Cosmology is the branch of astrophysics that studies the origin and dynamics of the Universe. Although the idea of a cosmo sets its root in human history, cosmology has entered the domain of proper science only about 100 years ago.
Back in the early 1920s, scientists were already aware that our solar system was located in a galaxy, i.e. a system of billion of stars gravitationally bounded to each other. However, it was unknown whether other objects similar to our own galaxy (the Milky Way) existed.
In 1923, Edwin Hubble realized that the astrophysical object that today we know as the Andromeda Galaxy was indeed a distant source composed of billions of stars, very much like our Milky Way. Since then, astronomers observed an ever growing number of galaxies. In 1929, Hubble made a second ground-breaking observation: he noticed that all the galaxies that he observed were recessing from us . He was able to determine that these galaxies were receding from each other with a velocity directly proportional to their distance.
v=H0 * d
where the constant linking the velocity and the galaxy distance, H0, is called the Hubble constant. Hubble had observed for the very first time that the Universe is expanding.
Despite this ground-breaking discovery by Hubble, the idea of an expanding Universe was not totally unexpected. In fact, between 1917 and 1922, W. De Sitter and A. Friedman showed that Einstein’ General Relativity predicted an expanding Universe if this was homogeeous and isotrpoic [2-3]. It was immediately recosnized that tha Hubble measurements can be explained with Einstein General Relativity. The galaxies were not departing each other, it was the fabric of the Universe, the spacetime, that was expanding.
This marked the birth of modern cosmology. Since then, scientists have learned more and more by observing the cosmo. We have learned that the Universe was born about 13 trillion years ago, that it was a dense and hot plasma, and we have observed its fingerprint, The Cosmic Microwave Background (CMB).
Despite our rapid proceedings in modern cosmology, there are still serious open issue, which challenge our knowledge of physics. Very recently, in 1998, it was observed that the Universe is not only expanding, but it is accelerating. According to Einstein theory of General Relativity, this is due to the presence of a cosmological constant, a form of energy which embed the 70% of our Universe and of which we ignore the physical origin. What is Dark Energy? Is is really a new form of energy of it just arise from the fact that general relativity is not really valid at cosmological scales?
Moreover, we have also experimental difficulties. Our model predicts the Hubble constant to be the same value at the level of the CMB and our galaxy neighborood. However, two indepdent experiments, find two different values which are not compatible each other. At the distance of the CMB, Planck observed a value of the Hubble cosnstant of 67 km/ Mpc s , while in the local Universe we observed a value of 72 km/ Mpc s . Why these observations are different? Is there a bias in the experimental setup or maybe we are observing a different physics at cosmological scales?
Gravitational waves might help to solve these open issues in cosmology. Gravitational waves are perturbation in the fabric of the spacetime which are propagating from extremely violent and energetic astrophysical events. This type of radiation is very week and have been observed for the first time only recently in 2015 from the coalescence of two black holes. However, gravitational waves are very special, since they do not interact with matter during their travel (they arrive to us as they depart) and from their detection we can directly measure the luminosity distance of the source. This is a crucial information for cosmological measurements.
In fact, in 2017, following the detection of a gravitational wave from a binary neutron star merger together with the identification of its hosting galaxy, we have been able to provide a new measurement for the Hubble constant. We inferred a measure of 70+12-8 km/Mpc s. This measurement will become more and more accurate as we combine more gravitational wave detections. By detecting further and further gravitational wave source we will be able to collect useful information for solving these open issues in modern cosmology.
At the Paris Centre for Cosmological physics we study how GW can help to solve these modern cosmological issues. In particular, we study what level of accuracy we will reach with future GW detectors for the measurement of the Hubble constant. In fact, the GW170817 Hubble constant measurement is strongly limited the the estimation of the GW170817 luminosity distance, which resulted about 40+4-7 Mpc. In order to get the best possible estimation of the source luminosity distance, our detectors needs to detect efficiently the two GW polarizations (The directions in which the GW oscillates). Unfortunately, our detectors are not sensitive to these polarizations at the same time and that is the reason why we need more GW detectors to localize a signal. In Fig. 3, we showed how increasing the number of operative GW detectors will help us to reduce the ‘problematic’ locations at which we are not able to separate the GW polarizations and give an accurate value for the luminosity distance. Switching from two detectors to 5 detectors, will reduce these sky locations from the 90% of the sky to only about the 5%. If we want to improve our measurments on the Hubble constant, we need more GW detectors.
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 de Sitter, W. 1917, MNRAS, 78, 3
 Friedman, A. A. 1922, Zeitschrift für Physik, 10, 377
 The Planck collaboration, 2016, AAP, 594, A13
 Reid, M. J. et al., 2019, APJL, 886,2
 The LIGO and Virgo collaboration, PRL, 116 (6): 061102
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