Hyperbolic Higgs inflation: Constructing Hyperinflation with a composite Higgs model

Sammanfattning

We explore Friedmann-Robertson-Lemaitre-Walker (FRLW) cosmology and introduce inflationas a means to fit observational data. Slow-roll inflation serves as an introduction to classical fieldtheory description of inflation through the inflaton field ϕ. We go in depth in a different modelof inflation called Hyperbolic inflation, or simply Hyperinflation, which has a negatively curvedfield space, and is favorable due to fewer constraints on the potential V (ϕ) of inflation. We goover curved field spaces through non-linear sigma models (NLSM), and extensively go through acomposite Higgs model as a NLSM with the non-compact group SO(4, 1)/SO(4).Our results show that the kinetic term for the psuedo-Goldstone bosons, along with the fieldspace metric, can be expressed in a closed form. We show that this composite Higgs model undergoesa Higgs mechanism similar to the Standard Model (SM), verifying it as a Higgs model. Our resultsshow that a connection between Hyperinflation and the composite Higgs models can be done throughthe simple relation f = L between the axion decay constant of the NLSM f and the curvaturelength scale L of Hyperinflation, and that other non-compact cosets can be used in a similar way toconnect to Hyperinflation with our methods. We state the predictions of this new Hyperinflationmodel, named hyperbolic Higgs inflation, based on energy scale restraints and general predictionsof rapid-turn inflation models.