Modified Dispersion Relation Research Articles

Quantum Gravity Effect on Neutrino Oscillation

The quantum gravity may have strong consequence for neutrino oscillation phenemomenon over a large distance.We found a significant modification of neutrino oscillation due to quantum gravity effects. Quantum gravity (Planck scale effects) leads to an effective SU(2)L×U(1) invariant dimension-5 Lagrangian involving, neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the neutrino masses and mixing. The gravitational interaction (MX=Mpl) demands that the element of this perturbation matrix should be independent of flavor indices. In this paper, we study the quantum gravity effects on neutrino oscillation, namely modified dispersion relation for neutrino oscillations parameter.

DETECTION METHOD AND OBSERVED DATA OF HIGH-ENERGY GAMMA RAYS UNDER THE INFLUENCE OF QUANTUM GRAVITY

The interaction of high-energy particles affected by quantum gravity is argued from the experimental viewpoint of raising a question, “our detection method for high-energy γ -rays supplies trustworthy observation data and we are now seeing the true image of the universe through high-energy γ -rays?” The modified dispersion relation (MDR) for particles’ energy and momentum is applied to the equation of energy–momentum conservation in particle reactions, to study the restriction imposed on the kinematic state of high-energy particles by the Lorentz invariance violation (LIV) due to quantum gravity, as a function of the incident particle energy of the reaction. The result suggests that the interaction utilized for γ -ray detection is not free from the effect of quantum gravity when γ -ray energy is higher than 10 13 ∼ 10 17 eV depending on models of MDR. Discussion is presented on the prospect of finding clear evidence of the LIV effect from γ -ray observations, as well as on the radiation and propagation mechanism of γ -rays under the influence of the LIV effect.

Observational constraints on dual intermediate inflation

We explore the observational implications of models of intermediate inflation driven by modified dispersion relations, specifically those representing the phenomenon of dimensional reduction in the ultraviolet limit. These models are distinct from the standard ones because they do not require violations of the strong energy condition, and this is reflected in their structure formation properties. We find that they can naturally accommodate deviations from exact scale-invariance. They also make clear predictions for the running of the spectral index and tensor modes, rendering the models straightforwardly falsifiable. We discuss the observational prospects for these models and the implications these may have for quantum gravity scenarios.

Kinematics and dynamics in a bipartite-Finsler spacetime

We study some properties of a recently proposed local Lorentz-violating Finsler geometry, the so-called bipartite space. This anisotropic structure deforms the causal null surface to an elliptic cone and provides an anisotropy to the inertia. We obtain the new modified dispersion relations and the geodesic equation for a massive particle. For a weak directional-dependence we find the dynamical and interaction terms analogous to the gravitational sector of the Standard Model Extension.

How Can the Modified Dispersion Relation Affect Friedmann Equations?

The appearance of the quantum gravitational effects in a very high energy regime necessitates some corrections to the thermodynamics of Friedmann-Robertson-Walker (FRW) universe. The modified dispersion relation (MDR) as a phenomenological approach to investigate the high energy physics provides a perturbation framework upon which the FRW universe thermodynamics can be corrected. In this letter, we obtain the corrected entropy-area relation of the apparent horizon of FRW universe by utilizing the extra dimensional form of MDR, leading to the modification of Friedmann equations. The influence of MDR on the Friedmann equations provides a good insight into the understanding of the FRW universe dynamics in the final quantum gravity theory.

Quantumness of discrete Hamiltonian cellular automata

We summarize a recent study of discrete (integer-valued) Hamiltonian cellular automata (CA) showing that their dynamics can only be consistently defined, if it is linear in the same sense as unitary evolution described by the Schr\"odinger equation. This allows to construct an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental scale. Presently, we emphasize general aspects of these findings, the construction of admissible CA observables, and the existence of solutions of the modified dispersion relation for stationary states.

Hawking radiation with dispersion versus breakdown of the WKB approximation

Inspired by the condensed matter analogues of black holes (a.k.a. dumb holes), we study Hawking radiation in the presence of a modified dispersion relation which becomes super-luminal at large wave-numbers. In the usual stationary coordinates $(t,x)$, one can describe the asymptotic evolution of the wave-packets in WKB, but this WKB approximation breaks down in the vicinity of the horizon, thereby allowing for a mixing between initial and final creation and annihilation operators. Thus, one might be tempted to identify this point where WKB breaks down with the moment of particle creation. However, using different coordinates $(\tau,U)$, we find that one can evolve the waves so that WKB in these coordinates is valid throughout this transition region -- which contradicts the above identification of the breakdown of WKB as the cause of the radiation. Instead, our analysis suggests that the tearing apart of the waves into two different asymptotic regions (inside and outside the horizon) is the major ingredient of Hawking radiation.

Lorentz Invariance Violation on UHECR propagation

In the present work possible consequences of the Lorentz symmetry breaking are presented. Those consequences are encoded through the modification of dispersion relations which are applied to the processes of pair and pion photo production generated at UHECR scale. The produced physics from such modifications contains scenarios where the expected photo production thresholds under Lorentz symmetry are shifted; the other scenarios predict that the cosmic ray flux will be recover at higher energies due to the suppression of the production processes. This phenomenon is repeated for different components of the diffuse photon background and generates opacity bands in distinct parts of the energy spectrum; we expose scenarios that have not been considered previously by other authors. Moreover, in contrast with previous studies, in this work the scenarios generated by the Lorentz symmetry breaking are measured by a generic parameter, unique for each process, independent of the correction origin (E2 or p2) in the dispersion relations, as well as the nature of the particle involved and possible corrections to the relations of conservation energy-momentum laws. Additionally, the Pierre Auger result for the pion photo production is used to estimate the energy scale parameter of the Lorentz symmetry breaking.

Dimensional reduction in momentum space and scale-invariant cosmological fluctuations

We adopt a framework where quantum gravity's dynamical dimensional reduction of spacetime at short distances is described in terms of modified dispersion relations. We observe that by subjecting such models to a momentum-space diffeomorphism one obtains a ``dual picture'' with unmodified dispersion relations, but a modified measure of integration over momenta. We then find that the UV Hausdorff dimension of momentum space which can be inferred from this modified integration measure coincides with the short-distance spectral dimension of spacetime. This result sheds light into why scale-invariant fluctuations are obtained if the original model for two UV spectral dimensions is combined with Einstein gravity. By studying the properties of the inner product we derive the result that it is only in two energy-momentum dimensions that microphysical vacuum fluctuations are scale invariant. This is true ignoring gravity, but then we find that if Einstein gravity is postulated in the original frame, in the dual picture gravity switches off, since all matter becomes conformally coupled. We argue that our findings imply that the following concepts are closely connected: scale invariance of vacuum quantum fluctuations, conformal invariance of the gravitational coupling, UV reduction to spectral dimension two in position space, and UV reduction to Hausdorff dimension two in energy-momentum space.

Anomalies in Conductance and Localization Length of Disordered Ladders

We discuss the conditions under which an anomaly occurs in conductance and localization length of Anderson model on a lattice. Using the ladder Hamiltonian and analytical calculation of average conductance we find the set of resonance conditions which complements the π-coupling rule for anomalies. We identify those anomalies that might vanish due to the symmetry of the lattice or the distribution of the disorder. In terms of the dispersion relation it is known from strictly one-dimensional model that the lowest order (i.e., the most strong) anomalies satisfy the equation E(k)=E(3k). We show that the anomalies of the generalized model studied here are also the solutions of the same equation with modified dispersion relation.

Generalizations of the Klein–Gordon and the Dirac Equations from Non-standard Lagrangians

We present various generalizations of the Klein–Gordon and Dirac formalisms based on non-standard Lagrangians within the framework of the calculus of variations characterized by a power-law Lagrangian \( {\mathsf{L}}^{1 + \gamma},\,\gamma \) being a free parameter. In the case of the bosonic scalar field, the modified dispersion relation has been derived and based on this, it was observed that for a particular choice of non-standard Lagrangians, the new field theory forbid the presence of massless particles. Besides, the Klein–Gordon equation is modified and becomes similar to the Barut equation which is a second order equation in the \( ({1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2},0) \oplus (0,{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}) \) representation of the Lorentz group, which explains the splitting of leptons. For the case of the spinor scalar field, the Barut-like equation was derived from a non-standard Lagrangian as well. For some specific class of non-standard Lagrangians, the modified dispersion is modified and prohibits the presence of massless particles.

Nonsingular rainbow universes

In this work, we study FRW cosmologies in the context of gravity rainbow. We discuss the general conditions for having a nonsingular FRW cosmology in gravity rainbow. We propose that gravity rainbow functions can be fixed using two known modified dispersion relation (MDR), which have been proposed in literature. The first MDR was introduced by Amelino-Camelia, et el. in [9] and the second was introduced by Magueijo and Smolin in [24]. Studying these FRW-like cosmologies, after fixing the gravity rainbow functions, leads to nonsingular solutions which can be expressed in exact forms.

Erratum to: Modified Proca equation and modified dispersion relation from a power-law Lagrangian functional

Erratum to: Modified Proca equation and modified dispersion relation from a power-law Lagrangian functional

Modified dispersion relation, photonʼs velocity, and Unruh effect

Motivated by the recently derived new form of generalized uncertainty principle we obtain the corresponding dispersion relation which is now modified. This modification can be interpreted as a possible mechanism that makes particles more massive. In addition, the modified velocity of photons is obtained and indicates that photonsʼ propagation depends on their energy, thus superluminal photons are permitted due to generalized uncertainty principle. Furthermore, we derive and solve the two-dimensional Klein–Gordon equation in the presence of GUP corrections, and therefore the GUP-corrected emission spectrum due to the Unruh effect is obtained.

The kinematics of cosmic reheating

We calculate the relaxation rate of a scalar field in a plasma of other scalars and fermions with gauge interactions using thermal quantum field theory. It yields the rate of cosmic reheating and thereby determines the temperature of the “hot big bang” in inflationary cosmology. The total rate originates from various processes, including decays and inverse decays as well as Landau damping by scatterings. It involves quantum statistical effects and off-shell transport. Its temperature dependence can be highly non-trivial, making it impossible to express the reheating temperature in terms of the model parameters in a simple way. We pay special attention to the temperature dependence of the phase space due to the modified dispersion relations in the plasma. We find that it can have a drastic effect on the efficiency of perturbative reheating, which depends on the way particles in the primordial plasma interact. For some interactions thermal masses can effectively close the phase space for the dominant dissipative processes and thereby impose an upper bound on the reheating temperature. In other cases they open up new channels of dissipation, hence increase the reheating temperature. At high temperatures we find that the universe can even be heated through couplings to fermions, which are often assumed to be negligible due to Pauli-blocking. These effects may also be relevant for baryogenesis, dark matter production, the fate of moduli and in scenarios of warm inflation.

Inertial Alfven waves in an inhomogeneous bi-Maxwellian plasma

Abstract The Vlasov kinetic equation is solved using gyrokinetic theory and the dielectric tensor for non-relativistic, magnetized, bi-Maxwellian plasmas is calculated. A generalized dispersion relation for kinetic Alfven waves is derived taking into account the density inhomogeneity and temperature anisotropy. The modified dispersion relation thus obtained is then used to examine the propagation characteristics of the kinetic Alfven waves in the inertial regime. The importance of density inhomogeneity and temperature anisotropy for Solar corona is highlighted. The growth rate of the inertial Alfven wave proves that density inhomogeneity acts as a source of free energy.

Dimensional reduction in the sky

We explore the cosmological implications of a mechanism found in several approaches to quantum gravity, whereby the spectral dimension of spacetime runs from the standard value of 4 in the infrared (IR) to a smaller value in the ultraviolet (UV). Specifically, we invoke the picture where the phenomenon is associated with modified dispersion relations. With minimal assumptions, we find that UV behavior leading to 2 spectral dimensions results in an exactly scale-invariant spectrum of vacuum scalar and tensor fluctuations, regardless of the equation of state. The fluctuation production mechanism is analogous to the one known for varying speed of sound/light models and, unlike in inflation, the spectrum is already scale invariant before leaving the horizon, remaining so after freeze-in. In the light of Planck's recent results we also discuss scenarios that break exact scale invariance, such as the possibility that the spectral dimension runs down to a value slightly higher than 2, or runs down to 2 but with an extremely slow transient. We further show that the tensor to scalar ratio is fixed by the UV ratio between the speed of gravity and the speed of light. Not only does our model not require inflation, but at its most minimal it seems incompatible with it. In contrast, we find that running spectral dimensions can improve the outlook of the cyclic/ekpyrotic scenario, solving the main problems present in its simplest and most appealing realizations.

Effects of modified dispersion relation on the thermodynamics of Achúcarro-Ortiz horizon and tunneling radiation probability

The modified dispersion relation was used to study the quantum gravitational effects on the Achucarro-Ortiz horizon. In continue, the quantum gravitationally modified entropy of Achucarro-Ortiz space-time is used to obtain the tunneling radiation probability. The results show that the tunneling radiation probability is modified.

MODIFIED WAVE EQUATION FOR SPINLESS PARTICLES AND ITS SOLUTIONS IN AN EXTERNAL MAGNETIC FIELD

The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the density matrix is obtained. The Schrödinger form of equations is presented and the quantum-mechanical Hamiltonian is found. Exact solutions of the wave equation are obtained for particles in the constant and uniform external magnetic field. The change of the synchrotron radiation radius due to quantum gravity corrections is calculated.

Modified dispersion relation and classically forbidden s-wave emission across the horizon

The classically forbidden s-wave emission of the horizon is studied in this work. The modified dispersion relation was used to obtain the quantum gravity effects. It is shown that the s-wave emission rate across the horizon is modified.