Forward Modeling of Space-borne Gravitational Wave Detectors

Planning is underway for several space-borne gravitational wave observatories to be built in the next ten to twenty years. Realistic and efficient forward modeling will play a key role in the design and operation of these observatories. Space-borne interferometric gravitational wave detectors operate very differently from their ground based counterparts. Complex orbital motion, virtual interferometry, and finite size effects complicate the description of space-based systems, while nonlinear control systems complicate the description of ground based systems. Here we explore the forward modeling of space-based gravitational wave detectors and introduce an adiabatic approximation to the detector response that significantly extends the range of the standard low frequency approximation. The adiabatic approximation will aid in the development of data analysis techniques, and improve the modeling of astrophysical parameter extraction.Comment: 14 Pages, 14 Figures, RevTex

Optimal filtering of the LISA data

The LISA time-delay-interferometry responses to a gravitational-wave signal are rewritten in a form that accounts for the motion of the LISA constellation around the Sun; the responses are given in closed analytic forms valid for any frequency in the band accessible to LISA. We then present a complete procedure, based on the principle of maximum likelihood, to search for stellar-mass binary systems in the LISA data. We define the required optimal filters, the amplitude-maximized detection statistic (analogous to the F statistic used in pulsar searches with ground-based interferometers), and discuss the false-alarm and detection probabilities. We test the procedure in numerical simulations of gravitational-wave detection.Comment: RevTeX4, 28 pages, 9 EPS figures. Minus signs fixed in Eq. (46) and Table II. Corrected discussion of F-statistic distribution in Sec. IV

Annual modulation of the Galactic binary confusion noise bakground and LISA data analysis

We study the anisotropies of the Galactic confusion noise background and its effects on LISA data analysis. LISA has two data streams of the gravitational waves signals relevant for low frequency regime. Due to the anisotropies of the background, the matrix for their confusion noises has off-diagonal components and depends strongly on the orientation of the detector plane. We find that the sky-averaged confusion noise level $\sqrt {S(f)}$ could change by a factor of 2 in three months, and would be minimum when the orbital position of LISA is either around the spring or autumn equinox.Comment: 13 pages, 6 figure

The Challenges in Gravitational Wave Astronomy for Space-Based Detectors

The Gravitational Wave (GW) universe contains a wealth of sources which, with the proper treatment, will open up the universe as never before. By observing massive black hole binaries to high redshifts, we should begin to explore the formation process of seed black holes and track galactic evolution to the present day. Observations of extreme mass ratio inspirals will allow us to explore galactic centers in the local universe, as well as providing tests of General Relativity and constraining the value of Hubble's constant. The detection of compact binaries in our own galaxy may allow us to model stellar evolution in the Milky Way. Finally, the detection of cosmic (super)strings and a stochastic background would help us to constrain cosmological models. However, all of this depends on our ability to not only resolve sources and carry out parameter estimation, but also on our ability to define an optimal data analysis strategy. In this presentation, I will examine the challenges that lie ahead in GW astronomy for the ESA L3 Cosmic Vision mission, eLISA.Comment: 12 pages. Plenary presentation to appear in the Proceedings of the Sant Cugat Forum on Astrophysics, Sant Cugat, April 22-25, 201

A small universe after all?

The cosmic microwave background radiation allows us to measure both the geometry and topology of the universe. It has been argued that the COBE-DMR data already rule out models that are multiply connected on scales smaller than the particle horizon. Here we show the opposite is true: compact (small) hyperbolic universes are favoured over their infinite counterparts. For a density parameter of Omega_o=0.3, the compact models are a better fit to COBE-DMR (relative likelihood ~20) and the large-scale structure data (sigma_8 increases by ~25%).Comment: 4 pages, RevTeX, 7 Figure

A survey of spinning test particle orbits in Kerr spacetime

We investigate the dynamics of the Papapetrou equations in Kerr spacetime. These equations provide a model for the motion of a relativistic spinning test particle orbiting a rotating (Kerr) black hole. We perform a thorough parameter space search for signs of chaotic dynamics by calculating the Lyapunov exponents for a large variety of initial conditions. We find that the Papapetrou equations admit many chaotic solutions, with the strongest chaos occurring in the case of eccentric orbits with pericenters close to the limit of stability against plunge into a maximally spinning Kerr black hole. Despite the presence of these chaotic solutions, we show that physically realistic solutions to the Papapetrou equations are not chaotic; in all cases, the chaotic solutions either do not correspond to realistic astrophysical systems, or involve a breakdown of the test-particle approximation leading to the Papapetrou equations (or both). As a result, the gravitational radiation from bodies spiraling into much more massive black holes (as detectable, for example, by LISA, the Laser Interferometer Space Antenna) should not exhibit any signs of chaos.Comment: Submitted to Phys. Rev. D. Follow-up to gr-qc/0210042. Figures are low-resolution in order to satisfy archive size constraints; a high-resolution version is available at http://www.michaelhartl.com/papers

Certain aspects of regularity in scalar field cosmological dynamics

We consider dynamics of the FRW Universe with a scalar field. Using Maupertuis principle we find a curvature of geodesics flow and show that zones of positive curvature exist for all considered types of scalar field potential. Usually, phase space of systems with the positive curvature contains islands of regular motion. We find these islands numerically for shallow scalar field potentials. It is shown also that beyond the physical domain the islands of regularity exist for quadratic potentials as well.Comment: 15 pages with 4 figures; typos corrected, final version to appear in Regular and Chaotic Dynamic

Inflationary and dark energy regimes in 2+1 dimensions

In this work we investigate the behavior of three-dimensional (3D) cosmological models. The simulation of inflationary and dark-energy-dominated eras are among the possible results in these 3D formulations; taking as starting point the results obtained by Cornish and Frankel. Motivated by those results, we investigate, first, the inflationary case where we consider a two-constituent cosmological fluid: the scalar field represents the hypothetical inflaton which is in gravitational interaction with a matter/radiation contribution. For the description of an old universe, it is possible to simulate its evolution starting with a matter dominated universe that faces a decelerated/accelerated transition due to the presence of the additional constituent (simulated by the scalar field or ruled by an exotic equation of state) that plays the role of dark energy. We obtain, through numerical analysis, the evolution in time of the scale factor, the acceleration, the energy densities, and the hydrostatic pressure of the constituents. The alternative scalar cosmology proposed by Cornish and Frankel is also under investigation in this work. In this case an inflationary model can be constructed when another non-polytropic equation of state (the van der Waals equation) is used to simulate the behavior of an early 3D universe.Comment: Latex file, plus 9 figures. To appear in General Relativity and Gravitatio

Ultraviolet Complete Quantum Gravity

An ultraviolet complete quantum gravity theory is formulated in which vertex functions in Feynman graphs are entire functions and the propagating graviton is described by a local, causal propagator. The cosmological constant problem is investigated in the context of the ultraviolet complete quantum gravity.Comment: 11 pages, no figures. Changes to text. Results remain the same. References added. To be published in European Physics Journal Plu

Data Analysis Challenges for the Einstein Telescope

The Einstein Telescope is a proposed third generation gravitational wave detector that will operate in the region of 1 Hz to a few kHz. As well as the inspiral of compact binaries composed of neutron stars or black holes, the lower frequency cut-off of the detector will open the window to a number of new sources. These will include the end stage of inspirals, plus merger and ringdown of intermediate mass black holes, where the masses of the component bodies are on the order of a few hundred solar masses. There is also the possibility of observing intermediate mass ratio inspirals, where a stellar mass compact object inspirals into a black hole which is a few hundred to a few thousand times more massive. In this article, we investigate some of the data analysis challenges for the Einstein Telescope such as the effects of increased source number, the need for more accurate waveform models and the some of the computational issues that a data analysis strategy might face.Comment: 18 pages, Invited review for Einstein Telescope special edition of GR