diff --git a/luigi/parameter.py b/luigi/parameter.py
index bc06127721..bb703aa775 100644
--- a/luigi/parameter.py
+++ b/luigi/parameter.py
@@ -508,7 +508,7 @@ class OptionalStrParameter(OptionalParameterMixin[str], Parameter[Optional[str]]
     expected_type = str
 
 
-_UNIX_EPOCH = datetime.datetime.utcfromtimestamp(0)
+_UNIX_EPOCH = datetime.datetime(1970, 1, 1)
 
 
 class _DateParameterBase(Parameter[datetime.date]):
diff --git a/luigi/tools/range.py b/luigi/tools/range.py
index f47c739c7a..e1294d1bf8 100755
--- a/luigi/tools/range.py
+++ b/luigi/tools/range.py
@@ -32,7 +32,7 @@
 import time
 import warnings
 from collections import Counter
-from datetime import date, datetime, timedelta
+from datetime import date, datetime, timedelta, timezone
 
 from dateutil.relativedelta import relativedelta
 
@@ -216,7 +216,7 @@ def requires(self):
             raise ParameterException("Can't have start > stop")
         # TODO check overridden complete() and exists()
 
-        now = datetime.utcfromtimestamp(time.time() if self.now is None else self.now)
+        now = datetime.fromtimestamp(time.time() if self.now is None else self.now, tz=timezone.utc).replace(tzinfo=None)
 
         moving_start = self.moving_start(now)
         finite_start = moving_start if self.start is None else max(self.parameter_to_datetime(self.start), moving_start)