Executive Summary : | Gravity, the oldest of the known forces, poses the most interesting questions to the physicists. Its strength is so weak compared to the other three forces at electroweak scale raises questions of hierarchy of scales and also, hence unification with all of them. Gravitational waves are also elusive so far. Terrestrial gravitational wave observatories have initiated a rich program for the direct detection of gravitational waves. One of the interesting possibilities for GW studies is the existence of a stochastic GW background generated by a first-order phase transition during the early history of the Universe [54. E. Witten, Cosmic Separation of Phases, Phys. Rev. D30 (1984) 272–285.]. However, the electroweak transition within the Standard Model is found to be too weak to produce an observable amplitude of GW. Therefore, detection of any primorial GW signal would be clear evidence for physics beyond the Standard Model. There is already data taken by the LIGO/Virgo and in future more sensitive experiments will probe large fractions of the relevant parameter space. It is a good time to invest time and generate the required work force needed to do the necessary calculations and carry on required analysis. The author has studied gravitational wave generation in classically conformal U(1) B-L type models which is believed to be a good prototype for generating strong GW signals and also a viable dark matter candidate. There is plenty of scope to do similar work and to search for suitable parameter space that can generate waves. If detected, that will also help rule out many of such existing models beyond the standard model. Many studies are still left where it is interesting to look at the GW spectra due to first-order phase transitions in various extensions of the Standard Model. A good starting point is to understand the SM supplemented by a dimension-6 operator in the scalar potential of the form $H^6$. Such a model has only one parameter, namely the scale $\Lambda$ and hence, is very much predictive. Many such extensions can be concocted to study GW signature in such future space as well as ground-based experiments. GW observations can become complementary searches against the collider searches. An usual early universe phase transition could have taken place in the 100 GeV ~ 100 TeV energy range which can generate GW that can be detected in interferometry experiments. The similar energy range will be probed by the HL-LHC and ILC/CLIC and particularly, the muon collider. People have already started pointing out such complementarity between two kinds of searches, yet there are many holes to be filled in before one could get a complete idea. Since, EWPT is responsible for the generation of GW signal, various robes related to Higgs e.g. Higgs self coupling, Higgs decay to new BSM particles etc could be the important searches in the collider. Similar GW-collider complementarity could also be invoked to study Supersymmetric models. |