the LIV for mesons and nucleons and apply it to study several effects, including the GZK anomaly., Comment: latex, 16 pages

Recently, we have remarked that the main effect of Quantum Gravity(QG) will be to modify the measure of integration of loop integrals in a renormalizable Quantum Field Theory. In the Standard Model this approach leads to definite predictions, depending on only one arbitrary parameter. In particular, we found that the maximal attainable velocity for particles is not the speed of light, but depends on the specific couplings of the particles within the Standard Model. Also birrefringence occurs for charged leptons, but not for gauge bosons. Our predictions could be tested in the next generation of neutrino detectors such as NUBE. In this paper, we elaborate more on this proposal. In particular, we extend the dimensional regularization prescription to include Lorentz invariance violations(LIV) of the measure, preserving gauge invariance. Then we comment on the consistency of our proposal., Comment: latex, 2 pages

Recent observations on ultra high energy cosmic rays (those cosmic rays with energies greater than $\sim 4 \times 10^{18}$ eV) suggest an abundant flux of incoming particles with energies above $1 \times 10^{20}$ eV. These observations violate the Greisen-Zatsepin-Kuzmin cutoff. To explain this anomaly we argue that quantum-gravitational effects may be playing a decisive role in the propagation of ultra high energy cosmic rays. We consider the loop quantum gravity approach and provide useful techniques to establish and analyze constraints on the loop quantum gravity parameters arising from observational data. In particular, we study the effects on the predicted spectrum for ultra high energy cosmic rays and conclude that is possible to reconcile observations., Comment: latex, 17 pages. Talk at The XVIIIth International Workshop High Energy Physics and Quantum Field Theory Saint-Petersburg, June 17-23, 2004

The most important problem of fundamental Physics is the quantization of the gravitational field. A main difficulty is the lack of available experimental tests that discriminate among the theories proposed to quantize gravity. Recently, Lorentz invariance violation by Quantum Gravity(QG) have been the source of a growing interest. However, the predictions depend on ad-hoc hypothesis and too many arbitrary parameters. Here we show that the Standard Model(SM) itself contains tiny Lorentz invariance violation(LIV) terms coming from QG. All terms depend on one arbitrary parameter $\alpha$ that set the scale of QG effects. This parameter can be estimated using data from the Ultra High Energy Cosmic Rays spectrum to be $|\alpha|<\sim 10^{-22}-10^{-23}$., Comment: latex 4 pages