International Journal of Modern Physics D

We offer a preliminary exploration of the two sides of the challenge provided by the recent OPERA data on superluminal neutrinos. On one side we stress that some aspects of this result are puzzling even from the perspective of the wild quantum-gravity literature, where arguments in favor of the possibility of superluminal propagation have been presented, but not considering the possibility of such a sizeable effect for neutrinos of such low energies. We feel this must encourage particularly severe scrutiny of the OPERA result. On the other side, we notice that the OPERA result is reasonably consistent with μ-neutrino-speed data previously obtained at FERMILAB, reported in papers of 2007 and 1979. And it is intriguing that these FERMILAB79 and FERMILAB07 results, when combined with the new OPERA result, in principle provide a window on μ-neutrino speeds at different energies broad enough to compare alternative phenomenological models. We test the discriminating power of such an approach by using as illustrative examples the case of special-relativistic tachyons, the case of momentum-independent violations of the special-relativistic speed law, and the cases of linear and quadratic energy dependence of the speed of ultrarelativistic muon neutrinos. Even just using μ-neutrino data in the range from ~3 GeVs to ~200 GeVs the special-relativistic tachyon and the quadratic-dependence case are clearly disfavoured. The linear-dependence case gives a marginally consistent picture and the momentum-independent scenario fits robustly the data. We also comment on Supernova 1987a and its relevance for consideration of other neutrino species, also in relation with some scenarios that appeared in the large-extra-dimension literature.

It is now known that when a massive star collapses under the force of its own gravity, the final fate of such a continual gravitational collapse will be either a black hole or a naked singularity under a wide variety of physically reasonable circumstances within the framework of general theory of relativity. The research of recent years has provided considerable clarity and insight on stellar collapse, black holes and the nature and structure of spacetime singularities. We discuss several of these developments here. There are also important fundamental questions that remain unanswered on the final fate of collapse of a massive matter cloud in gravitation theory, especially on naked singularities which are hypothetical astrophysical objects and on the nature of cosmic censorship hypothesis. These issues have key implications for our understanding on black hole physics today, its astrophysical applications, and for certain basic questions in cosmology and possible quantum theories of gravity. We consider these issues here and summarize recent results and current progress in these directions. The emerging astrophysical and observational perspectives and implications are discussed, with particular reference to the properties of accretion disks around black holes and naked singularities, which may provide characteristic signatures and could help distinguish these objects.

We discuss whether black holes could persist in a universe which recollapses and then bounces into a new expansion phase. Whether the bounce is of classical or quantum gravitational origin, such cosmological models are of great current interest. In particular, we investigate the mass range in which black holes might survive a bounce and ways of differentiating observationally between black holes formed just after and just before the last bounce. We also discuss the consequences of the universe going through a sequence of dimensional changes as it passes through a bounce.

By following the general guiding principle that nothing should be prescribed or imposed on the universal entity, spacetime, we establish that it is the homogeneity (by which we mean homogeneity and isotropy of space and homogeneity of time) that requires not only a universally constant invariant velocity but also an invariant length given by its constant curvature, Λ and spacetime is completely free of dynamics. Thus c and Λ are the only two true constants of the spacetime structure and no other physical constant could claim this degree of fundamentalness. When matter is introduced, the spacetime becomes inhomogeneous and dynamic, and its curvature then determines by the Bianchi differential identity, the equation of motion for the Einstein gravity. The homogeneity thus demands that the natural state of free spacetime is of constant curvature and the cosmological constant thus emerges as a clear prediction which seems to be borne out by the observations of accelerating expansion of the Universe. However it has no relation to the vacuum energy and it could be envisioned that in terms of the Planck area, the Universe measures 10¹²⁰ units!

Gravitational potentials in the cosmos are deeper than expected from observed visible objects, a phenomenon usually attributed to dark matter, presumably in the form of a new fundamental particle. Until such a particle is observed, the jury remains out on dark matter, and modified gravity models must be considered. The class of models reducing to modified Newtonian dynamics (MOND) in the weak field limit does an excellent job fitting the rotation curves of galaxies, predicting the relation between baryonic mass and velocity in gas-dominated galaxies, and explaining the properties of the local group. Several of the initial challenges facing MOND have been overcome, while others remain. Here we point out the most severe challenge facing MOND.

Accretion onto a black hole transforms the darkest objects in the universe to the brightest. The high energy radiation emitted from the accretion flow before it disappears forever below the event horizon lights up the regions of strong spacetime curvature close to the black hole, enabling strong field tests of General Relativity. I review the observational constraints on strong gravity from such accretion flows, and show how the data strongly support the existence of such fundamental General Relativistic features of a last stable orbit and the event horizon. However, these successes also imply that gravity does not differ significantly from Einstein's predictions above the event horizon, so any new theory of quantum gravity will be very difficult to test.

Given some assumptions, it is possible to derive the most general post-general relativistic theory of gravity for the distant field of a point mass. The force law derived from this theory contains a Rindler term in addition to well-known contributions, a Schwarzschild mass and a cosmological constant. The same force law recently was confronted with solar system precision data. The Rindler force, if present in Nature, has intriguing consequences for gravity at large distances. In particular, the Rindler force is capable of explaining about 10% of the Pioneer anomaly and simultaneously ameliorates the shape of galactic rotation curves.

We consider a nonsingular origin for the universe starting from an Einstein static universe in the framework of a theory which uses two volume elements and Φd⁴x, where Φ is a metric independent density, also curvature, curvature square terms, first order formalism and for scale invariance a dilaton field ϕ are considered in the action. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe and ϕ → -∞, describing our present universe. Surprisingly, avoidance of singularities and stability as ϕ → ∞ imply a positive but small vacuum energy as ϕ → -∞. Zero vacuum energy density for the present universe is the "threshold" for universe creation.

Since the appearance of General Relativity, its intrinsec general covariance has been very often misinterpreted as implying that physically meaningful quantities (and conclusions extracted from the theory) have to be absolutely independent on observers. This incorrect point of view is sometimes expressed by discarding the very concept of observer in the structure and applications of the theory. As we shall stress in this essay, through some examples, the concept of observer is as essential to General Relativity as it is to any physical theory.

The holographic bound asserts that the entropy S of a system is bounded from above by a quarter of the area of a circumscribing surface measured in Planck areas: . This bound is widely regarded a desideratum of any fundamental theory of nature. In fact, the bound is known to be valid for generic systems in three spatial dimensions. However, in this essay we explicitly show that hyperentropic systems (those violating the holographic entropy bound) do exist in higher-dimensional spacetimes. This is a new and surprising result which should be taken into account in the construction of any fundamental quantum theory of gravity.

In this essay we discuss the geometrical embedding method (GEM) for the analysis of the stability of Hamiltonian systems using geometrical techniques familiar from general relativity. This method has proven to be very effective. In particular, we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, this geometrical analysis predicts the observed stability. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very intricate but periodic trajectory. The geometric approach predicts the correct stable motion in this case as well.

We derive an uncertainty relation for the energy density and pressure of a quantum scalar field in a time-dependent, homogeneous and isotropic, classical background, which implies the existence of large fluctuations comparable to their vacuum expectation values. A similar uncertainty relation is known to hold for the field square since the field can be viewed as a Gaussian random variable. We discuss possible implications of these results for the reheating process in scalar field driven inflationary models, where reheating is achieved by the decay of the coherently oscillating inflaton field. Specifically we argue that the evolution after backreaction can seriously be altered by the existence of these fluctuations. For example, in one model the coherence of the inflaton oscillations is found to be completely lost in a very short time after backreaction starts. Therefore we argue that entering a smooth phase in thermal equilibrium is questionable in such models and reheating might destroy the smoothness attained by inflation.

In this essay, we address two long-standing problems of massive gravity: The ghost mode found by Boulware and Deser, and the incompatibility with General Relativity in the massless limit, better known as the vDVZ discontinuity. We present a recent candidate for a ghost-free theory, and show how Einstein's gravity is recovered within a certain macroscopic radius from a mass source, via the Vainshtein mechanism. We also exhibit an exact solution which could account for the late time acceleration of the Universe by means of a small graviton mass.

Brane-world models, where observers are trapped within the thickness of a 3-brane, offer novel perspectives on gravitation and cosmology. In this essay, it is argued that the problem of a late epoch acceleration of the universe is well explained in the framework of a 4-dimensional de Sitter universe embedded in a 5-dimensional de Sitter spacetime. While a 5-dimensional Anti-de Sitter space background is important for studying conformal field theories for its role in the AdS/CFT correspondence, the existence of a 5-dimensional de Sitter space is crucial for finding an effective 4-dimensional Newton constant that remains finite and a normalizable zero-mode graviton wave function.

There is considerable evidence to suggest that field equations of gravity have the same conceptual status as the equations of hydrodynamics or elasticity. We add further support to this paradigm by showing that Einstein"s field equations are identical in form to Navier–Stokes equations of hydrodynamics, when projected on to any null surface. In fact, these equations can be obtained directly by extremizing of entropy associated with the deformations of null surfaces thereby providing a completely thermodynamic route to gravitational field equations. Several curious features of this remarkable connection (including a phenomenon of "dissipation without dissipation") are described and the implications for the emergent paradigm of gravity is highlighted.

Supernovae observations strongly support the presence of a cosmological constant, but its value, which we will call apparent, is normally determined assuming that the universe can be accurately described by a homogeneous model. Even in the presence of a cosmological constant we cannot exclude nevertheless the presence of a small local inhomogeneity which could affect the apparent value of the cosmological constant. Neglecting the presence of the inhomogeneity can in fact introduce a systematic misinterpretation of cosmological data, leading to the distinction between an apparent and the true value of the cosmological constant. But is such a difference distinguishable? Recently we set out to model the local inhomogeneity with a ΛLTB solution and computed the relation between the apparent and the true value of the cosmological constant. In this essay we reproduce the essence of our model with the emphasis on its physical implications.

It is a remarkable fact that all processes occurring in the observable universe are irreversible, whereas the equations through which the fundamental laws of physics are formulated are invariant under time reversal. The emergence of irreversibility from the fundamental laws has been a topic of consideration by physicists, astronomers and philosophers since Boltzmann's formulation of his famous "H" theorem. In this paper, we shall discuss some aspects of this problem and its connection with the dynamics of spacetime, within the framework of modern cosmology. We conclude that the existence of cosmological horizons allows a coupling of the global state of the universe with the local events determined through electromagnetic processes.

One of the manifestations of Einstein Equivalence Principle (EEP) is that a freely falling particle in a gravitational field is following a geodesic. In Einstein's general relativity (GR) this is built in the formulation by assuming the connection to be the Levi-Civita connection. The latter may, however, be demanded to be implied by the dynamics of a generic modified gravity theory, within the Palatini formulation. We show that for extensions of the Einstein GR which are described by a Lagrangian , where g_μν is the metric and R_μαβν is the Riemann curvature tensor, this manifestation of EEP is only fulfilled for a special class of Lagrangians, the Lovelock gravity theories. Our analysis also implies that within the above mentioned set of modified gravity theories only for Lovelock gravity theories metric and Palatini formulations are equivalent.

Infrared gravitons are continually produced during inflation. Like all particles, their contribution to the vacuum energy comes not only from their bare kinetic energy but also from the interactions they have with other gravitons. These interactions can be substantial — despite the particles being highly infrared — because they occur over the enormous spatial volume of the universe. Furthermore, the interactions grow with time evolution because more and more such gravitons come into causal contact with one another. Since gravity is universally attractive, these interactions can act to slow and eventually stop accelerated expansion.

There are discernible and fundamental differences between clocks, waves and physical states in classical physics. These fundamental concepts find a common expression in the context of quantum physics in gravitational fields; matter and light waves, quantum states and oscillator clocks become quantum synonymous through the Planck–Einstein–de Broglie relations and the equivalence principle. With this insight, gravitational effects on quantum systems can be simply and accurately analyzed. Apart from providing a transparent framework for conceptual and quantitative thinking on matter waves and quantum states in a gravitational field, we address and resolve with clarity the recent controversial discussions on the important issue of the relation and the crucial difference between gravimetery using atom interferometers and the measurement of gravitational time dilation.

Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when the corresponding stimulated creation of quanta is considered, the characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary expansion and can be imprinted in the spectrum of primordial inhomogeneities. The non-gaussianities (particularly in the so-called squeezed configuration) in the cosmic microwave background and galaxy distribution can then tell us about the state of the universe that existed at the time when quantum field theory in curved spacetime first emerged as a plausible effective theory.

We describe a recently introduced principle of relative locality which we propose governs a regime of quantum gravitational phenomena accessible to experimental investigation. This regime comprises phenomena in which ℏ and G_N may be neglected, while their ratio, the Planck mass , is important. We propose that M_p governs the scale at which momentum space may have a curved geometry. We find that there are striking consequences for the concept of locality. The description of events in spacetime now depends on the energy used to probe it. But there remains an invariant description of physics in phase space. There is furthermore a reasonable expectation that the geometry of momentum space can be measured experimentally using astrophysical observations.

We make the cosmological constant, Λ, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and is the requirement that the cosmological wave function possess a classical limit. When applied to the Friedmann metric it requires that the cosmological constant measured today, t_U, be , as observed. This is the classical value of Λ that dominates the wave function of the universe. Our new field equation determines Λ in terms of other astronomically measurable quantities. Specifically, it predicts that the spatial curvature parameter of the universe is , which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological history.

If a system falls through a black hole horizon, then its information is lost to an observer at infinity. But we argue that the accessible information is lost before the horizon is crossed. The temperature of the hole limits information carrying signals from a system that has fallen too close to the horizon. Extremal holes have T = 0, but there is a minimum energy required to emit a quantum in the short proper time left before the horizon is crossed. If we attempt to bring the system back to infinity for observation, then acceleration radiation destroys the information. All three considerations give a critical distance from the horizon , where r_H is the horizon radius and ΔE is the energy scale characterizing the system. For systems in string theory where we pack information as densely as possible, this acceleration constraint is found to have a geometric interpretation. These estimates suggest that in theories of gravity we should measure information not as a quantity contained inside a given system, but in terms of how much of that information can be reliably accessed by another observer.

We propose a connection between global physics and local galactic dynamics via quantum gravity. The salient features of cold dark matter (CDM) and modified Newtonian dynamics (MOND) are combined into a unified scheme by introducing the concept of MONDian dark matter which behaves like CDM at cluster and cosmological scales but emulates MOND at the galactic scale.