Higgs Boson (messenger particle of Higgs field) accounts for inertial mass, not gravitational mass.
So, how could it account for formation of universe as we know it today? I think, gravity accounts for such formations.. not inertia.
Is there a relation between both in Standard Model? Or, is there another way with which Higgs Boson contributed in the formation of everything?
From here:
Higgs is an atheist, and is displeased that the Higgs particle is nicknamed the "God particle", because the term "might offend people who are religious".Usually this inappropriate nickname for the Higgs boson is attributed to Leon Lederman, the author of the book The God Particle: If the Universe Is the Answer, What Is the Question?, but the name is the result of the insistence of Lederman's publisher: Lederman had originally intended to refer to it as the "goddamn particle".
So, originaly it was "goddamn" particle. And it is publishers to be blamed.
The term "God Particle" is used only by journalists. It's a wholly inappropriate term and I'd be very surprised if any physicist used it (outside of the lower end popular science TV programmes).
General Relativity tells us that inertial and gravitation mass is the same thing. The Standard Model isn't going to say anything directly about gravitational mass since it doesn't include gravity.
The reason Leon Lederman made up the name "God particle" is because anything with "God" in it sells books. So he called the Higgs the God particle, to sell books. The term didn't catch on, but he sold a lot of books.
