Do tenets of 'cosmic, transcendental and providential vision' of New England theological writers still linger in American culture?

What an interesting question.  I assume you're referring
to the Colonial American writers, such as Bradford, as those writing about "cosmic,
transcendental and providential vision."  Anything past that becomes more secular, as is
the case with Thoreau and Emerson--the next most cosmic and literally Transcendental
writers in America.  I'm certainly not a scholar on this particular kind of writing;
however, it seems to me there are plenty of cosmic and transcendental writers still
writing today.  Consider the naturalist writers, like Annie Dillard and Gene Eisely, as
well as the more philosphical/spiritual writers such as James Redfield and Eckart Tolle.
The difference to me is that those early writers seemed to have a clear sense that God
was their source, that His laws and prinicples were, indeed, transcendant, and their
very presence here in America was providential--that is, part of a God-inspired plan in
which He prepared and provided for them.  To that extent, I just don't see much current
writing which includes that aspect of things.  You will certainly find it in some books
written about that time period (such as The Light and the
Glory and From Sea to Shining Sea by Peter Marshall and
David Manuel).  Authors such as Newt Gingrich and other political-type writers are
reminding us of the providential history of America in their historical writings (such
as Gingrich's historical series including Gettysburg) and their
non-fiction treatises on why America needs to get back to the tenets and principles of
the Founding Fathers.  Oh, and some biographers are including those aspects in their
works on the Founding Fathers and other influential men of that day.  In short, I think,
the only current work containing the providential aspects of those early settlers is
about the past or an invocation of the past as being the path of the future.  It
lingers, there's a vestige, but it's certainly not prevalent. Again, good
question.