Derivative of the light frequency shift as a measure of spacetime curvature for gravitational wave detection

The measurement of frequency shifts for light beams exchanged between two test masses nearly in free fall is at the heart of gravitational wave detection. It is envisaged that the derivative of the frequency shift is in fact limited by differential forces acting on those test masses. We calculate the derivative of the frequency shift with a fully covariant, gauge-independent and coordinate-free method. This method is general and does not require a congruence of nearby beams' null geodesics as done in previous work. We show that the derivative of the parallel transport is the only means by which gravitational effects shows up in the frequency shift. This contribution is given as an integral of the Riemann tensor --the only physical observable of curvature-- along the beam's geodesic. The remaining contributions are: the difference of velocities, the difference of non-gravitational forces, and finally fictitious forces, either locally at the test masses or non-locally integrated along the beam's geodesic. As an application relevant to gravitational wave detection, we work out the frequency shift in the local Lorentz frame of nearby geodesics.Comment: 4 pages, 1 figur

Measuring test mass acceleration noise in space-based gravitational wave astronomy

The basic constituent of interferometric gravitational wave detectors -- the test mass to test mass interferometric link -- behaves as a differential dynamometer measuring effective differential forces, comprising an integrated measure of gravity curvature, inertial effects, as well as non-gravitational spurious forces. This last contribution is going to be characterised by the LISA Pathfinder mission, a technology precursor of future space-borne detectors like eLISA. Changing the perspective from displacement to acceleration can benefit the data analysis of LISA Pathfinder and future detectors. The response in differential acceleration to gravitational waves is derived for a space-based detector's interferometric link. The acceleration formalism can also be integrated into time delay interferometry by building up the unequal-arm Michelson differential acceleration combination. The differential acceleration is nominally insensitive to the system free evolution dominating the slow displacement dynamics of low-frequency detectors. Working with acceleration also provides an effective way to subtract measured signals acting as systematics, including the actuation forces. Because of the strong similarity with the equations of motion, the optimal subtraction of systematic signals, known within some amplitude and time shift, with the focus on measuring the noise provides an effective way to solve the problem and marginalise over nuisance parameters. The $\mathcal{F}$-statistic, in widespread use throughout the gravitation waves community, is included in the method and suitably generalised to marginalise over linear parameters and noise at the same time. The method is applied to LPF simulator data and, thanks to its generality, can also be applied to the data reduction and analysis of future gravitational wave detectors.Comment: 10 pages, 3 figures, 1 tabl

Spacetime Metrology with LISA Pathfinder

LISA is the proposed ESA-NASA gravitational wave detector in the 0.1 mHz - 0.1 Hz band. LISA Pathfinder is the down-scaled version of a single LISA arm. The arm -- named Doppler link -- can be treated as a differential accelerometer, measuring the relative acceleration between test masses. LISA Pathfinder -- the in-flight test of the LISA instrumentation -- is currently in the final implementation and planned to be launched in 2014. It will set stringent constraints on the ability to put test masses in geodesic motion to within the required differential acceleration of 3\times10^{-14} m s^{-2} Hz^{-1/2} and track their relative motion to within the required differential displacement measurement noise of 9\times10^{-12} m Hz^{-1/2}, around 1 mHz. Given the scientific objectives, it will carry out -- for the first time with such high accuracy required for gravitational wave detection -- the science of spacetime metrology, in which the Doppler link between two free-falling test masses measures the curvature. This thesis contains a novel approach to the calculation of the Doppler response to gravitational waves. It shows that the parallel transport of 4-vectors records the history of gravitational wave signals. In practice, the Doppler link is implemented with 4 bodies in LISA and 3 bodies in LISA Pathfinder. To compensate for noise sources a control logic is implemented during the measurement. The closed-loop dynamics of LISA Pathfinder can be condensed into operators acting on the motion coordinates, handling the couplings, as well as the cross-talks. The scope of system identification is the optimal calibration of the instrument. This thesis describes some data analysis procedures applied to synthetic experiments and shows the relevance of system identification for the success of LISA Pathfinder in demonstrating the principles of spacetime metrology for all future space-based missions.Comment: PhD thesis defended at University of Trento on 26th March 2012. Advisors: Stefano Vitale, Mauro Hueller. Committee: Eugenio Coccia (Univ. of Rome, Tor Vergata), Philippe Jetzer (Univ. of Z\"urich), Eric Plagnol (APC-CNRS, Paris), Rita Dolesi (Univ. Of Trento

Detection principle of gravitational wave detectors

With the first two detections in late 2015, astrophysics has officially entered into the new era of gravitational wave observations. Since then, much has been going on in the field with a lot of work focussing on the observations and implications for astrophysics and tests of general relativity in the strong regime. However much less is understood about how gravitational detectors really work at their fundamental level. For decades, the response to incoming signals has been customarily calculated using the very same physical principle, which has proved so successful in the first detections. In this paper we review the physical principle that is behind such a detection at the very fundamental level, and we try to highlight the peculiar subtleties that make it so hard in practice. We will then mention how detectors are built starting from this fundamental measurement element.Comment: 12 pages, proceedings of the "Fifth Joint Italian-Pakistani Workshop on Relativistic Astrophysics", 21-23 July 2016, Lecce, Ital

Space tests of the strong equivalence principle:BepiColombo and the Sun-Earth Lagrangian points opportunity

The validity of General Relativity, after 100 years, is supported by solid experimental evidence. However, there is a lot of interest in pushing the limits of precision by other experiments. Here we focus our attention on the equivalence principle, in particular the strong form. The results of ground experiments and lunar laser ranging have provided the best upper limit on the Nordtvedt parameter {\eta} that models deviations from the strong equivalence principle. Its uncertainty is currently {\sigma}[{\eta}] =4.4 $\times$ $10^{-4}$. In the first part of this paper we will describe the experiment, to measure {\eta}, that will be done by the future mission BepiColombo. The expected precision on {\eta} is $\approx$ $10^{-5}$. In the second part we will consider the ranging between the Earth and a spacecraft orbiting near the Sun-Earth Lagrangian points to get an independent measurement of {\eta}. In this case, we forecast a constraint similar to that achieved by lunar laser ranging.Comment: 11 pages, 2 figure

Space-borne gravitational wave detectors as time-delayed differential dynamometers

The basic constituent of many space-borne gravitational missions, in particular for interferometric gravitational waves detectors, is the so-called link made out of a satellite sending an electromagnetic beam to a second satellite. We illustrate how, by measuring the time derivative of the frequency of the received beam, the link behaves as a differential, time-delayed dynamometer in which the effect of gravity is exactly equivalent to an effective differential force applied to the two satellites. We also show that this differential force gives an integrated measurement of curvature along the beam. Finally, we discuss how this approach can be implemented to benefit the data analysis of gravitational wave detectors.Comment: 5 pages, 1 figur

Data from a dynamic simulation in a free-floating and continuous regime of a solar greenhouse modelled in TRNSYS 17 considering simultaneously different thermal phenomena

This dataset supports the research article “Complete green- house dynamic simulation tool to assess the crop thermal well-being and energy needs”[1] . In the agricultural sector, the use of energy can be very intensive [2] and the sim- ulation of solar greenhouses is a very complex work [3] . This dataset provides the results of thermal modeling and dynamic simulation of a solar greenhouse considering si- multaneously several thermal phenomena. The analysis was performed by TRNSYS 17 software (TRaNsient SYstem Sim- ulation)