Gravitational and High Energy Theory

Gravitational physics has grown over the past few decades from a small area of research concerned mainly with mathematical properties of Einstein's theory of general relativity into a broad field whose theoretical aspects range from astrophysics and cosmology to quantum gravity, one of the most challenging boundaries of our current understanding of the nature of matter and spacetime. Gravitational physics has also developed a solid experimental side with the building of a variety of gravitational wave detectors and with high-precision tests of gravitational effects on Earth and in orbit; it has found practical applications in the GPS system as well as in the guidance of spacecraft.

For more details on the gravitational and high-energy theory research program at Ole Miss, see the GR website.

About the Gravitational and High Energy Theory Group

Faculty: Bombelli, Cavaglià, Seggev, and Torma.
Research Scientist: Cardoso

Research in gravitational physics at Ole Miss covers both classical and quantum aspects of gravitational theories. Among the classical aspects, of particular interest are the study of the predictions of the theory, with its highly nonlinear dynamics, for the motion of gravitating bodies, the emission of gravitational waves during the gravitational collapse of massive objects, and for the evolution of the early universe. The quantum aspects are motivated by the current attempts to construct a complete theory of quantum gravity and to understand the geometrical structure of spacetime at the smallest scales.

Classical General Relativity

The simplest systems subject to gravitational forces where one can look for relativistic effects not predicted by Newtonian gravitation are binary systems. In fact, some of the classical tests of relativity involve the dynamics of planets in the solar system. Members of the Ole Miss group have studied various aspects of the relativistic dynamics of gravitating binary systems, including the onset of chaos in the motion around perturbed black holes (this work has generated interest because of its potential consequences for the emitted pattern of gravitational radiation) and the effect of the global evolution of the universe on binary systems (the general issue had been around for a long time, and it is known that the effects are very small, but a qualitatively new contribution to the precession of the orbits was found).

Regarding the structure of the gravitating objects themselves, although they involve an infinite number of degrees of freedom, one can study many of their features using simplified models with a high degree of symmetry or lower-dimensional models of gravity, useful for addressing issues in classical gravity that are too difficult to study in four dimensions. Gravitational collapse in three dimensions, for example, can be discussed analytically for a variety of models. Although gravity in three dimensions does not have propagating degrees of freedom (there are no vacuum gravitational waves), black hole solutions with constant curvature have been found. These analytical solutions allow us to test and compare numerical methods and to discuss in detail the nonlinear dynamics of the gravitational field.

In classical cosmology, Ole Miss researchers have studied the dynamics of models of the early universe, in which the evolution of the gravitational field itself is chaotic; this may have consequences for our understanding of how the present universe emerged from the initial state. In addition, the amplification of the metric quantum fluctuations which are created during inflation is expected to produce a cosmic background of gravitons which, if seen today as relics of the early universe, would give us unique information about the primordial state of our universe. Recent studies of Ole Miss researchers include inflationary graviton production in brane-world models, mixing of massless and massive modes of the tensor perturbation spectrum, and the enhancement of the massless spectral amplitudes.

Another important aspect studied by researchers in the group concerns the stability and perturbation of black holes. The existence of a certain metric satisfying Einstein's equations does not mean it is seen in nature: it has to be stable. The study of perturbations of these objects is of great importance, since it allows one to study gravitational radiation and the interaction of with other objects. For instance, a perturbed black hole radiates energy much like a church bell does: through characteristic ringing tones, called quasinormal modes. We are now studying how can we infer the "shape" of the black hole (its mass and angular momentum) through the detection of these modes.

Quantum Gravity - Theory

The theory of quantum gravity is still in the process of being built. However, several approaches are being actively developed and can be considered promising candidates for the theory. In particular, over the past two decades, two approaches have emerged as the leading ones because they have been developed to a considerable extent and include many features that should be present in a theory of quantum gravity: superstrings and loop quantum gravity.

The loop quantum gravity approach is one in which priority is given to a consistent, non-perturbative, rigorous quantization of gravity as a theory of the spacetime geometry, based on a canonical formalism; matter is then added when the theory is sufficiently well understood. Techniques developed over the past 10 years or so have put loop quantum gravity on a firm mathematical ground and have made it similar to theories of other interactions, particularly gauge theories. The aspects studied at Ole Miss are based mainly on geometrical aspects of this approach, in which the quantum geometry of spacetime at the smallest scales indicates that the continuum picture drawn from our experience at large scales breaks down. Problems studied here include calculating the macroscopic observational effects of the microscopic quantum geometry, and finding quantum states for gravity which have the property that the appear like a classical continuum at large scales.

The gravitational group is also active in string theory. A consistent quantum string theory is only possible in more than four spacetime dimensions. The extra spatial dimensions must either be compactified to a finite size, or a mechanism is needed to localize matter fields on a lower dimensional space, or brane. Randall and Sundrum have proposed a scenario in which the higher-dimensional spacetime is a Z₂-symmetric five-dimensional Anti-de Sitter space with an embedded three-brane to which matter and gauge fields are confined. This model has turned out to be simple enough to obtain analytic results but rich enough to display many of the most fascinating aspects of the brane-world scenario, such as holography and the conjectured AdS/CFT duality between classical gravity in Anti-de Sitter spaces and conformal field theories on the boundary. These new theoretical perspectives have appeared at a time when there has been an explosion in the amount and precision of observational data in cosmology. These data encode information about the early universe, where Einstein's general relativity may be modified. The early universe is a potential laboratory for testing theoretical developments towards quantum gravity.

Quantum Gravity - Phenomenology

Although quantum gravity theory does not yet have an experimental counterpart, there are already a number of ways in which one can look for quantum gravity effects which show up as modifications to results obtained in existing experiments. While this is true even for "conventional" quantum gravity, associated with Planck energy scales of the order of 10¹⁹ GeV, higher-dimensional gravity models lead to the revolutionary possibility that the quantum gravity scale could be well below the Planck scale, even down to electroweak levels. This raises the exciting prospect that quantum gravity effects could be accessible via events at the TeV-scale.

The higher-dimensional nature of gravity in superstring theory gives rise to massive Kaluza-Klein states of the graviton which determine the low-energy phenomenology of extra-dimensional scenarios. By contrast, high-energy scattering events are dominated by non-perturbative gravitational effects, the most striking phenomenon being the formation of gravitational objects such as black holes, string balls, and branes. These objects will be formed at a threshold just above the fundamental energy scale.

If the fundamental gravitational scale is as low as a few TeV, current cosmic ray detectors and the upcoming generation of particle colliders such as the Large Hadron Collider will begin to observe the signatures of gravitational events. On the other hand, the absence of such signatures will place valuable constraints on extra-dimensional models. High-energy physics may be on the verge of a new era of exciting discoveries. Studies at Ole Miss focus on non-perturbative formation of black holes and other exotic objects at super-Planckian scales in particle colliders such as the Large Hadron Collider and the proposed lepton colliders.

Astroparticle Physics

Part of the group's research activity is devoted to the study of ultrahigh energy cosmic rays. UHECRs are particles of unknown origin and composition propagating in space. Collisions of UHECRs with Earth's atmosphere generate air showers that can be detected with terrestrial or space observatories. UHECRs have been observed with energies above 10⁸ TeV, corresponding to a collisional center-of-mass energy of hundreds of TeV. This scale is many orders of magnitude larger than the energy currently accessible in particle collider experiments.

Therefore, UHECRs provide a natural means of investigating high-energy particle physics. Small violations of Lorentz symmetry due to quantum gravity effects might also affect various UHECR-related astrophysical observations, such as the evaluation of the GZK limit. In all these models, departures from the standard model predictions are expected in interaction cross sections and air shower development.

Mathematical Physics

Techniques from integrable systems are very effective in the study of many different classical and quantum models. Often this approach clarifies issues that cannot be addressed by more conventional methods of investigation. The theory of quantization of constrained systems with a finite number of degrees of freedom is essential in the discussion of formal issues in quantum cosmology and lower-dimensional gravity. For instance, two-dimensional dilaton gravity with an arbitrary potential is proved to be completely integrable by a Backlünd transformation. The integrability properties of two-dimensional dilaton gravity show that the system can be cast in a two-dimensional conformal nonlinear sigma model. Group averaging procedure can be successfully applied to kinematical coherent states to obtain physical semi-classical states. This technique turns out to be surprisingly efficient, suggesting that it may well be possible to use kinematical structures to analyze the semi-classical behavior of physical states of an interesting class of constrained systems.