ost is an uncountable noun when you speak of cheese in general, so it appears bare: ost = “cheese.” After utan (“without”) you leave it bare: utan ost = “without cheese.”
– utan en ost is ungrammatical, because you don’t count cheese that way.
– utan någon ost (“without any cheese”) is possible if you want extra emphasis, but usually utan ost suffices.
utan means “without” and links two things (e.g. a sandwich and its missing ingredient). It specifies absence of something.
inte is the general negation particle that negates a verb or clause.
– Jag äter inte = “I do not eat.”
– Jag äter en smörgås utan ost = “I eat a sandwich without cheese.”
If you said Jag äter inte ost, you’d mean “I don’t eat cheese” (ever), not “the sandwich has no cheese.”
You only change the verb tense: