Introduction to the gravitational wave background from the primordial universe

Being genuine propagating degrees of freedom of the spacetime metric, gravitational waves (GWs) serve as an independent "eye" through which we can probe the evolution history of our universe. They are complementary to electromagnetic observables such as cosmic microwave background (CMB) and can act as direct messengers from the earliest stage of the universe, where conventional probes lose access. In particular, a stochastic background of GWs is widely regarded as a smoking gun of cosmic inflation.
In this talk, I introduce the basic theoretical framework for GWs produced in the primordial universe and discuss how they arise from vacuum fluctuations of the metric. I also outline additional production mechanisms sourced by matter fields in the early universe and contrast their characteristic observational signatures with those of vacuum tensor modes. The emphasis of my talk will be on physical intuition and analytic derivations, with the aim of making the subject accessible to non-specialists in the astrophysics community.