it can be seen that increasing the observing time towards a given direction, will increase the number of detected events.\\
\noindent
Other ways to improve duty cycle is to increase the observable volume: this can be achieved by spending time on hardware to improve sensitivity on a given frequency bandwidth \cite{kisseltalk1}.
Other ways to increase the number of detectable events is to increase the observable volume: this can be achieved by spending time on hardware to improve sensitivity on a given frequency bandwidth \cite{kisseltalk1}.
\begin{figure}[h!]
\centering
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@@ -78,7 +78,6 @@ We started our design on the chambers on the X arm. Along this direction, the In
%\label{imc}
%\end{figure}\\
\noindent
In the next section we will demonstrate that CPS are good witnesses to sense differential motion and that they also can be used to lock the chambers with each other.
@@ -10,7 +10,7 @@ A detailed structure of the thesis then follows.
Gravitational waves are an astrophysical event that takes place when massive objects move with a quadrupolar momentum and deform the fabric of spacetime \footnote{An in-depth source about how gravitational waves have been computed and their features is \cite{mag}.}. They have been theorized by Albert Einstein in 1915 and discovered a hundred years later by a joint collaboration of two detectors \cite{nar}\cite{first}, which was worthy of the Nobel Prize for Physics in 2017 \footnote{See Appendix C for some information about the first detection of gravitational waves.}.\\
\noindent
The effect of gravitational waves when they pass through an object is to produce a deformation of the physical lengths (L). This effect is very small ($\Delta$L/L $\sim$ 10$^{-21}$): masses able to deform the fabric of spacetime and generate gravitational waves are of the order of more than the solar mass $M_{\odot}$, so such massive objects need to be looked for in the Universe.\\
The effect of the gravitational-wave radiation is to produce a strain $h$ that induces a deformation of the physical lengths. This strain is typically very small ($h$$\sim$ 10$^{-21}$), because the strain amplidute scales as $\sim GQ/c^4$, where $G =6,67\time10^{-11}$ Nm$^2$/Kg$^2$, Q is the quadrupole mass moment of the wave and c is the speed of light \cite{mag}. The quadrupole mass moment is directly proportional to the mass of the object involved: masses able to deform the fabric of spacetime and generate gravitational-wave amplitudes detectable on the Earth are of the order of more than the solar mass $M_{\odot}$, so such massive objects need to be looked for in the Universe.\\
\subsection{A challenging detection}
Detecting gravitational waves is particularly challenging, because the effect is very small, and the sensitivity required for an instrument to see it must be suitably high.\\
@@ -71,15 +71,10 @@ A significant contribution to this goal could be added by the opening of the low
\subsection{Duty cycle of the detector}
The ground-based instruments are currently tuned to detect inspiraling binaries: the duty cycle of the detector is then very important for assessing its sensitivity. This quantity represents the number of cycles $N_c$ spent by the instrument in the frequency bandwidth of interest. As we will see in Chapter \ref{CPSdiff}, this depends on how much time the detector can maintain resonance, i.e. on its stability, and it is given by \cite{mag}:
\begin{equation}
\centering
N_c = \int f_{gw}(t) dt.
\end{equation}
The ground-based instruments are currently tuned to detect inspiraling binaries: the duty cycle of the detector is then very important for assessing its sensitivity. This quantity represents the time spent by the instrument in observing mode. As we will see in Chapter \ref{CPSdiff}, this depends on how much time the detector can maintain resonance, i.e. on its stability.
\noindent
This quantity defines for how many cycles (and hence how much time) the detector can follow the evolution of a signal in a given frequency band. The ground-based detectors are sensitive to operate for thousands of cycles \footnote{Interesting examples on typical duty cycles for ground- and space-based detectors can be found in \cite{mag}.}. Lowering the frequency band and increasing the sensitivity would increase the number of cycles, allowing the following of a signal for longer \cite{mag}. The consequent advantage is more precise waveform predictions based on these observations, in addition to the detection of objects still unknown.
Duty cycle tells us for how much time the detector can follow the evolution of a signal in a given frequency band. Lowering the frequency band and increasing the sensitivity would improve the duty cycle, allowing the following of a signal for longer time, as we will see in Chapter 5. The consequent advantage is more precise waveform predictions based on these observations, in addition to the detection of a higher number of objects.
\section{The goals of the gravitational-wave collaboration}
The efforts of the scientific collaboration, towards the opening of the low frequency window, are devoted to the development of new technologies for active control of the noise sources, responsible for the lack of sensitivity below 30 Hz \cite{lf1}\cite{lf2}\cite{lf3}. This has been the target of focus during the workshops dedicated to the low frequency band, which I attended between 2018 and 2021.\\
I confirm that the work presented in this thesis is original and has been entirely carried out by the author, started and completed at the University of Birmingham. The work done in collaboration with other scientific groups and/or abroad has been suitably highlighted throughout the thesis.\\
