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Register a new userCan we use next-generation gravitational wave detectors for terrestrial precision measurements of Shapiro delay?
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Shapiro time delay is one of the fundamental tests of general relativity and post-Newtonian theories of gravity. Consequently, its measurements can be used to probe the parameter $gamma$ which is related to spacetime curvature produced by a unit mass in the post-Newtonian formalism of gravity. To date all measurements of time delay have been conducted on astronomical scales. It was asserted in 2010 that gravitational wave detectors on Earth could be used to measure Shapiro delay on a terrestrial scale via massive rotating systems. Building on that work, we consider how measurements of Shapiro delay can be made using next-generation gravitational wave detectors. We perform an analysis for measuring Shapiro delay with the next-generation gravitational wave detectors Cosmic Explorer and Einstein Telescope to determine how precisely the effect can be measured. Using a rotating mass unit design, we find that Cosmic Explorer and Einstein Telescope can measure the Shapiro delay signal with amplitude signal to noise ratios upwards of $sim28 $ and $sim43$ in 1 year of integration time, respectively. By measuring Shapiro delay with this technique, next-generation interferometers will allow for terrestrial measurements of $gamma$ in the paramaterized post-Newtonian formalism of gravity with sub-percent precision.
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Direct detection of gravitational radiation in the audio band is being pursued with a network of kilometer-scale interferometers (LIGO, Virgo, KAGRA). Several space missions (LISA, DECIGO, BBO) have been proposed to search for sub-Hz radiation from massive astrophysical sources. Here we examine the potential sensitivity of three ground-based detector concepts aimed at radiation in the 0.1 -- 10,Hz band. We describe the plethora of potential astrophysical sources in this band and make estimates for their event rates and thereby, the sensitivity requirements for these detectors. The scientific payoff from measuring astrophysical gravitational waves in this frequency band is great. Although we find no fundamental limits to the detector sensitivity in this band, the remaining technical limits will be extremely challenging to overcome.
Second-generation interferometric gravitational-wave detectors will be operating at the Standard Quantum Limit, a sensitivity limitation set by the trade off between measurement accuracy and quantum back action, which is governed by the Heisenberg Uncertainty Principle. We review several schemes that allows the quantum noise of interferometers to surpass the Standard Quantum Limit significantly over a broad frequency band. Such schemes may be an important component of the design of third-generation detectors.
Current terrestrial gravitational-wave detectors operate at frequencies above 10 Hz. There is strong astrophysical motivation to construct low-frequency gravitational-wave detectors capable of observing 10 mHz - 10Hz signals. While space-based detectors provide one means of achieving this end, one may also consider terretrial detectors. However, there are numerous technological challenges. In particular, it is difficult to isolate test masses so that they are both seismically isolated and freely falling under the influence of gravity at millihertz frequencies. We investigate the challenges of low-frequency suspension in a hypothetical terrestrial detector. As a case study, we consider a Magnetically Assisted Gravitational-wave Pendulum Intorsion (MAGPI) suspension design. We construct a noise budget to estimate some of the required specifications. In doing so, we identify what are likely to be a number of generic limiting noise sources for terrestrial millihertz gravitational-wave suspension systems (as well as some peculiar to the MAGPI design). We highlight significant experimental challenges in order to argue that the development of millihertz suspensions will be a daunting task. Any system that relies on magnets faces even greater challenges. Entirely mechanical designs such as Zollner pendulums may provide the best path forward.
Space-based gravitational wave detectors cannot keep rigid structures and precise arm length equality, so the precise equality of detector arms which is required in a ground-based interferometer to cancel the overwhelming laser noise is impossible. The time-delay interferometry method is applied to unequal arm lengths to cancel the laser frequency noise. We give analytical formulas of the averaged response functions for tensor, vector, breathing and longitudinal polarizations in different TDI combinations, and obtain their asymptotic behaviors. At low frequencies, $fll f_*$, the averaged response functions of all TDI combinations increase as $f^2$ for all six polarizations. The one exception is the averaged response functions of $zeta$ for all six polarizations increase as $f^4$ in the equilateral-triangle case. At high frequencies, $fgg f_*$, the averaged response functions of all TDI combinations for the tensor and breathing modes fall off as $1/f^2$, the averaged response functions of all TDI combinations for the vector mode fall off as $ln(f)/f^2$ , and the averaged response functions of all TDI combinations for the longitudinal mode fall as $1/f$. We also give LISA and TianQin sensitivity curves in different TDI combinations for tensor, vector, breathing and longitudinal polarizations.
The second-generation of gravitational-wave detectors are just starting operation, and have already yielding their first detections. Research is now concentrated on how to maximize the scientific potential of gravitational-wave astronomy. To support this effort, we present here design targets for a new generation of detectors, which will be capable of observing compact binary sources with high signal-to-noise ratio throughout the Universe.
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