Highlights of 2010–2011

It is known that the curvature perturbation on uniform energy density (or comoving or uniform Hubble) slices on superhorizon scales is conserved to full nonlinear order if the pressure is only a function of the energy density (i.e. if the perturbation is purely adiabatic), independent of the gravitational theory. Here, we explicitly show that the same conservation holds for a universe dominated by a single scalar field provided that the field is in an attractor regime, for a very general class of scalar-field theories. However, we also show that if the scalar-field equation contains a second time derivative of the metric, as in the case of the Galileon (or kinetic braiding) theory, one has to invoke the gravitational-field equations to show the conservation.

Here we review the basic construction and cosmological implications of a power-counting renormalizable theory of gravitation, recently proposed by Hořava. We explain that (i) at low energy this theory does not exactly recover general relativity but instead mimics general relativity plus dark matter; (ii) higher spatial curvature terms allow bouncing and cyclic universes as regular solutions; (iii) the anisotropic scaling with the dynamical critical exponent z = 3 solves the horizon problem and leads to scale-invariant cosmological perturbations even without inflation. We also comment on issues related to an extra scalar degree of freedom called scalar graviton. In particular, for spherically-symmetric, static, vacuum configurations we prove non-perturbative continuity of the λ → 1 + 0 limit, where λ is a parameter in the kinetic action and general relativity has the value λ = 1. We also derive the condition under which linear instability of the scalar graviton does not show up.

A cosmological model with a cyclic interpretation is introduced, which is subject to quantum back-reaction and yet can be treated rather completely by physical coherent states as well as effective constraint techniques. By this comparison, the role of quantum back-reaction in quantum cosmology is unambiguously demonstrated. Also the complementary nature of strengths and weaknesses of the two procedures is illustrated. Finally, effective constraint techniques are applied to a more realistic model filled with radiation, a context in which physical coherent states are not available.

We study the asymptotic behavior of vacuum Bianchi type A spacetimes close to their singularity. It has been conjectured that this behavior is driven by a certain circle map, called the Kasner map. As a step toward this conjecture, we prove that some orbits of the Kasner map do indeed attract some solutions of the system of ODEs which describes the behavior of vacuum Bianchi type A spacetimes. The orbits of the Kasner map for which we can prove such a result are those which are not periodic and do not accumulate on any periodic orbit. This shows the existence of Bianchi spacetimes with aperiodic oscillatory asymptotic behavior.

Recently, in [3] Hořava and Melby–Thompson proposed a nonrelativistic gravity theory with extended gauge symmetry that is free of the spin-0 graviton. We propose a minimal substitution recipe to implement this extended gauge symmetry which reproduces the results obtained by them. Our prescription has the advantage of being manifestly gauge invariant and immediately generalizable to other fields, like matter. We briefly discuss the coupling of gravity with scalar and vector fields found by our method. We show also that the extended gauge invariance in gravity does not force the value of λ to be λ = 1 as claimed in [3]. However, the spin-0 graviton is eliminated even for general λ.

An introductory review to emergent noncommutative gravity within Yang–Mills matrix models is presented. Spacetime is described as a noncommutative brane solution of the matrix model, i.e. as a submanifold of . Fields and matter on the brane arise as fluctuations of the bosonic resp. fermionic matrices around such a background, and couple to an effective metric interpreted in terms of gravity. Suitable tools are provided for the description of the effective geometry in the semi-classical limit. The relation to non-commutative gauge theory and the role of UV/IR mixing are explained. Several types of geometries are identified, in particular 'harmonic' and 'Einstein' types of solutions. The physics of the harmonic branch is discussed in some detail, emphasizing the non-standard role of vacuum energy. This may provide a new approach to some of the big puzzles in this context. The IKKT model with D = 10 and close relatives are singled out as promising candidates for quantum theory of fundamental interactions including gravity.

In these two lectures I will review classic results on four-dimensional supersymmetric gauge theory, which are a useful prerequisite to learn more recent advances in the field. The lectures were given at the CERN Winter School on Supergravity, Strings and Gauge Theory (CERN, 25–29 January 2010).

This paper gives an overview of the recently-formulated fluid/gravity correspondence, which was developed in the context of gauge/gravity duality. Mathematically, it posits that Einstein's equations (with negative cosmological constant) in d + 1 dimensions capture the (generalized) Navier–Stokes equations in d dimensions. Given an arbitrary fluid dynamical solution, we can systematically construct a corresponding asymptotically AdS black hole spacetime with a regular horizon whose properties mimic that of the fluid flow. Apart from an overview of this construction, we describe some of its applications and implications.

We explore the integrability of five-dimensional minimal supergravity in the presence of three commuting Killing vectors. We argue that to see the integrability structure of the theory one necessarily has to perform an Ehlers reduction to two dimensions. A direct dimensional reduction to two dimensions does not allow us to see the integrability of the theory in an easy way. This situation is in contrast with vacuum five-dimensional gravity. We derive the Belinski–Zakharov (BZ) Lax pair for minimal supergravity based on a symmetric 7 × 7 coset representative matrix for the coset . We elucidate the relationship between our BZ Lax pair and the group theoretic Lax pair previously known in the literature. The BZ Lax pair allows us to generalize the well-known BZ dressing method to five-dimensional minimal supergravity. We show that the action of the three-dimensional hidden symmetry transformations on the BZ dressing method is simply the group action on the BZ vectors. As an illustration of our formalism, we obtain the doubly spinning five-dimensional Myers–Perry black hole by applying solitonic transformations on the Schwarzschild black hole. We also derive the Cveti–Youm black hole by applying solitonic transformations on the Reissner–Nordström black hole.

We consider an Unruh–DeWitt particle detector, coupled to a massless scalar field, undergoing 'acceleration with drift' in a (1 + 3)-dimensional Minkowski spacetime. We use this to model inertial motion in a (1 + 2)-dimensional Minkowski heat bath, in particular motion within a 2-plane parallel (and near) to the horizon of a black 2-brane. We compute the angular response of the detector in its own rest frame. The response to particles arriving from within the 2-plane is isotropic and Planckian for zero drift velocity. For small drift velocities, and in the ultra-violet limit in which the excitations behave like a classical gas, the response is just Doppler shifted. However, we find discrepancies with the Doppler-shifted formula in the infrared limit, and qualitatively different behaviour when the drift velocity is not small. We discuss possible explanations for this result and potential implications for observations of the cosmic microwave background radiation.

We consider asymptotically anti de Sitter gravity coupled to a scalar field with mass slightly above the Breitenlohner–Freedman bound. This theory admits a large class of consistent boundary conditions characterized by an arbitrary function W. An important open question is to determine which W admit stable ground states. It has previously been shown that the total energy is bounded from below if W is bounded from below, and the bulk scalar potential V(ϕ) admits a suitable superpotential. We extend this result and show that the energy remains bounded even in some cases where W can become arbitrarily negative. As one application, this leads to the possibility that in gauge/gravity duality, one can add a double trace operator with negative coefficient to the dual field theory and still have a stable vacuum.

Using analytical methods, we derive and extend previously obtained numerical results on the low temperature properties of holographic duals to four-dimensional gauge theories at finite density in a nonzero magnetic field. We find a new asymptotically AdS₅ solution representing the system at zero temperature. This solution has vanishing entropy density, and the charge density in the bulk is carried entirely by fluxes. The dimensionless magnetic field to charge density ratio for these solutions is bounded from below, with a quantum critical point appearing at the lower bound. Using matched asymptotic expansions, we extract the low temperature thermodynamics of the system. Above the critical magnetic field, the low temperature entropy density takes a simple form, linear in the temperature, and with a specific heat coefficient diverging at the critical point. At the critical magnetic field, we derive the scaling law s ∼ T^1/3 inferred previously from the numerical analysis. We also compute the full scaling function describing the region near the critical point and identify the dynamical critical exponent: z = 3. These solutions are expected to holographically represent boundary theories in which strongly interacting fermions are filling up a Fermi sea. They are fully top–down constructions in which both the bulk and boundary theories have well-known embeddings in the string theory.

Communicated by S F Ross

A model of Lorentz invariant random fluctuations in photon polarization is presented. The effects are frequency dependent and affect the polarization of photons as they propagate through space. We test for this effect by confronting the model with the latest measurements of polarization of cosmic microwave background photons.

This article is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity.

For the study of Planck-scale modifications of the energy–momentum dispersion relation, which had been previously focused on the implications for ultrarelativistic particles, we consider the possible role of experiments involving nonrelativistic particles, and particularly atoms. We extend a recent result establishing that measurements of 'atom-recoil frequency' can provide an insight that is valuable for some theoretical models. From a broader perspective we analyze the complementarity of the nonrelativistic and the ultrarelativistic regimes in this research area.

In this paper we study the Josephson tunneling for a quantum fluid (a Bose–Einstein condensate) in the presence of a weak gravitational wave. Starting from a Lagrangian formulation in the framework of linearized gravity, we deduce the Gross–Pitaevskii equation for the fluid in a weak gravitational background. We use such an equation to investigate the influence of a gravitational wave on the Josephson effect. Considering a double-well trap, made of two identical boxes placed orthogonally to each other and weakly coupled through a small junction, we show how the trap geometry influences the coupling between the gravitational wave and the quantum field modes in the two sides of the trap. Namely, the macroscopic wavefunction of the condensate acquires a different phase shift on the two sides, hence giving rise to a gravitationally induced ac-Josephson effect through the trap junction. Although small, such an effect is theoretically interesting, since it represents the influence of a gravitational wave on a mesoscopic quantum system. Also the effect exhibits polarimetric properties. Possible experimental detection of such an effect is briefly discussed at the end of the paper.

The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as our main tool. A set of moves we define in the set of the operator spin foams (among other operations) allows us to split the faces and the edges of the foams. We assign to each operator spin foam a contracted operator, by using the contractions at the vertices and suitably adjusted face amplitudes. The emergence of the face amplitudes is the consequence of assuming the invariance of the contracted operator with respect to the moves. Next, we define spin foam models and consider the class of models assumed to be symmetric with respect to the moves we have introduced, and assuming their partition functions (state sums) are defined by the contracted operators. Briefly speaking, those operator spin foam models are invariant with respect to the cellular decomposition, and are sensitive only to the topology and colouring of the foam. Imposing an extra symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with assumed invariance with respect to the edge splitting move, determines a complete characterization of a general natural model. It can be obtained by applying arbitrary (quantum) constraints on an arbitrary BF spin foam model. In particular, imposing suitable constraints on a spin(4) BF spin foam model is exactly the way we tend to view 4D quantum gravity, starting with the BC model and continuing with the Engle–Pereira–Rovelli–Livine (EPRL) or Freidel–Krasnov (FK) models. That makes our framework directly applicable to those models. Specifically, our operator spin foam framework can be translated into the language of spin foams and partition functions. Among our natural spin foam models there are the BF spin foam model, the BC model, and a model corresponding to the EPRL intertwiners. Our operator spin foam framework can also be used for more general spin foam models which are not symmetric with respect to one or more moves we consider.

We consider spinfoam quantum gravity. We show in a simple case that the amplitude projects over a nontrivial (curved) classical geometry. This suggests that, at least for spinfoams without bubbles and for large values of the boundary spins, the amplitude takes the form of a path integral over Regge metrics, thus enforcing discrete Einstein equations in the classical limit. The result relies crucially on a new interpretation of the semiclassical limit for the amplitudes truncated to a fixed 2-complex.

We analyze the δ = 2 Tomimatsu–Sato spacetime in the context of the proposed Kerr/CFT correspondence. This four-dimensional vacuum spacetime is not only asymptotically flat and has a well-defined ADM mass and angular momentum but also involves several exotic features including a naked ring singularity, and two disjoint Killing horizons separated by a region with closed timelike curves and a rod-like conical singularity. We demonstrate that the near-horizon geometry belongs to a general class of Ricci-flat metrics with symmetry that includes both the extremal Kerr and extremal Kerr–Bolt geometries. We calculate the central charge and temperature for the CFT dual to this spacetime and confirm that the Cardy formula reproduces the Bekenstein–Hawking entropy. We find that all of the basic parameters of the dual CFT are most naturally expressed in terms of charges defined intrinsically on the horizon, which are distinct from the ADM charges in this geometry.

Optical (or Robinson) structures are one generalization of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the Goldberg–Sachs theorem to five dimensions. To be precise, we find a new algebraic condition on the Weyl tensor, which generalizes the Petrov type II condition, in the sense that it ensures the existence of such congruences on a five-dimensional spacetime, vacuum or under weaker assumptions on the Ricci tensor. This results in a significant simplification of the field equations. We discuss possible degenerate cases, including a five-dimensional generalization of the Petrov type D condition. We also show that the vacuum black ring solution is endowed with optical structures, yet fails to be algebraically special with respect to them. We finally explain the generalization of these ideas to higher dimensions, which has been checked in six and seven dimensions.

We show that the hypothesis of analyticity in the uniqueness theory of vacuum, or electrovacuum, static black holes is not needed. More generally, we show that prehorizons covering a closed set cannot occur in well-behaved domains of outer communications.

Loop gravity provides a microscopic derivation of black hole entropy. In this paper, I show that the microstates counted admit a semiclassical description in terms of shapes of a tessellated horizon. The counting of microstates and the computation of the entropy can be done via a mapping to an equivalent statistical mechanical problem: the counting of conformations of a closed polymer chain. This correspondence suggests a number of intriguing relations between the thermodynamics of black holes and the physics of polymers.

Using effective field theory (EFT) techniques, we calculate the next-to-leading-order (NLO) spin–orbit contributions to the gravitational potential of inspiralling compact binaries. We use the covariant spin supplementarity condition (SSC), and explicitly prove the equivalence with previous results by Faye et al (2006 Phys. Rev. D 74 104033 (arXiv:gr-qc/0605139)). We also show that the direct application of the Newton–Wigner SSC at the level of the action leads to the correct dynamics using a canonical (Dirac) algebra. This paper then completes the calculation of the necessary spin dynamics within the EFT formalism that will be used in a separate paper to compute the spin contributions to the energy flux and phase evolution to NLO.

We present a new cubic theory of gravity in five dimensions which has second-order traced field equations, analogous to BHT new massive gravity in three dimensions. Moreover, for static spherically symmetric spacetimes all the field equations are of second order, and the theory admits a new asymptotically locally flat black hole. Furthermore, we prove the uniqueness of this solution, study its thermodynamical properties and show the existence of a C-function for the theory following the arguments of Anber and Kastor (2008 J. High Energy Phys. JHEP05(2008)061 (arXiv:0802.1290 [hep-th])) in pure Lovelock theories. Finally, we include the Einstein–Gauss–Bonnet and cosmological terms and find new asymptotically AdS black holes at the point where the three maximally symmetric solutions of the theory coincide. These black holes may also possess a Cauchy horizon.

Within the framework of the scalar–tensor models of gravitation and by relying on analytical and numerical techniques, we establish the existence of a class of spherically symmetric spacetimes containing a naked singularity. Our result relies on and extends a work by Christodoulou on the existence of naked singularities for the Einstein–scalar field equations. We establish that a key parameter in Christodoulou's construction couples to the Brans–Dicke field and becomes a dynamical variable, which enlarges and modifies the phase space of solutions. We recover analytically many properties first identified by Christodoulou, in particular the loss of regularity (especially at the center), and then investigate numerically the properties of these spacetimes.

Deriving the motion of a compact mass or charge can be complicated by the presence of large self-fields. Simplifications are known to arise when these fields are split into two parts in what is known as a Detweiler–Whiting decomposition. One component satisfies vacuum field equations, while the other does not. The force and torque exerted by the (often ignored) inhomogeneous 'S-type' portion are analyzed here for extended scalar charges in curved spacetimes. This field has previously been shown to effectively renormalize a body's linear and angular momenta. We show here that if the geometry is sufficiently smooth, it actually shifts all multipole moments of the body's stress–energy tensor (and does nothing else). This greatly expands the validity of statements that the homogeneous R field determines the self-force and self-torque up to renormalization effects. The forces and torques exerted by the S field directly measure the degree to which a spacetime fails to admit Killing vectors inside the body. A number of mathematical results related to the use of generalized Killing fields are therefore derived, and may be of wider interest. As an example of their application, the effective shift in the quadrupole moment of a charge's stress–energy tensor is explicitly computed to lowest nontrivial order.

The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by γ one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime (M, g_ab). First, it is shown that it is always possible to select a synchronized family of causal geodesics Γ and an open neighbourhood of a final segment of γ in M such that comprises members of Γ, and suitable local coordinates can be defined everywhere on provided that γ does not terminate either on a tidal force tensor singularity or on a topological singularity. It is also shown that if, in addition, the spacetime (M, g_ab) is globally hyperbolic, and the components of the curvature tensor, and its covariant derivatives up to order k − 1 are bounded on , and also the line integrals of the components of the kth-order covariant derivatives are finite along the members of Γ—where all the components are meant to be registered with respect to a synchronized frame field on —then there exists a C^{k −} extension so that for each , which is inextendible in (M, g_ab), the image, , is extendible in . Finally, it is also proved that whenever γ does terminate on a topological singularity (M, g_ab) cannot be generic.

We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress–energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.

We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation-preserving 3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume (for the spatially compact case). Locally, this symmetry is identical to that of Hořava–Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.

We present an alternative method to estimate the numerical viscosity in simulations of astrophysical objects, which is based on the damping of fluid oscillations. We apply the method to general relativistic hydrodynamic simulations using spherical coordinates. We perform 1D spherical and 2D axisymmetric simulations of radial oscillations in spherical systems. We first calibrate the method with simulations with physical bulk viscosity and study the differences between several numerical schemes. We apply the method to radial oscillations of neutron stars and we conclude that the main source of numerical viscosity in this case is the surface of the star. We expect that this method could be useful to compute the resolution requirements and limitations of the numerical simulations in different astrophysical scenarios in the future.

We present details of a new numerical code designed to study the formation and evaporation of two-dimensional black holes within the Callan–Giddings–Harvey–Strominger model. We explain several elements of the scheme that are crucial to resolve the late-time behavior of the spacetime, including regularization of the field variables, compactification of the coordinates, the algebraic form of the discretized equations of motion and the use of a modified Richardson extrapolation scheme to achieve high-order convergence. Physical interpretation of our results will be discussed in detail elsewhere.

This paper discusses linearized vacuum gravitational perturbations of the Kerr spacetime in a neighbourhood of future null infinity . Unlike earlier discussion of perturbations of the Kerr spacetime we avoid the use of spheroidal harmonics and harmonic time dependence. Instead we develop the theory in terms of Hertz potentials and spherical harmonics with coupling between modes. The 'master equation' is a single complex scalar wave equation which, in the Minkowski limit, reduces to the Euler–Poisson–Darboux equation. We solve this by Picard iteration making extensive use of the flat spacetime Riemann–Green function. As an application we consider the problem of outer boundary conditions for numerical relativity and generalize earlier results of Buchman and Sarbach (2006 Class. Quantum Grav. 23 6709–44, 2007 Class. Quantum Grav. 24 S307–26) for the Schwarzschild case.

An axisymmetric collapse of non-rotating gravitational waves is numerically investigated in the subcritical regime where no black holes form but where curvature attains a maximum and decreases, following the dispersion of the initial wave packet. We focus on a curvature invariant with dimensions of length, and find that near the threshold for black hole formation it reaches a maximum along concentric rings of finite radius around the axis. In this regime the maximal value of the invariant exhibits a power-law scaling with the approximate exponent 0.38, as a function of a parametric distance from the threshold. In addition, the variation of the curvature in the critical limit is accompanied by increasing amount of echos, with nearly equal temporal and spatial periods. The scaling and the echoing patterns, and the corresponding constants, are independent of the initial data and coordinate choices.

We present an up-to-date, comprehensive summary of the rates for all types of compact binary coalescence sources detectable by the initial and advanced versions of the ground-based gravitational-wave detectors LIGO and Virgo. Astrophysical estimates for compact-binary coalescence rates depend on a number of assumptions and unknown model parameters and are still uncertain. The most confident among these estimates are the rate predictions for coalescing binary neutron stars which are based on extrapolations from observed binary pulsars in our galaxy. These yield a likely coalescence rate of 100 Myr⁻¹ per Milky Way Equivalent Galaxy (MWEG), although the rate could plausibly range from 1 Myr⁻¹ MWEG⁻¹ to 1000 Myr⁻¹ MWEG⁻¹ (Kalogera et al 2004 Astrophys. J. 601 L179; Kalogera et al 2004 Astrophys. J. 614 L137 (erratum)). We convert coalescence rates into detection rates based on data from the LIGO S5 and Virgo VSR2 science runs and projected sensitivities for our advanced detectors. Using the detector sensitivities derived from these data, we find a likely detection rate of 0.02 per year for Initial LIGO–Virgo interferometers, with a plausible range between 2 × 10⁻⁴ and 0.2 per year. The likely binary neutron–star detection rate for the Advanced LIGO–Virgo network increases to 40 events per year, with a range between 0.4 and 400 per year.

In this paper, we briefly review some of the applications to fundamental physics and cosmology of the observations that will be made with the future space-based gravitational wave (GW) detector LISA. This includes detection of GW bursts generated by cosmic strings, measurement of a stochastic GW background, mapping the spacetime around massive compact objects in galactic nuclei using extreme-mass-ratio inspirals and testing the predictions of general relativity for the strong dynamical fields generated by inspiralling binaries. We give particular attention to some new results which demonstrated the capability of LISA to constrain cosmological parameters using observations of coalescing massive black hole binaries.

This technical paper of mathematical physics arose as an aftermath of the 2002 Cassini experiment (Bertotti et al 2003 Nature 425 374–6), in which the PPN parameter γ was measured with an accuracy σ_γ = 2.3 × 10⁻⁵ and found consistent with the prediction γ = 1 of general relativity. The Orbit Determination Program (ODP) of NASA's Jet Propulsion Laboratory, which was used in the data analysis, is based on an expression (8) for the gravitational delay Δt that differs from the standard formula (2); this difference is of second order in powers of m—the gravitational radius of the Sun—but in Cassini's case it was much larger than the expected order of magnitude m²/b, where b is the distance of the closest approach of the ray. Since the ODP does not take into account any other second-order terms, it is necessary, also in view of future more accurate experiments, to revisit the whole problem, to systematically evaluate higher order corrections and to determine which terms, and why, are larger than the expected value. We note that light propagation in a static spacetime is equivalent to a problem in ordinary geometrical optics; Fermat's action functional at its minimum is just the light-time between the two end points A and B. A new and powerful formulation is thus obtained. This method is closely connected with the much more general approach of Le Poncin-Lafitte et al (2004 Class. Quantum Grav. 21 4463–83), which is based on Synge's world function. Asymptotic power series are necessary to provide a safe and automatic way of selecting which terms to keep at each order. Higher order approximations to the required quantities, in particular the delay and the deflection, are easily obtained. We also show that in a close superior conjunction, when b is much smaller than the distances of A and B from the Sun, say of order R, the second-order correction has an enhanced part of order m²R/b², which corresponds just to the second-order terms introduced in the ODP. Gravitational deflection of the image of a far away source when observed from a finite distance from the mass is obtained up to O(m²).

As the LIGO interferometric gravitational wave detectors have finished gathering a large observational data set, an intense effort is underway to upgrade these observatories to improve their sensitivity by a factor of ∼10. High circulating power in the arm cavities is required, which leads to the possibility of parametric instability due to three-mode opto-acoustic resonant interactions between the carrier, transverse optical modes and acoustic modes. Here, we present detailed numerical analysis of parametric instability in a configuration that is similar to Advanced LIGO. After examining parametric instability for a single three-mode interaction in detail, we examine instability for the best and worst cases, as determined by the resonance condition of transverse modes in the power and signal recycling cavities. We find that, in the best case, the dual recycling detector is substantially less susceptible to instability than a single cavity, but its susceptibility is dependent on the signal recycling cavity design, and on tuning for narrow band operation. In all cases considered, the interferometer will experience parametric instability at full power operation, but the gain varies from 3 to 1000, and the number of unstable modes varies between 7 and 30 per test mass. The analysis focuses on understanding the detector complexity in relation to opto-acoustic interactions, on providing insights that can enable predictions of the detector response to transient disturbances, and of variations in thermal compensation conditions.

We present a frequency modulation technique for calibration of the displacement actuators of the LIGO 4 km long interferometric gravitational-wave detectors. With the interferometer locked in a single-arm configuration, we modulate the frequency of the laser light, creating an effective length variation that we calibrate by measuring the amplitude of the frequency modulation. By simultaneously driving the voice coil actuators that control the length of the arm cavity, we calibrate the voice coil actuation coefficient with an estimated 1σ uncertainty of less than 1%. This technique enables a force-free, single-step actuator calibration using a displacement fiducial that is fundamentally different from those employed in other calibration methods.

Thermal noise arising from mechanical dissipation in dielectric reflective coatings is expected to critically limit the sensitivity of precision measurement systems such as high-resolution optical spectroscopy, optical frequency standards and future generations of interferometric gravitational wave detectors. We present measurements of the effect of post-deposition heat treatment on the temperature dependence of the mechanical dissipation in ion-beam sputtered tantalum pentoxide between 11 K and 300 K. We find that the temperature dependence of the dissipation is strongly dependent on the temperature at which the heat treatment was carried out, and we have identified three dissipation peaks occurring at different heat treatment temperatures. At temperatures below 200 K, the magnitude of the loss was found to increase with higher heat treatment temperatures, indicating that heat treatment is a significant factor in determining the level of coating thermal noise.

The laser frequency stabilization subsystem is one of the most significant parts within the interferometric measurement system of LISA. Arm locking as a proposed frequency stabilization technique synthesizes an adequately filtered linear combination of the interferometry signals as a frequency reference. Until now all the benchtop experiments on arm locking verified only the basic single arm locking configuration with unrealistic short signal travel times. At the University of Florida we developed the hardware-based University of Florida LISA Interferometer Simulator (UFLIS) to study and verify laser frequency noise reduction and suppression techniques under realistic LISA-like conditions. These conditions include the Doppler shifts between the spacecraft, LISA-like signal travel times, realistic laser frequency and timing noise. In this paper we will report about preliminary experiments on advanced arm locking schemes including dual arm locking and modified dual arm locking with realistic 33 s light travel times. In our experiments the implementation of a dual/modified dual arm locking sensor and controller is realized using several digital signal processing boards. We demonstrated the closed-loop stability of arm locking setup and measured the noise suppression in these experiments.

This paper develops a general framework for studying the effectiveness of networks of interferometric gravitational wave detectors and then uses it to show that enlarging the existing LIGO–VIRGO network with one or more planned or proposed detectors in Japan (LCGT), Australia, and India brings major benefits, including much larger detection rate increase than previously thought. I focus on detecting bursts, i.e. short-duration signals, with optimal coherent data-analysis methods. I show that the polarization-averaged sensitivity of any network of identical detectors to any class of sources can be characterized by two numbers—the visibility distance of the expected source from a single detector and the minimum signal-to-noise ratio (SNR) for a confident detection—and one angular function, the antenna pattern of the network. I show that there is a universal probability distribution function (PDF) for detected SNR values, which implies that the most likely SNR value of the first detected event will be 1.26 times the search threshold. For binary systems, I also derive the universal PDF for detected values of the orbital inclination, taking into account the Malmquist bias; this implies that the number of gamma-ray bursts associated with detected binary coalescences should be 3.4 times larger than expected from just the beaming fraction of the gamma burst. Using network antenna patterns, I propose three figures of merit (f.o.m.'s) that characterize the relative performance of different networks. These measure (a) the expected rate of detection by the network and any sub-networks of three or more separated detectors, taking into account the duty cycle of the interferometers, (b) the isotropy of the network antenna pattern, and (c) the accuracy of the network at localizing the positions of events on the sky. I compare various likely and possible networks, based on these f.o.m.'s. Adding any new site to the planned LIGO–VIRGO network can dramatically increase, by factors of 2–4, the detected event rate by allowing coherent data analysis to reduce the spurious instrumental coincident background. Moving one of the LIGO detectors to Australia additionally improves direction finding by a factor of 4 or more. Adding LCGT to the original LIGO–VIRGO network not only improves direction finding but will further increase the detection rate over the extra-site gain by factors of almost 2, partly by improving the network duty cycle. Including LCGT, LIGO-Australia, and a detector in India gives a network with position error ellipses a factor of 7 smaller in area and boosts the detected event rate a further 2.4 times above the extra-site gain over the original LIGO–VIRGO network. Enlarged advanced networks could look forward to detecting 300–400 neutron star binary coalescences per year.