Deformed Dispersion Relations Research Articles

Note about string theory with deformed dispersion relations

The goal of this short paper is to find Lagrangian for bosonic string with deformed dispersion relation proposed by J. Magueijo and L. Smolin in 2004. We also show that in the preferred case \(f=g\) this Lagrangian reduces into Nambu-Gotto form of relativistic string without modification of the dispersion relation.

Effects of modified dispersion relations on free Fermi gas: Equations of state and applications in astrophysics

Deformed dispersion relations are considered in the study of equations of state of Fermi gas with applications to compact objects. Different choices of deformed energy relations are used in the formulation of our model. As a first test, we consider a relativistic star with a simple internal structure. The mass-radius diagrams obtained suggest a positive influence of deformed Fermi gas, depending of the functions employed. In addition, we comment on how realistic equations of state, in which interactions between nucleons are taken into account, can be addressed.

Superfluid vacuum theory and deformed dispersion relations

Using the logarithmic superfluid model of physical vacuum, one can formulate an essentially quantum post-relativistic theory, which successfully recovers Einstein’s theory of relativity in low-momenta limit, but otherwise has different foundations and predictions. We present an analytical example of the dispersion relation and show that it should have a Landau form which ensures the suppression of dissipative fluctuations. We show that in the low-momentum sector of the theory, a dispersion relation becomes relativistic with small deformations, such that a photon acquires effective mass, but a much more complex picture arises at large momenta.

Fermionic string theories with deformed dispersion relations

Fermionic string theories with deformed dispersion relations

Solving the flatness problem with an anisotropic instanton in Hořava-Lifshitz gravity

In Ho\v{r}ava-Lifshitz gravity a scaling isotropic in space but anisotropic in spacetime, often called anisotropic scaling with the dynamical critical exponent z=3, lies at the base of its renormalizability. This scaling also leads to a novel mechanism of generating scale-invariant cosmological perturbations, solving the horizon problem without inflation. In this paper we propose a possible solution to the flatness problem, in which we assume that the initial condition of the Universe is set by a small instanton respecting the same scaling. We argue that the mechanism may be more general than the concrete model presented here, and rely simply on the deformed dispersion relations of the theory, and on equipartition of the various forms of energy at the starting point.

Quantum Gravity Effects in Statistical Mechanics with Modified Dispersion Relation

Planck scale inspired theories which are also often accompanied with maximum energy and/or momentum scale predict deformed dispersion relations compared to ordinary special relativity and quantum mechanics. In this paper, we resort to the methods of statistical mechanics in order to determine the effects of a deformed dispersion relation along with an upper bound in the partition function that maximum energy and/or momentum scale can have on the thermodynamics of photon gas. We also analyzed two distinct quantum gravity models in this paper.

Noncommutative scalar fields in compact spaces: quantization and implications

In this paper we consider a two component scalar field theory, with noncommutativity in its conjugate momentum space. We quantize such a theory in a compact space with the help of dressing transformations and we reveal a significant effect of introducing such noncommutativity as the splitting of the energy levels of each individual mode that constitutes the whole system. We further compute the thermal partition function exactly with predicted deformed dispersion relations from noncommutative theories and compare the results with usual results. It is found that thermodynamic quantities in noncommutative models, irrespective of whether the model is more deformed in infrared/UV region, show deviation from standard results in high temperature region.

Reappraisal of a model for deformed special relativity

We revisit one of the earliest proposals for deformed dispersion relations in the light of recent results on dynamical dimensional reduction and production of cosmological fluctuations. Depending on the specification of the measure of integration and the addition rule in momentum space the model may be completed so as to merely deform Lorentz invariance, or so as to introduce a preferred frame. Models which violate Lorentz invariance have a negative UV asymptotic dimension and a very red spectrum of quantum vacuum fluctuations. Instead, models which preserve frame independence can exhibit running to a UV dimension of two, and a scale-invariant spectrum of fluctuations. The bispectrum of the fluctuations is another point of divergence between the two casings proposed here for the original model.

Vacuum fluctuations in theories with deformed dispersion relations

We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations undeformed and transferring all the nontrivial effects to the integration measure in momentum space. Using this description we propose a general quantization procedure, which should be applicable whether or not the theory explicitly introduces a preferred frame. Based on this scheme we evaluate the power spectrum of quantum vacuum fluctuations. We find that in all theories which run to two dimensions in the ultraviolet the vacuum fluctuations, in the ultraviolet regime, are scale invariant. This is true in flat space but also for ``inside the horizon'' modes in an expanding universe. We spell out the conditions upon the gravity theory for this scale invariance to be preserved as the modes are frozen-in outside the horizon. We also digress on the meaning of dimensionality (in momentum and position space) and suggest that the spectral index could itself provide an operational definition of dimensionality.

Intermediate inflation from rainbow gravity

It is possible to dualize theories based on deformed dispersion relations and Einstein gravity so as to map them into theories with trivial dispersion relations and rainbow gravity. This often leads to ``dual inflation'' without the usual breaking of the strong energy condition. We identify the dispersion relations in the original frame which map into ``intermediate'' inflationary models. These turn out to be particularly simple: power-laws modulated by powers of a logarithm. The fluctuations predicted by these scenarios are near, but not exactly scale-invariant, with a red running spectral index. These dispersion relations deserve further study within the context of quantum gravity and the phenomenon of dimensional reduction in the ultraviolet.

Rainbow gravity and scale-invariant fluctuations

We reexamine a recently proposed scenario where the deformed dispersion relations associated with a flow of the spectral dimension to a UV value of 2 leads to a scale-invariant spectrum of cosmological fluctuations, without the need for inflation. In that scenario Einstein gravity was assumed. The theory displays a wavelength-dependent speed of light but by transforming to a suitable ``rainbow frame'' this feature can be removed, at the expense of modifying gravity. We find that the ensuing rainbow gravity theory is such that gravity switches off at high energy (or at least leads to a universal conformal coupling). This explains why the fluctuations are scale invariant on all scales: there is no horizon scale as such. For dispersion relations that do not lead to exact scale invariance we find instead esoteric inflation in the rainbow frame. We argue that these results shed light on the behavior of gravity under the phenomenon of dimensional reduction.

Conceptual problem for noncommutative inflation and the new approach for nonrelativistic inflationary equation of state

In a previous paper, we connected the phenomenological non-commutative inflation of Alexander, Brandenberger and Magueijo (2003) and Koh S and Brandenberger (2007) with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group like procedure in which even Hopf algebras (roughly the symmetries of non-commutative spaces) could lead to the equation of state of inflationary radiation. In this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons is bounded from above) and the group structure of the representation which leads to the fundamental inflationary equations of state. We show that such a group structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like in scattering theory, for example. Therefore, it follows that the procedure to obtain those equations should be modified according to one of two possible proposals that we consider here. One of them relates to the general theory of Hopf algebras while the other is based on a representation theorem of Von Neumann algebras, a proposal already suggested by us to take into account interactions in the inflationary equation of state. This reopens the problem of finding inflationary deformed dispersion relations and all developments which followed the first paper of Non-commutative Inflation.

PHOTON-NEUTRINO INTERACTION IN θ-EXACT COVARIANT MODEL: PHENOMENOLOGY AND QUANTUM PROPERTIES

We construct the theta-exact covariant noncommutative model and obtain various closed constraints on the noncommutative scale from inelastic neutrino-nucleon scatterings, from plasmon decay into neutrino pair, from the Big Bang Nucleosynthesis and from the reheating phase after inflation, respectively. We find neutrino two-point function in a closed form and decoupling of the UV divergent term from softened UV/IR mixing term. Deformed dispersion relations at low energies are capable to account for the recent results from the OPERA collaboration on the superluminal speed of the muon neutrinos.

Quantum gravity, field theory and signatures of noncommutative spacetime

A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what extent noncommutative gauge theories may be regarded as gauge theories of gravity. UV/IR mixing is explained in detail and we describe its relations to renormalization, to gravitational dynamics, and to deformed dispersion relations in models of quantum spacetime of interest in string theory and in doubly special relativity. We also discuss some potential experimental probes of spacetime noncommutativity.

κ-Minkowski spacetime as the result of Jordanian twist deformation

Two one-parameter families of twists providing $\ensuremath{\kappa}$-Minkowski $*$ product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module algebra point of view, which is strictly related with Drinfeld's twisting tensor technique. The other one relies on an appropriate extension of ``deformed realizations'' of nondeformed Lorentz algebra by the quantum Minkowski algebra. This extension turns out to be de Sitter Lie algebra. We show the way both approaches are related. The second path allows us to calculate deformed dispersion relations for toy models ensuing from different twist parameters. In the Abelian case, one recovers $\ensuremath{\kappa}$-Poincar\'e dispersion relations having numerous applications in doubly special relativity. Jordanian twists provide a new type of dispersion relations which in the minimal case (related to Weyl-Poincar\'e algebra) takes an energy-dependent linear mass deformation form.

TRANS-PLANCKIAN PHYSICS AND NON-COMMUTATIVE INFLATION

Non-commutativity of spacetime at the Planck scale may deform the usual dispersion relations. And these deformed dispersion relations could lead to the accelerating phase without a scalar field. In this paper, we have calculated the spectral index and the running of spectral index in a non-commutative inflation model. Non-commutative inflation with thermal radiation gives a scale invariant spectrum in the limit w → −1 and negative running spectral index which are consistent with the WMAP 3-year results.

Thermodynamics of a photon gas and deformed dispersion relations

We resort to the methods of statistical mechanics in order to determine the effects that a deformed dispersion relation has upon the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function, pressure, internal energy, entropy, and specific heat are calculated. It will be shown that the breakdown of Lorentz invariance can be interpreted as a repulsive interaction, among the photons. Additionally, it will be proved that the presence of a deformed dispersion relation entails an increase in the entropy of the system. In other words, as a consequence of the loss of the aforementioned symmetry the number of microstates available to the corresponding equilibrium state grows.

Constraining Lorentz violations with gamma ray bursts

Gamma ray bursts are excellent candidates for constraining physical models which breakLorentz symmetry. We consider deformed dispersion relations which break theboost invariance and lead to an energy-dependent speed of light. In these models,simultaneously emitted photons from cosmological sources reach Earth with a spectral timedelay that depends on the symmetry breaking scale. We estimate the possiblebounds which can be obtained by comparing the spectral time delays with thetime resolution of available telescopes. We discuss the best strategy to reach thestrongest bounds. We compute the probability of detecting bursts that improve thecurrent bounds. The results are encouraging. Depending on the model, it is possibleto build a detector that within several years will improve the present limits of0.015 mpl.

Deformed dispersion relations and the degree of the coherence function

The analysis of the modifications that the presence of a deformed dispersion relation entails in the roots of the so--called degree of coherence function, for a beam embodying two different frequencies and moving in a Michelson interferometer, is carried out. The conditions to be satisfied, in order to detect this kind of quantum gravity effect, are also obtained.

Deformed dispersion relations and the Hanbury–Brown–Twiss Effect

In the present work we analyze the possibility of detecting some deformed dispersion relations, emerging in some quantum--gravity models, resorting to the so--called Hanbury--Brown--Twiss effect. It will be proved that in some scenarios the possibilities are not pessimistic. Forsooth, for some values of the corresponding parameters the aforementioned effect could render interesting outcomes.