In the first part of the talk I will discuss gravitational wave signature arising from first order phase transition in two different models featuring neutrino mass generation
through type-I seesaw mechanism. The expected gravitational wave spectra from these models will be confronted with sensitivities of ground-based detectors such as LIGO as
well as several future space-based observatories. I will show that in case current and future gravitational wave observatories
find stochastic gravitational wave component that is not of astrophysical origin, such beyond the Standard Model signature would hint scale-invariant dynamics.
In the second part of the talk I will discuss recent work on the gravitational wave production from topological defects. The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported strong evidence for a stochastic common-spectrum process affecting the pulsar timing residuals in its 12.5-year data set.
I will show that this process admits an interpretation in terms of a stochastic gravitational-wave background emitted by a cosmic-string network in the early Universe.