We describe a scheme for the exploration of quantum gravity phenomenology focussing on effects that could be thought as arising from a fundamental granularity of space-time. In contrast with the simplest assumptions, such granularity is assumed to respect Lorentz Invariance but is otherwise left unspecified. The proposal is fully observer covariant, it involves non-trivial couplings of curvature to matter fields and leads to a well defined phenomenology. We present the effective Hamiltonian which could be used to analyze concrete experimental situations, some of which are briefly described, and we shortly discuss the degree to which the present proposal is in line with the fundamental ideas behind the equivalence principle.
In the past decade the phenomenology of quantum gravity has been dominated by the search of violations of Lorentz invariance. However, there are very serious arguments that led us to assume that this invariance is a symmetry in Nature. This motivated us to construct a phenomenological model describing how a Lorentz invariant granular structure of spacetime could become manifest. The proposal is fully covariant, it involves non-trivial couplings of curvature to matter fields and leads to a well defined phenomenology.
Theories of gravitation without Lorentz invariance are candidates of low-energy descriptions of quantum gravity. In this review we will describe the phenomenological consequences of the candidates associated to the existence of a preferred time direction
Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a phenomenological model of massive particles propagating in a Minkowski spacetime which arises from an underlying causal set. The particles undergo a Lorentz invariant diffusion in phase space, and we speculate on whether this could have any bearing on the origin of high energy cosmic rays.
If quantum gravity violates Lorentz symmetry, the prospects for observational guidance in understanding quantum gravity improve considerably. This article briefly reviews previous work on Lorentz violation (LV) and discusses aspects of the effective field theory framework for parametrizing LV effects. Current observational constraints on LV are then summarized, focusing on effects in QED at order E/M_Planck.
Violations of spacetime symmetries have recently been identified as promising signatures for physics underlying the Standard Model. The present talk gives an overview over various topics in this field: The motivations for spacetime-symmetry research, including some mechanisms for Lorentz breaking, are reviewed. An effective field theory called the Standard-Model Extension (SME) for the description of the resulting low-energy effects is introduced, and some experimental tests of Lorentz and CPT invariance are listed.
The notion that gravitation might lead to a breakdown of standard space-time structure at small distances, and that this might affect the propagation of ordinary particles has led to a program to search for violations of Lorentz invariance as a probe of quantum gravity. Initially it was expected that observable macroscopic effects caused by microscopic violations of Lorentz invariance would necessarily be suppressed by at least one power of the small ratio between the Planck length and macroscopic lengths. Here we discuss the implications of the fact that this expectation is in contradiction w…
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 reso…
We describe a refined version of a previous proposal for the exploration of quantum gravity phenomenology. Unlike the original scheme, the one presented here is free from sign ambiguities while it shares with the previous one the essential features. It focuses on effects that could be thought as arising from a fundamental granularity of quantum space-time. The sort of schemes we consider are in sharp contrast with the simplest scenarios in that such granularity is assumed to respect Lorentz Invariance but it remains otherwise unspecified. The proposal is fully observer covariant, it involves n…
A consistent theory of quantum gravity (QG) at Planck scale almost sure contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models with nonlinear dispersions and related Finsler metrics and fundamental geometric objects (nonlinear and linear connections) depending on velocity/ momentum variables. We prove that the trapping brane mechanism provides an accurate description of gravitational and matter field phenomena with LV over a wide range of distance scales and recovering in a systema…
Quantum gravity phenomenology is the strategy towards quantum gravity where the priority is to make contact with experiments. Here I describe what I consider to be the best procedure to do quantum gravity phenomenology. The key step is to have a generic parametrization which allows one to perform self-consistency checks and to deal with many different experiments. As an example I describe the role that the Standard Model Extension has played when looking for Lorentz violation.
The search for a quantum theory of gravity has been one of the main aims of theoretical physics for many years by now. However the efforts in this direction have been often hampered by the lack of experimental/observational tests able to select among, or at least constrain, the numerous quantum gravity models proposed so far. This situation has changed in the last decade thanks to the realization that some QG inspired violations of Lorentz symmetry could be constrained using current experiments and observations. This study it is not only allowing us to test at higher and higher energies a fund…
We consider a model of Quantum Gravity phenomenology, based on the idea that space-time may have some unknown granular structure that respects the Lorentz symmetry. The proposal involves non-trivial couplings of curvature to matter fields and leads to a well defined phenomenology. In this manuscript, a brief description of the model is presented together with some results obtained using linearized gravity and the Newtonian limit, which could be useful when comparing with real experiments.
It is well-known that the Universe is opaque to the propagation of Ultra-High-Energy Cosmic Rays (UHECRs) since these particles dissipate energy during their propagation interacting with the Cosmic Microwave Background (CMB) mainly in the so-called GZK cut-off phenomenon. Some experimental evidence seems to hint at the possibility of a dilation of the GZK predicted opacity sphere. It is well-known that kinematical perturbations caused by supposed quantum gravity (QG) effects can modify the foreseen GZK opacity horizon. The introduction of Lorentz Invariance Violation (LIV) can indeed reduce, i…
We study the post-Newtonian expansion of a class of Lorentz-violating gravity theories that reduce to khronometric theory (i.e. the infrared limit of Horava gravity) in high-acceleration regimes, and reproduce the phenomenology of the modified Newtonian dynamics (MOND) in the low-acceleration, non-relativistic limit. Like in khronometric theory, Lorentz symmetry is violated in these theories by introducing a dynamical scalar field (the "khronon") whose gradient is enforced to be timelike. As a result, hypersurfaces of constant khronon define a preferred foliation of the spacetime, and the khro…
In this paper we perform a full gauge-fixing of the phase space of four dimensional General Relativity (GR) of Lorentzian signature for the time symmetric case, using the CDJ variables. In particular, the Gauss' law constraint in the chosen gauge meets the conditions of the Cauchy-Kovalevskaya theorem for first order, quasilinear PDEs. This implies the existence of a unique analytic solution to the initial value constraints problem in some region of 3-space, featuring four free functions per spacetime point. This result constitutes a step toward addressal of the reduced phase space problem of …
Over the last few years the study of possible Planck-scale departures from classical Lorentz symmetry has been one of the most active areas of quantum-gravity research. We now have a satisfactory description of the fate of Lorentz symmetry in the most popular noncommutative spacetimes and several studies have been devoted to the fate of Lorentz symmetry in loop quantum gravity. Remarkably there are planned experiments with enough sensitivity to reveal these quantum-spacetime effects, if their magnitude is only linearly suppressed by the Planck length. Unfortunately, in some quantum-gravity sce…
The idea that quantum gravity manifestations would be associated with a violation of Lorentz invariance is very strongly bounded and faces serious theoretical challenges. Other related ideas seem to be drowning in interpretational quagmires. This leads us to consider alternative lines of thought for such phenomenological search. We discuss the underlying viewpoints and briefly mention their possible connections with other current theoretical ideas.
Investigations of the possibility that some novel ``quantum" properties of spacetime might induce a modification dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry. More recently several studies have considered the possibility of a ``doubly special relativity", in which the modification of the dispersion relation emerges from a framework with both the Planck scale and the speed-of-light scale as characteristic scales of a deformation of the Lorentz transformations. For the schemes with broken Lorentz symmetry at the Planck scale there is a large …
Covariant models of loop quantum gravity generically imply dynamical signature change at high density. This article presents detailed derivations that show the fruitful interplay of this new kind of signature change with wave-function proposals of quantum cosmology, such as the no-boundary and tunneling proposals. In particular, instabilities of inhomogeneous perturbations found in a Lorentzian path-integral treatment are naturally cured. Importantly, dynamical signature change does not require Planckian densities when off-shell instantons are relevant.
New phenomenological models of Quantum Gravity have suggested that a Lorentz-Invariant discrete spacetime structure may become manifest through a nonstandard coupling of matter fields and spacetime curvature. On the other hand, there is strong experimental evidence suggesting that neutrino oscillations cannot be described by simply considering neutrinos as massive particles. In this manuscript we motivate and construct one particular phenomenological model of Quantum Gravity that could account for the so-called neutrino anomalies.
In this paper, we present a non-geometrodynamic quantum Yang-Mills theory of gravity based on the homogeneous Lorentz group within the general framework of the Poincare gauge theories. The obstacles of this treatment are that first, on the one hand, the gauge group that is available for this purpose is non-compact. On the other hand, Yang-Mills theories with non-compact groups are rarely healthy, and only a few instances exist in the literature. Second, it is not clear how the direct observations of space-time waves can be explained when space-time has no dynamics. We show that the theory is u…
Over the last few years part of the quantum-gravity community has adopted a more optimistic attitude toward the possibility of finding experimental contexts providing insight on non-classical properties of spacetime. I review those quantum-gravity phenomenology proposals which were instrumental in bringing about this change of attitude, and I discuss the prospects for the short-term future of quantum-gravity phenomenology.
Quantum gravity effects are traditionally tied to short distances and high energies. In this essay we argue that, perhaps surprisingly, quantum gravity may have important consequences for the phenomenology of the infrared. We center our discussion around a conception of quantum gravity involving a notion of quantum spacetime that arises in metastring theory. This theory allows for an evolution of a cosmological Universe in which string-dual degrees of freedom decouple as the Universe ages. Importantly such an implementation of quantum gravity allows for the inclusion of a fundamental length sc…
The main idea in the present work is the definition of an experimental proposal for the detection of the number of extra{compact dimensions contained as a core feature in String Theory. This goal will be achieved as a consequence of the fact that the density of states of a bosonic gas does depend upon the number and geometry of the involved space{like dimensions. In particular our idea concerns the detection of the discontinuity of the specific heat at the condensation temperature as a function of the number of particles present in the gas. It will be shown that the corresponding function betw…
In this talk, results from the gravitational sector of the Standard-Model Extension (SME) are discussed. The weak-field phenomenology of the resulting modified gravitational field equations is explored. The application of the results to a variety of modern gravity experiments, including lunar laser ranging, Gravity Probe B, binary pulsars, and Earth-laboratory tests, shows promising sensitivity to gravitational coefficients for Lorentz violation in the SME.
The idea that quantum gravity manifestations would be associated with a violation of Lorentz invariance is very strongly bounded and faces serious theoretical challenges. This leads us to consider an alternative line of thought for such phenomenological search. We discuss the underlying viewpoint and briefly mention its possible connections with current theoretical ideas. We also outline the challenges that the experimental search of the effects would seem to entail.
Different proposals for the wave function of the universe are analyzed, with an emphasis on various forms of the tunneling proposal. The issues discussed include the equivalence of the Lorentzian path integral and outgoing-wave proposals, the definitions of the outgoing waves and of superspace boundaries, topology change and the corresponding modification of the Wheeler-DeWitt equation. Also discussed are the "generic" boundary conditions and the third quantization approach.
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to develop a model of angular corrections to local, continuum flat-space 3-geometries. The physical effects involve neither breaking of local Lorentz invariance nor Planck scale suppression, but rather reply on only the combinatorics of SU(2) recouping theory. Bhabha scattering is discussed as an example of how the effects might be observationally accessible…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to develop a model of angular corrections to local, continuum flat-space 3-geometries. The physical effects involve neither breaking of local Lorentz invariance nor Planck scale suppression, but rather reply on only the combinatorics of SU(2) recoupling. Bhabha scattering is discussed as an example of how the effects might be observationally accessible.
Spontaneous Lorentz violation is a viable mechanism to look for Planck scale physics. In this work, we study spontaneous Lorentz violation models, in flat spacetime, where a vector field produces such a violation and matter is modeled by a complex scalar field. We show that it is possible to construct a Hamilton density for which the evolution respects the dynamical constraints. However, we also find that the initial data, as required by standard field theory, does not determine the fields evolution in a unique way. In addition, we present some examples where the physical effects of such ambig…
We present a method to calculate the nonrelativistic hamiltonian for the minimal Standard-Model Extension matter sector in a uniform gravitational field. The resulting hamiltonian coincides with earlier results in the corresponding limits but it also includes spin-dependent terms that were previously unknown. The phenomenology associated with this hamiltonian is briefly discussed.
Motivated by scenarios of quantum gravity, Planck-suppressed deviations from Lorentz invariance are expected at observable energies. Ultra-High-Energy Cosmic Rays, the most energetic particles ever observed in nature, yielded in the last two years strong constraints on deviations suppressed by $O(E^{2}/\Mpl^{2})$ and also, for the first time, on space-time foam, stringy inspired models of quantum gravity. We review the most important achievements and discuss future outlooks.
Research during the last decade demonstrates that effects originating on the Planck scale are currently being tested in multiple observational contexts. In this review we discuss quantum gravity phenomenological models and their possible links to loop quantum gravity. Particle frameworks, including kinematic models, broken and deformed Poincaré symmetry, non-commutative geometry, relative locality and generalized uncertainty principle, and field theory frameworks, including Lorentz violating operators in effective field theory and non-commutative field theory, are discussed. The arguments rela…
The standard approaches of phenomenology of Quantum Gravity have usually explicitly violated Lorentz invariance, either in the dispersion relation or in the addition rule for momenta. We investigate whether it is possible in 3+1 dimensions to have a non local deformation that preserves fully Lorentz invariance, as it is the case in 2+1D Quantum Gravity. We answer positively to this question and show for the first time how to construct a homogeneously curved momentum space preserving the full action of the Lorentz group in dimension 4 and higher, despite relaxing locality. We study the property…
One of the most difficult questions in present-day physics concerns a fundamental theory of space, time, and matter that incorporates a consistent quantum description of gravity. There are various theoretical approaches to such a quantum-gravity theory. Nevertheless, experimental progress is hampered in this research field because many models predict deviations from established physics that are suppressed by some power of the Planck scale, which currently appears to be immeasurably small. However, tests of relativity theory provide one promising avenue to overcome this phenomenological obstacl…
We propose general f(R,T,R_{μν}T^{μν}) theory as generalization of covariant Horava-like gravity with dynamical Lorentz symmetry breaking. FRLW cosmological dynamics for several versions of such theory is considered. The reconstruction of the above action is explicitly done, including the numerical reconstruction for the occurrence of ΛCDM universe. De Sitter universe solutions in the presence of non-constant fluid are also presented. The problem of matter instability in f(R,T,R_{μν}T^{μν}) gravity is discussed.
In recent work, we introduced Picard-Lefschetz theory as a tool for defining the Lorentzian path integral for quantum gravity in a systematic semiclassical expansion. This formulation avoids several pitfalls occurring in the Euclidean approach. Our method provides, in particular, a more precise formulation of the Hartle-Hawking no boundary proposal, as a sum over real Lorentzian four-geometries interpolating between an initial three-geometry of zero size, {\it i.e}, a point, and a final three-geometry. With this definition, we calculated the no boundary amplitude for a closed universe with a c…
We discuss new possible tunneling processes in the presence of gravity. We formulate quantum tunneling using the Wheeler-deWitt canonical quantization and the WKB approximation. The distinctive feature of our formulation is that it accommodates the coexistence of Euclidean and Lorentzian evolution. It opens up a new possibility of quantum tunneling; e.g. a bubble wall itself tunnels the potential barrier pulling the field nearby, where the wall region experiences the Euclidean evolution while the other regions experience the Lorentzian evolution simultaneously. We execute numerical analysis an…
Hořava gravity is a attempt to construct a renormalizable theory of gravity by breaking the Lorentz Invariance of the gravitational action at high energies. The underlying principle is that Lorentz Invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low energy limit of Hořava gravity in its non-projectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than $cH_0…
We discuss situations under which Lorentz symmetry is violated in effective gravitational field theories that arise in the low-energy limit of strings. In particular, we discuss spontaneous violation of the symmetry by the ground state of the system. In the flat space-time limit, the effective theory of the broken Lorentz Symmetry acquires a form that belongs to the general framework of the so-called Standard Model Extension (SME) formalism. A brief review of this formalism is given before we proceed to describe a concrete example, where we discuss a Lorentz-symmetry-Violating (LV) string-insp…
We construct a positive complexifier, differentiable almost everywhere on the classical phase space of real triads and $SU(2)$ connections, which generates a Wick Transform from Euclidean to Lorentzian gravity everywhere except on a phase space set of measure zero. This Wick transform assigns an equal role to the self dual and anti-self dual Ashtekar variables in quantum theory. We argue that the appropriate quantum arena for an analysis of the properties of the Wick rotation is the diffeomorphism invariant Hilbert space of Loop Quantum Gravity (LQG) rather than its kinematic Hilbert space. We…
The class of covariant gravity theories which have nice ultraviolet behavior and seem to be (super)-renormalizable is proposed. The apparent breaking of Lorentz invariance occurs due to the coupling with the effective fluid which is induced by Lagrange multiplier constrained scalar field. Spatially-flat FRW cosmology for such covariant field gravity may have accelerating solutions. Renormalizable versions of more complicated modified gravity which depends on Riemann and Ricci tensor squared may be constructed in the same way.
We present an analogue spacetime model that reproduces the salient features of the most common ansatz for quantum gravity phenomenology. We do this by investigating a system of two coupled Bose-Einstein condensates. This system can be tuned to have two "phonon" modes (one massive, one massless) which share the same limiting speed in the hydrodynamic approximation [Phys. Rev. D72 (2005) 044020, gr-qc/0506029; cond-mat/0409639]. The system nevertheless possesses (possibly non-universal) Lorentz violating terms at very high energies where "quantum pressure" becomes important. We investigate the p…
So called "analogue models" use condensed matter systems (typically hydrodynamic) to set up an "effective metric" and to model curved-space quantum field theory in a physical system where all the microscopic degrees of freedom are well understood. Known analogue models typically lead to massless minimally coupled scalar fields. We present an extended "analogue space-time" programme by investigating a condensed-matter system - in and beyond the hydrodynamic limit - that is in principle capable of simulating the massive Klein-Gordon equation in curved spacetime. Since many elementary particles h…
Astrophysical tests of Planck-suppressed Lorentz violations had been extensively studied in recent years and very stringent constraints have been obtained within the framework of effective field theory. There are however still some unresolved theoretical issues, in particular regarding the so called "naturalness problem" - which arises when postulating that Planck-suppressed Lorentz violations arise only from operators with mass dimension greater than four in the Lagrangian. In the work presented here we shall try to address this problem by looking at a condensed-matter analogue of the Lorentz…
Among the most studied approaches to introduce the breaking of Lorentz symmetry, the generic approach is one of the most frequently used for phenomenology, it converges on the modification of the free particle dispersion relation. Using this approach in the photon sector, we have calculated the squared probability amplitude for vacuum Cherenkov radiation and photon decay by correcting the QED coupling at tree level and first order in LIV parameters. For the lower order energy correction we calculate the emission and decay rate for each process.
I give a brief overview of some Quantum-Gravity-Phenomenology research lines, focusing on studies of cosmic rays and gamma-ray bursts that concern the fate of Lorentz symmetry in quantum spacetime. I also stress that the most valuable phenomenological analyses should not mix too many conjectured new features of quantum spacetime, and from this perspective it appears that it should be difficult to obtain reliable guidance on the quantum-gravity problem from the analysis of synchrotron radiation from the Crab nebula and from the analysis of phase coherence of light from extragalactic sources. Fo…
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…
The minimal theory of quasidilaton massive gravity with or without a Horndeski-type kinetic term for the quasidilaton field propagates only three physical modes: the two massive tensor polarizations and one scalar mode. This reduced number of degrees of freedom is realized by a Lorentz symmetry violation at cosmological scales and the presence of appropriate constraints that remove unwanted modes. Vacuum cosmological solutions have been considered in a previous work, and it has been shown that the late-time de Sitter attractor is stable under inhomogeneous perturbations. In this work, we explo…
A handful of recent papers has been devoted to proposals of experiments capable of testing some candidate quantum-gravity phenomena. These lecture notes emphasize those aspects that are most relevant to the questions that come to mind when one is exposed for the first time to these research developments: How come theory and experiments are finally meeting in spite of all the gloomy forecasts that pervade traditional reviews? Is this a case of theorists having put forward more and more speculative ideas until a point was reached at which conventional experiments could rule out the proposed phen…
We investigate the minimal theory of massive gravity (MTMG) recently introduced. After reviewing the original construction based on its Hamiltonian in the vielbein formalism, we reformulate it in terms of its Lagrangian in both the vielbein and the metric formalisms. It then becomes obvious that, unlike previous attempts in the literature of Lorentz-violating massive gravity, not only the potential but also the kinetic structure of the action is modified from the de Rham-Gabadadze-Tolley (dRGT) massive gravity theory. We confirm that the number of physical degrees of freedom in MTMG is two at …
Local Lorentz transformations play an important role in teleparallel gravity theories, in which a tetrad is conventionally employed as a fundamental field variable describing the gravitational field. It is commonly understood that modifications of general relativity in the teleparallel framework break a certain notion of local Lorentz invariance, which is present in the pure tetrad formulation of such theories, while another notion present in the covariant formulation is preserved. We illuminate these different notions from a geometric perspective, and distinguish them from what is commonly un…
We show that coupling the Standard Model to a Lorentz symmetry violating sector may co-exist with viable phenomenology, provided that the interaction between the two is mediated by higher-dimensional operators. In particular, if the new sector acquires anisotropic scaling behavior above a "Horava-Lifshitz" energy scale L_HL and couples to the Standard Model through interactions suppressed by M_P, the transmission of the Lorentz violation into the Standard Model is protected by the ratio L_HL^2/M_P^2. A wide scale separation, L_HL<<M_P, can then make Lorentz-violating terms in the Standard Mode…
In this brief, and by no means complete, review I discuss situations in string theory, in which Lorentz Invariance Violation may occur in a way consistent with world-sheet conformal invariance, thereby leading to acceptable, in principle, string backgrounds. In particular, I first discuss spontaneous Lorentz violation in (non supersymmetric) open string field theory. Then, I move onto a discussion of gravity-induced modified dispersion relations in non-critical (Liouville) strings, in the sense of an induced Finsler-like geometry depending on both coordinates and momenta, for string propagatio…
