The evolution of density fluctuations in the early universe inevitably generates gravitational waves. Cosmic microwave background observations measured such primordial density fluctuations on the largest scales in our universe (> Mpc). These large-scale fluctuations began their evolution days or years after the Big Bang. How was the universe at earlier times and on smaller scales? At the moment, we do not know much. But gravitational wave observations will provide new information in the next decades. In this talk, I will provide an overview of the so-called induced gravitational waves and how they can be used to probe the presence of primordial black holes. I will place emphasis on the effect of particle interactions on the resulting gravitational wave spectrum. On the occasion of the MITP conference, I will briefly discuss the implications of detecting high-frequency GWs for the primordial black hole scenario.

We consider 2 coupled Higgs doublets which transform in the usual way under SU(2)⊗U(1). By constructing marginal operators which satisfy an operator product expansion based on the SU(2) Lie algebra, we can obtain a rich pattern of renormalization group (RG) flows which includes lines of fixed points and more interestingly, cyclic RG flows which are unavoidable in this model. The hamiltonian is pseudo-hermitian, $H^\dagger = K H K$ with $K$ unitary satisfying $K^2 = 1$, thus the model is non-unitary. The hamiltonian still has real eigenvalues, but the non-unitarity is manifested in negative norm states. One can use the operator K to define projection operators onto positive norm states, and in this sub-Hilbert space the time evolution is unitary with positive probabilities. Upon spontaneous symmetry breaking, the Higgs fields have an infinite number of vacuum expectation values $v_n$ which satisfy “Russian Doll” scaling $v_n \sim e^{2n \lambda}$ where n= 1,2,3,...and $\lambda$ is the period of one RG cycle which is an RG invariant. We speculate that this Russian Doll RG flow can perhaps resolve the so-called hierarchy problem and may shed light on the origin of “families” in the Standard Model of particle physics

Experiments at rare isotope beam facilities have revealed 'halo nuclei' at the edge of the nuclear chart, which are exotic systems featuring a molecular-like structure of a core and halo nucleons. These nuclei play a crucial role in the astrophysical synthesis of elements. Effective field theory (EFT), combined with a nuclear cluster model, provides a robust framework for accurately describing the structure and dynamics of these halos. This talk will cover the fundamentals of halo EFT and demonstrate its application to key observables, including binding energies and radii, as well as essential reaction processes such as photo-disintegration and radiative nucleon captures
Slides here...