How to get the start time and end time in utc of a day for a specified timezone in javascript?

Depending on what exactly you want to do:

// for the current day
var start = moment.tz(timezone).startOf('day').utc();
var end = moment.tz(timezone).endOf('day').utc();

// for a specific moment (m)
var start = m.clone().tz(timezone).startOf('day').utc();
var end = m.clone().tz(timezone).endOf('day').utc();

// for a specific calendar date
var m = moment.tz(date, format, timezone);
var start = m.clone().startOf('day').utc();
var end = m.clone().endOf('day').utc();

You can then format start and end however you like with the format function.

Keep in mind also that not every day starts at midnight in every time zone, nor do all local days have 24 hours.