Recently I have posted the question Einstein-Hilbert action as an effective field theory. I have received a lot of downvotes and it's ok because it was unclear: in order to repair I tried to close it opening a more precise one of the same but now they are downvoting both. I would like to know what is so wrong with them. The new one is Breaking of diffeomorphism invariance after fixing a background metric.
As it was explained many times, the downvoters don't need to explain their reason. It is because the anonymity of the votes are considered more important by the SE.
We can't do too much with it, if they would require to give an explanation, there would be much fewer downvotes, and it would open the door to revenge attacks.
What the other answerers didn't explain clearly: yes, it is not okay. It is particularly evil, if:
- it is a first downvote
- there are many downs, all without explanation
- if the reason of the downvote isn't obvious
You can consider this like an election. It would be hilarious if a not elected politician could challenge the people, why they didn't elect him. Although it is quite possible that their reason wasn't fair.
So, it is not okay, but it seems it is the lesser evil.
There are major differences between the behavior of the SE sites. I think, most people using multiple SE sites actively agree that the Physics SE isn't the friendliest one.
Furthermore, most of the downers won't go back to the post, thus the downvotes remain even if you already fixed your post. And you have no way to ask them to consider a vote change. You can ask this in a comment, but most of them wouldn't see also that.
On the meta SE, it is a quite common suggestion to implement some feature into the SE software, which could - anonymously - re-attract the attention of the downvoters, after the OP thinks he fixed his post. Unfortunately, the SE (company) doesn't seem very sedulous to implement similar user requests since some years.
There are some tricky ways, most of them is on the border case of misusing the site. Deleting the post and re-posting it would solve the problem, but it would be surely considered as a serious misuse, don't do it (10k+ users would see, what you did).
To address your concern that people are downvoting both of your questions: I think that's appropriate. Please don't re-post a question that wasn't well-received. Instead follow this advice to improve and promote the original question:
- You can "bump" your question by editing the question to provide status and progress updates resulting from your own continued efforts to answer the question yourself. I usually do that unless I really hit a dead end with no further clues to follow. Some times I eventually bring about enough understanding to realise the answer, and thus post a resolution to my own problem.
- If you have at least 75 rep points, you can offer a bounty, promising to give some of your points to the person who correctly answers your question.
- Upvote the original question - every upvote helps increase its profile on the site.
- Use the share button beneath the original question to advertise it to your networks.
To these bits of advice I might add:
- Ask for guidance about the questions on Meta (hello!) or in the chat, and take any advice you get there to heart for present and future questions.
For what it's worth I have closed your second question as a duplicate of the first.
I can't speak to the physics content of your question, which is outside of my specialty, but I personally think it looks interesting.
I'd like to address some points that rob didn't touch upon.
First of all, I want to say something about your comment
I just want to understand how to improve a post is good, maybe I made confusion because of my English
Let me tell you that I sympathise with you because English is not my first language either, and I too sometimes find it difficult to express my thoughts clearly. Like it or not, poor grammar will reduce the overall quality of the post. The reception of a post with poor grammar is automatically worse than than of a post with good grammar, even if the physical content is the same. And this happens even though most users try to focus on the physical content of the question; it is a subconscious process.
For this reason you (and I) have to make an extra effort when posting Q&A here. You'll have to live with that. In any case, don't fret too much about it, as most users here have good intentions and they'll try to help.
Now back to your post(s). Your first question was edited several times. The first version is indeed unclear, and unfortunately it mentions diffeomorphisms invariance. Later on you edited it and deleted the part about diff. inv., but the question was still rather unclear. You got an answer but it did not address your concerns (it didn't address your true question, because it was not clear what your true question was).
At this point you had two options:
To edit your question and introduce some changes in order to make it clear what your true question is. The problem is that major edits that change the meaning of the question are discouraged if the question does already contain an answer.
To post a new question, which clearly highlights your concerns. You should only do this if the new question is significantly different than the first one; otherwise, it will be closed as a duplicate.
As you can see, your case is very complicated because a major edit to your first question is discouraged, but posting a new one was not well received either, as the second one was similar to the first one (the culprit seems to be that you mentioned diffeomorphism invariance in the first question, even though you deleted that part later on). If you hadn't mentioned diff. inv. in the first question, the second one would have been significantly different and not closed as a duplicate.
When I first read your first question I didn't understand it, and when I read the second one I felt that you were asking the same thing twice. Now I realise that you didn't really have an alternative but to repost the question, because the first question didn't ask what you really wanted to ask. If only you hadn't mentioned diff. inv. in the first one! In its current state, the first question does not mention diff. inv. anymore. Therefore, I would say that the second one is not a duplicate of the first one. Maybe we could ask to the rest of users to consider voting to reopen it.
At this moment, your first question is
How can we construct the interaction terms of the Einstein-Hilbert Lagrangian as a function of $h$?
and your second question is
How can we be sure that the diffeomorphism invariance of the Einstein-Hilbert Lagrangian is not lost upon the field redefinition $g=\eta+h$? Moreover, how can we prove that such an invariance is kept order by order in $h$?
The first one is about the construction of the Lagrangian, and JamalS's answer addresses that. The second one is about the symmetries of the Lagrangian once expanded, and as such, I'd say that it is significantly different than the first one.
The problem is that you also mentioned diff. inv. in the first question, but that part is already deleted and JamalS's answer does not address that. To me, the second question should be reopened (and I have already voted to reopen it).
 Consider replacing "define" with "construct".
 Of course, it is possible that I have misunderstood your questions again. If that's the case please correct me in the comments.