I frequently do a search with the following:
[cosmology] answers:0 .
I would like the questions ordered by the date they were asked with the most recent first. How can I make this happen?
This is actually a pretty easy feature, I think you may have just passed over it.
All you have to do it change from "Relevance" to "Newest" in that tab there, and it will sort based on when they were asked.
Here is how it looks on mobile browser, it's in approximately the same place and clicking on it brings up options to change the ordering.
If you don't want to have to put in the same settings every time, you can also create your own custom filter:
First, click "Create a custom filter" on the side bar
then you can specify that you want questions with no answers, sorted by date (Newest), and with the Cosmology tag.
You can save this filter using the "Save custom filter" button and name it whatever you want. For example, you could name it "Cosmology: 0 Answers by Date"
And now the filter is ready for you to just click on to access
What is also nice about this method is that the custom filter will indicate when a new question that matches the filter is made, so you don't even need to search for anything if there isn't anything new.