Final Report Summary - LOWMEDGWEST (Precise Parameter Estimation of Gravitational Waves Sources of Low and Medium Frequencies.) Gravitational Waves (GWs) are predicted as a consequence of Einstein's general theory of relativity. Observational evidence for their existence has been obtained through precise measurements of the orbital decay of binary pulsars, like PSR 1913+16, the discovery and study of which earned the 1993 Nobel prize in physics for Hulse and Taylor. GWs are generated by the relative acceleration of massive bodies travelling at very high speeds. These are highly energetic processes, which produce spacetime oscillations (gravitational waves) that modify the distance between spacetime points and propagate at the speed of light away from the source. GWs have not yet been directly detected by man-made detectors, but now, four decades after the discovery of the Hulse and Taylor pulsar, GW astronomy is about to become a reality. In 2015 a network of ground-based interferometric GW detectors, including Advanced Virgo & Advanced LIGO, will begin data taking in the 10Hz-1kHz frequency range. In addition, pulsar timing arrays (PTAs) should detect a background of nanohertz GWs within this decade. To open up the millihertz band, ESA has selected The Gravitational Universe as the science theme to be addressed by the European L3 large satellite mission. To realise this theme, the space-based interferometer eLISA will be launched in 2034, with a precursor technology mission LISA Pathfinder to be launched by the end of this year. The research supported by this project has provided essential theoretical results that will help to realise the scientific objectives of these ambitious GW detection experiments.According to our best understanding most (perhaps all) galaxies host a massive black hole (MBH) in their centre. These MBHs are typically surrounded by clusters of stars and large angle scattering encounters between objects in these stellar cusps can lead to a stellar compact object (SCO) with mass in the range 1 to 100 solar masses (such as a neutron star or a stellar mass black hole) to become gravitationally bound to the MBH, forming an extreme-mass-ratio binary. The SCO will typically be on a highly eccentric orbit, which then shrinks and circularises due to the loss of energy and angular momentum through the emission of GWs. This process is known as an Extreme-Mass-Ratio Inspiral (EMRI) and, for black holes with mass in the range one hundred thousand to ten million solar masses, these systems generate gravitational waves in the millihertz band, making EMRIs one of the key sources for space-based detectors like eLISA. Some cosmological theories predict the existence of less massive (intermediate) mass black holes (IMBHs) with masses between 100 and 10,000 solar masses. IMBHs may have contributed significantly to the epoch of reionization and could be strong sources of GWs. We do not yet have firm observational evidence that they exist, but GW detections may provide the first direct evidence. IMBHs can form EMRI like systems known as Intermediate-Mass-Ratio Inspirals (IMRIs), either (i) when an IMBH falls into a massive black hole, emitting at approximately 0.0001-0.01 Hz, or (ii) when a SCO inspirals into a IMBH, emitting in the ~0.1 − 100Hz range detectable by ground-based detectors like LIGO. Hence, IMRIs can be detected by both space- and ground- based detectors. E/IMRIs waveforms are rich with information; in particular they carry details of the SCO orbit, which is determined by the spacetime geometry outside the MBH. These systems can therefore be used to determine with high accuracy the physical parameters characterising the MBH spacetime and reveal whether gravity in the strong field regime behaves as predicted by General Relativity.GWs from E/IMRIs and other binary sources are complex signals and their detection will rely heavily on our capacity to accurately model them, as these signals must be identified in the presence of detector noise by matched filtering. This presents both technical and computational difficulties, since the template waveforms depend on many parameters, and one needs to compare the observed data with a huge number of waveform templates over the parameter space describing the system. Overall, the whole process is extremely computationally expensive, or even prohibitive. Furthermore, modelling GWs from E/IMRIs requires an accurate calculation of the self-force or radiation reaction that is responsible for driving the orbital evolution of the SCO, which is as yet an unsolved analytical problem.The main goal of the “LowMedGWEst” project was to contribute to the efficient and accurate acquisition of new astrophysical knowledge from GWs sources detected at low and medium frequencies. To achieve this ultimate goal, the project was focussed on (i) developing techniques to carry out fast extraction of parameter information from observed GW signals; (ii) modelling the evolution of IMRIs and EMRIs; and (iii) understanding how E/IMRIs can be used to test deviations in the theory of gravity away from the predictions of General Relativity.To address (i) the MC fellow has developed and transferred up-to-date applied mathematics techniques to develop a new numerical algorithm to perform quick and efficient Bayesian parameter estimation for GW sources of all types. This method relies on constructing a reduced basis - a set of templates (typically many fewer than the number of time samples in the waveform), a linear combination of which can be used to approximate any other model waveform to a specified precision. This basis is then used to identify a set of frequency sub-samples at which it is sufficient to know the waveform to obtain a good match to the data. This can reduce the overall computational cost of doing a waveform overlap (a comparison of a template with the data) by an order of magnitude or more. This methodology can be applied to all types of GW sources and detectors and the work supported by the proposal developed these methods for cosmic string burst sources and neutron star binary inspirals, that are expected to be observed in the near future by ground-based detectors. Extension to more complex cases, including E/IMRIs, is underway. During this research project, the MC fellow acquired diverse computational and theoretical skills and initiated new international collaborations with several research groups in the United States. The outcome of this research has been to speed up parameter estimation calculations implemented within the LIGO Algorithm Library (LAL) (the software package that will be used to analyse data from ground-based detectors over the coming years) by orders of magnitude.Regarding objectives (ii) and (iii) of the proposal, during the “LowMedGWEst” project, the MC fellow has addressed one of the main bottlenecks in the computation of the gravitational self-force, namely its dependence on the gauge used to compute it. In collaboration with a Spanish research group, she has developed a methodology to overcome the gauge problem associated with the computation of the gravitational self-force to carefully model E/IMRI evolutions and, subsequently, perform accurate parameter estimation and data analysis studies. In addition, the researcher has worked on new models of EMRIs. In particular, they have explored the impact of transient resonances on EMRI signals. It was recently realised that E/IMRIs generically pass through resonances at which two of the three frequencies characterising the motion of the SCO become commensurate. This leads to a change in the rate of evolution since the averaging of the mean radiation field that occurs off-resonance no longer takes place on-resonance. The researcher has studied the impact of resonances on EMRI waveforms and the corresponding implications for observations of these systems with eLISA. The researcher also explored how EMRIs can be used to test general relativity by developing EMRI waveforms in modified gravity spacetimes and studying the ability of space-based GW detectors to distinguish them from EMRIs occurring in normal black hole spacetimes. The researcher focused on dynamical Chern-Simons modified gravity spacetimes (a parity-violating modification of general relativity motivated by string theory) and explored the ability of eLISA to place constraints on such a theory. Finally, the researcher also explored the possible signatures of electromagnetic waves interacting with GWs, as a possible mechanism for multi-messenger observations of GW sources.This project has provided crucial results for the success of the new generation of ground- and space-based GW detectors. These results will have a significant impact on the new field of GW astronomy, and contribute significantly to EU leadership in the advancement in this new field.