Cosmology with Gravitational Waves



The direct detection of Gravitational Waves (GWs) by the ground-based LIGO/Virgo interferometers in 2015 has opened up gravitational wave astronomy in the regime of high-frequencies.  New sources have already been found – namely black-holes with masses larger than those expected from remnants of supernovae explosions and stellar evolution – and it is likely that other unexpected phenomena will be revealed by GW observations in the low redshift universe. Furthermore, with LIGO/Virgo one can start to probe fundamental physics, as for example cosmic strings, exotic inflationary scenarios and possible modifications to Einstein Gravity. It is however the space-based interferometer LISA (Laser Interferometer Space Antenna) that has the biggest potential in probing fundamental physics and cosmology. It will access low-frequency, high-redshift, regimes out of the reach of ground-based interferometers, and provide a GW window on the TeV energy-scale in the early universe. GW interferometers, possibly in conjunction with electromagnetic and neutrino telescopes for the detection of counterparts, will provide very valuable information helping cosmologists to tackle some of the many puzzles of our universe, namely dark energy (measure of its equation of state through standard sirens), dark matter (could dark matter consist of massive primordial black holes?), and the processes occurring in the early universe “dark era” going from the end of inflation to the occurrence of the QCD phase transition (unaccessible by only other means since photons are tightly coupled). 

The context of this PhD is the study of different aspects of early and late-time cosmology in the context of the science behind LISA and LIGO/Virgo.  The work will be carried out in the theory group of APC, which has close links to the APC gravitation group containing many experimentalists working on LIGO/Virgo and LISA.  At the international level, the student will take advantage of the lively and stimulating environment of the LISA cosmology-consortium, and his/her work will be relevant for LISA science case and possibly inscribed in the context of the scientific analyses within the consortium.  Other than becoming a specialist at the forefront of understanding of early- and late-time cosmology and gravitational waves, during the PhD, the student will develop a number of different skills including techniques of mathematical physics, quantum field theory, statistics and numerical methods.

Plan of PhD research:

Year one (approximately): 

The first part of the PhD, ideally to be completed within one year, deals with sources of gravitational radiation operating in the early universe. In particular, we will tackle phase transitions in the early universe, and the stochastic background of GWs that they can produce. In first order phase transitions, the signal has at least four origins:  the direct collision of the bubble walls ; the sound waves in the hot plasma surrounding the bubbles created by the bubble expansion ; the magnetohydrodynamic turbulence due to the bubble wall collisions; finally, if the phase transition gives rise to topological defects such as cosmic strings, they can also act as powerful sources of gravitational radiation. Initially, and following on from the stage, the focus will be on sound waves and the possible generation of shocks leading to turbulence in the plasma, both through analytical modeling and numerical estimations. In the context, we will also study possible signatures from the formation of current carrying cosmic strings. These results will be important to establish to which level LISA will be able to put constrains on models beyond the standard model of particle physics leading to first order phase transitions, and to the breaking of symmetries leading to topological defects.  

Year two (approximately):

In the second year of PhD, we will turn to late time cosmology and the use of the GW signal from compact binaries to probe cosmological parameters. The main issue in this context is the possibility to identify the redshift of the GW source. This can be done via direct detection of an electromagnetic counterpart, the difficulty residing in the poor angular resolution of the GW detector. We will concentrate on two alternative methods to probe the cosmological parameters. The first consists in developing statistical methods to extract the redshift: the GW source is assigned to an error box in redshift using the cosmology, and if a sufficient number of GW detections are available the cosmological parameters can be extracted as the error will cancel out. The second method consists in determining the effect of the large-scale matter perturbations on the GW propagation, and construct cross-correlations of GW catalogues and large scale galactic surveys to investigate whether information on the  cosmological parameters can be extracted. 

Year three (approximately):

The evolution of cosmological perturbations depends on the theory of gravity.  In the third year of the thesis the student will turn to theories of gravity beyond General Relativity [which will have been the basis of the previous parts of the thesis]. In particular the focus will be on those theories of modified gravity which are of interest to solve the cosmological puzzle of the accelerated expansion of the universe.   To start with, and for specific theories of modified gravity (including f(R) gravity), the student will build on work developed in his/her second year and return to the question of  the effect of large-scale matter perturbations on GW propagation . He/she will also investigate the traces of modified gravity theories in the GW-form, and more particularly in the merger phase of the 2 black-holes where the disformal coupling of matter to the modified gravity theory is expected to lead to important effects.  


Chiara Caprini et Daniele Steer






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