On Big Bang Theory, Sheldon is distraught because the discovery of the Higgs boson invalidates his work on string theory.
Assuming this is accurate, and that I’ve understood the situation correctly, what exactly is the connection between the two? 
You’ll get a physicist answering pretty soon, but one thing I’ve heard about string theory is it really isn’t a theory because it has no falsifiable implications (yet at least). But the nonexistence of a Higgs particle is certainly falsifiable, so Sheldon’s string theory is at least apparently not a standard one. Certainly all those physicists actually doing string theory have not said something similar.
So Sheldon must have a very particular version of string theory – perhaps a particular parameterization which says something like the Higgs mass must be 10 times as large ans what was found.
The discovery of the Higgs doesn’t invalidate the string model: Nothing can really do that, since the model is way too flexible (this is its primary failing, in fact). It may well invalidate Sheldon’s particular work on it, but to know the details of how this happened, we would have to know the details of Sheldon’s work.
And neither the Higgs nor the string model particularly relates to cosmology (the study of the Universe as a whole). They’re both topics in particle physics.
From what I’ve seen of the show, I seriously doubt the writers even have the slightest idea about the details, other than “hey these are fancy words people might have heard of…”
Is this the episode you are thinking of? If so, he doesn’t say what you said.
Separate from the show: You can have incarnations of string theory that predict certain properties for the Higgs, but seeing a Higgs doesn’t blow string theory out of the water in any generalized way.
Quite the opposite. The show is renown for its accuracy. David Saltzberg of UCLA is the show’s science consultant.
I can’t find a cite that he is still doing it, but for at least the first 6 seasons they had David Saltzberg as a consultant to make sure the science was right.
“Bona fides: Bachelor’s degree in physics from Princeton. Ph.D. in physics from the University of Chicago. Post-doc at CERN. Currently a professor of physics at UCLA.”
Also, “the character Amy Farrah Fowler, the actress that plays her is Mayim Bialik and she has a Ph.D. in neuroscience” so she helps out too.
And as far as the writers go, Saltzberg says “These writers know a lot of science. Sometimes they’ll have a whole piece of science dialog that they’ve come up with and I just have to check it. For example, the script I’m reading right now I changed one letter.”
What, specifically, have you seen if the show that supported that doubt?
As I recall, Sheldon began considering shifting his research after the Higgs breakthrough when it was pointed out to him that even if he wrote the correct string equations, there would probably never be an experimental confirmation for him like the one Peter Higgs just got. Not what you said.
If only they had a few comedy consultants, then it might actually be worth watching!
I believe so. This, and the final episode of Season 7, where he’s refused permission to swich from string to inflationary theory.
I get it now. Thanks for all the clarifications!