Handling date and time can be tricky on a query interface. If you create an end-user search interface, you may want to adapt to the user's timezone. You may decide to determine the user's timezone based on the locale, which makes sense in certain cases, but not always. You could use IP address, etc., but this may not work well in many corporate environments. My office is in Oslo, but the gateway out of the corporate network happens to be in Ireland. Hence, many applications tend to believe that I'm in Ireland.
If you look at how the SharePoint search web parts works, you will see that they are timezone aware. In the following search result, there are two test documents with different date/time in the write managed property. The first date is just showing the content of the write managed property. In the index, all datetime properties are represented as UTC. The second date is added by the web part, and is adjusted to my locale. I'm located in Oslo, which is one hour ahead of Greenwich.
In FAST Search for SharePoint, you can choose between two different query languages. The Keyword Syntax is the default query language in SharePoint. When using this language, you should be aware that all dates are adjusted according to the locale of the user. When using the Query OM, this is determined by the culture property. If you use the FAST Query Language (FQL), all dates should be specified in UTC syntax, and the search client should perform the necessary mapping. This is in most cases the preferred approach for search driven applications.
If you use query refinement, there are some other concerns. The default statistical binning in FAST Search Server will not give you datetime bins with reasonable date boundaries. What you typically want instead, is buckets such as 'today', 'yesterday', 'last week', 'last month', etc. You can do that as well, but then you need to create the (non-overlapping) bins per query in the client, based on the time when the user performs the query. Then you can combine these to provide possibly overlapping bins such as 'yesterday' and 'last week'. This is described in more detail in Query Refinement. If you want to adapt the bins to the user's time zone, you must specify the bins on date and hour boundaries to reflect change of day in the user's timezone, but specified in UTC.
See also part 2, which discusses datetime query syntax.