Narrow Results

In the summer of 2023, the pulsar timing arrays (PTAs) announced a compelling evidence for the existence of a nanohertz stochastic gravitational wave background (SGWB). Despite this breakthrough, however, several critical questions remain unanswered: What is the source of the signal? How can cosmic variance be accounted for? To what extent can we constrain nanohertz gravity? When will individual supermassive black hole binaries become observable? And how can we achieve a stronger detection? These open questions have spurred significant interests in PTA science, making this an opportune moment to revisit the astronomical and theoretical foundations of the field, as well as the data analysis techniques employed. In this review, we focus on the theoretical aspects of the SGWB as detected by PTAs. We provide a comprehensive derivation of the expected signal and its correlation, presented in a pedagogical manner, while also addressing current constraints. Looking ahead, we explore future milestones in the field, with detailed discussions on emerging theoretical considerations such as cosmic variance, the cumulants of the one- and two-point functions, subluminal gravitational waves, and the anisotropy and polarization of the SGWB.

A possible solution to the problem of providing a spacetime description of the transmission of signals for quantum entangled states is obtained by using a bimetric spacetime structure, in which quantum entanglement measurements alter the structure of the classical relativity spacetime. A bimetric gravity theory locally has two lightcones, one which describes classical special relativity and a larger lightcone which allows light signals to communicate quantum information between entangled states, after a measurement device detects one of the entangled quantum states. This theory would remove the tension that exists between macroscopic classical, local gravity and macroscopic nonlocal quantum mechanics.

We investigate the possibility of obtaining non-singular black-hole solutions in the brane world model by solving the effective field equations for the induced metric on the brane. The Reissner–Nordstrom solution on the brane was obtained by Dadhich et al. by imposing the null energy condition on the 3-brane for a bulk having non-zero Weyl curvature. In this work, we relax the condition of vanishing scalar curvature R, however, retaining the null condition. We have shown that it is possible to obtain a class of static non-singular spherically symmetric brane space–times which admits horizon. We obtain one such class of solution which is a regular version of the Reissner–Nordstrom solution in the standard general relativity.

In this paper, a complex daor field which can be regarded as the square root of space–time metric is proposed to represent gravity. The locally complexified geometry is set up, and the complex spin connection constructs a bridge between gravity and SU(1, 3) gauge field. Daor field equations in empty space are acquired, which are one-order differential equations and do not conflict with Einstein's gravity theory.

We show that a suitably chosen position-momentum commutator can elegantly describe many features of gravity, including the IR/UV correspondence and dimensional reduction ("holography"). Using the most simplistic example based on dimensional analysis of black holes, we construct a commutator which qualitatively exhibits these novel properties of gravity. Dimensional reduction occurs because the quanta size grow quickly with momenta, and thus cannot be "packed together" as densely as naively expected. We conjecture that a more precise form of this commutator should be able to quantitatively reproduce all of these features.

In this essay, we explore the hypothesis that gravity is best viewed as a non-quantized field, at least not in the usual sense of being quantized. It is linked to the energy localization hypothesis that energy, including the contribution from gravity, is localized in the region of the energy–momentum tensor. Evidence is gathered from among other aspects, the peculiar nature of gravitational plane waves and indirectly from the fact that there are no experimental results that point to a necessity for quantization. Should this hypothesis prove to be correct, it would favor the negation of the very existence of gravitons since gravitational waves would be seen as purely classical general relativistic constructs which carry no energy. Most significantly, unquantized gravity would turn the evidently unsolvable cosmological constant problem, viewed by various experts as the major crisis of modern physics, into a non-problem. In spite of this, there are indications to suggest that the study of limiting properties will lead to new insights into both the essence of space–time and the quantum world.

In general relativity, gravitational waves propagate at the speed of light, and so gravitons are massless. The masslessness can be traced to symmetry under diffeomorphisms. However, another elegant possibility exists: masslessness can instead arise from spontaneous violation of local Lorentz invariance. We construct the corresponding theory of gravity. It reproduces the Einstein–Hilbert action of general relativity at low energies and temperatures. Detectable signals occur for sensitive experiments, and potentially profound implications emerge for our theoretical understanding of gravity.

Theoretical speculations about the quantum nature of the gravitational interaction have motivated many recent experiments. But perhaps the most profound and puzzling questions that these investigations address surround the observed cosmic acceleration, or Dark Energy. This mysterious substance comprises roughly 2/3 of the energy density of the universe. Current gravitational experiments may soon have the sensitivity to detect subtle clues that will reveal the mechanism behind the cosmic acceleration. On the laboratory scale, short-range tests of the Newtonian inverse-square law (ISL) provide the most sensitive measurements of gravity at the Dark Energy length scale, λ_d = (ħc/ρ_d)^1/4 ≈ 85 μm, where ρ_d ≈ 3.8 keV/cm³ is the observed Dark Energy density. This length scale may also have fundamental significance that could be related to the "size" of the graviton. At the University of Washington, we are conducting the world's most sensitive, short-range test of the Newtonian ISL.

We introduce a simple and straightforward averaging procedure, which is a generalization of one which is commonly used in electrodynamics, and show that it possesses all the characteristics we require for linearized averaging in general relativity and cosmology — for weak-field and perturbed FLRW situations. In particular, we demonstrate that it yields quantities which are approximately tensorial in these situations, and that its application to an exact FLRW metric yields another FLRW metric, to first-order in integrals over the local coordinates. Finally, we indicate some important limits of any linearized averaging procedure with respect to cosmological perturbations which are the result of averages over large amplitude small and intermediate scale inhomogeneities, and show our averaging procedure can be approximately implemented by that of Zotov and Stoeger in these cases.

A time varying space–time metric is shown to be a source of electromagnetic radiation even in the absence of charge sources. The post-Newtonian approximation is used as a realistic model of the connection between the space–time metric and a time-varying gravitational potential. Rapid temporal variations in the metric from the coalescence of relativistic stars are shown to be likely progenitors of gamma ray burst and millisecond pulsars.

We discuss the motivation for high accuracy relativistic gravitational experiments in the solar system and complementary cosmological tests. We focus our attention on the issue of distinguishing a generic scalar theory of gravity as the underlying physical theory from the usual general-relativistic picture, where one expects the presence of fundamental scalar fields associated, for instance, with inflation, dark matter and dark energy.

Spontaneous breaking of Lorentz symmetry has been suggested as a possible mechanism that might occur in the context of a fundamental Planck-scale theory, such as string theory or a quantum theory of gravity. However, if Lorentz symmetry is spontaneously broken, two sets of questions immediately arise: What is the fate of the Nambu–Goldstone (NG) modes, and can a Higgs mechanism occur? A brief summary of some recent work looking at these questions is presented here.

STEP, the Satellite Test of the Equivalence Principle, is reviewed and the current status of the project is discussed. This space-based experiment will test the universality of free fall and is designed to advance the present state of knowledge by over five orders of magnitude. The international STEP collaboration is pursuing a development plan to improve and verify the technology readiness of key systems. We discuss recent advances with an emphasis on accelerometer fabrication and tests. Critical technologies successfully demonstrated in flight by the Gravity Probe B mission also contribute to progress.

APOLLO (the Apache Point Observatory Lunar Laser-ranging Operation) is a new effort in lunar laser ranging that uses the Apollo-landed retroreflector arrays to perform tests of gravitational physics. It achieved its first range return in October 2005, and began its science campaign the following spring. The strong signal (> 2500 photons in a ten-minute period) translates to one-millimeter random range uncertainty, constituting at least an order-of-magnitude gain over previous stations. One-millimeter range precision will translate into order-of-magnitude gains in our ability to test the weak and strong equivalence principles, the time rate of change of Newton's gravitational constant, the phenomenon of gravitomagnetism, the inverse-square law, and the possible presence of extra dimensions. An outline of the APOLLO apparatus and its initial performance is presented, as well as a brief discussion on future space technologies that can extend our knowledge of gravity by orders of magnitude.

I briefly discuss some attempts to construct a consistent modification to general relativity (GR) that might explain the observed late-time acceleration of the Universe and provide an alternative to dark energy. I describe the issues facing extensions to GR, illustrate these with a specific example, and discuss the resulting observational and theoretical obstacles.

We derive the exact equations of motion (in Newtonian, F = ma, form) for test masses in Schwarzschild and Gullstrand–Painlevé coordinates. These equations of motion are simpler than the usual geodesic equations obtained from Christoffel tensors, in that the affine parameter is eliminated. The various terms can be compared against tests of gravity. In force form, gravity can be interpreted as resulting from a flux of superluminal particles (gravitons). We show that the first order relativistic correction to Newton's gravity results from a two-graviton interaction.

Lowering the string scale in the TeV region provides a theoretical framework for solving the mass hierarchy problem and unifying all interactions. The apparent weakness of gravity can then be accounted by the existence of large internal dimensions, in the submillimeter region, and transverse to a braneworld where our universe must be confined. The author reviews the main properties of this scenario and its implications for observations at both particle colliders, and in non-accelerator gravity experiments.

We are investigating the dynamics of a new Poincaré gauge theory of gravity model, which has cross coupling between the spin-0⁺ and spin-0^- modes. To this end we here consider a very appropriate situation — homogeneous-isotropic cosmologies — which is relatively simple, and yet all the modes have nontrivial dynamics which reveals physically interesting and possibly observable results. More specifically we consider manifestly isotropic Bianchi class A cosmologies; for this case we find an effective Lagrangian and Hamiltonian for the dynamical system. The Lagrange equations for these models lead to a set of first-order equations that are compatible with those found for the FLRW models and provide a foundation for further investigations. Typical numerical evolution of these equations shows the expected effects of the cross parity coupling.

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!

Traditional derivations of general relativity (GR) from the graviton degrees of freedom assume spacetime Lorentz covariance as an axiom. In this paper, we survey recent evidence that GR is the unique spatially-covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of GR, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector. From this point of view, Lorentz covariance is a necessary feature of low-energy graviton dynamics, not a property of spacetime. This result has revolutionary implications for fundamental physics.