let today = Date()
let datePredicate = NSPredicate(format: "date == %@", today)

// Get the current calendar with local time zone
var calendar = Calendar.current
calendar.timeZone = NSTimeZone.local

// Get today's beginning & end
let dateFrom = calendar.startOfDay(for: Date()) // eg. 2016-10-10 00:00:00
let components = calendar.dateComponents([.year, .month, .day, .hour, .minute],from: dateFrom)
components.day! += 1
let dateTo = calendar.date(from: components)! // eg. 2016-10-11 00:00:00
// Note: Times are printed in UTC. Depending on where you live it won't print 00:00:00 but it will work with UTC times which can be converted to local time

// Set predicate as date being today's date
let datePredicate = NSPredicate(format: "(%@ <= date) AND (date < %@)", argumentArray: [dateFrom, dateTo])
fetchRequest.predicate = datePredicate

let dateFrom = calendar.startOfDay(for: Date()) // eg. 2016-10-10 00:00:00
let dateTo = calendar.date(byAdding: .day, value: 1, to: dateFrom)