Can antibiotic resistant bacteria compete with normal one in an antibiotic free environment? The question is based on an intuition that antibiotic resistance can't come along. This mutation will probably make bacteria less tenacious. Is there any research how AR bacteria compete with normal one in an antibiotic free environment? Because if them generally lose to normal bacteria then AR bacteria is not a big threat and they can't spread to much.

The antibiotic resistance adds to growth cost. In an antibiotic free medium the antibiotic-susceptible strains will outgrow the resistant ones. See this