Alex,
One of the points of the article was to determine how long the inflation period lasted by studying antimatter, not the existance of inflation.
Seems like you were reading the article subjectively rather than objectively.
Having stated that, there is something very wrong with the article.
Antimatter in the form of the positron was discovered in cosmic rays in 1932.
Antideuteron, antihelium nuclei and antihydrogen have been produced in particle accelerators and while not being primordial shows that antimatter can exist in the Universe.
The journalist who wrote up the article doesn't know the difference between antiparticles and antimatter. (Let's hope the scientists didn't make the same mistake.
)
Antiparticles in the form of antiquarks may have existed during the early stages of inflation, but if the inflation period is extended so far out that matter/antimatter was formed, the Universe may have become too large to allow matter to coalesce into planets, stars and galaxies.
We would be in real trouble then.
.
Regards
Steven