My question is about the use of the adverb "consistently" at the beginning of a sentence. For instance, in the sentence
Consistently with literature that pertains to acculturation and intercultural adaptation, our findings resulted in (...)".
I was told to correct the adverb to "consistent", in this sentence as well as in others (ex: "Consistently with the literature that asserts (...)", "Again consistently with literature, (...)"). What I mean is that the findings in our work are consistent with the findings of other works (after which I proceed to explaing in detail our findings).
Can you please explain to me if the use of this adverb here is incorrect, and if yes, why? It just feels strange to use an adjective here. I know I can change the sentence in a way that changes words and word order while maintaining the same meaning, but I would still like to learn if this usage is correct or not, for future reference.
If I should be posting this elsewhere, please indicate the proper forum/website.