I have a new Carrier 25HBR 13 Seer 1.5 ton heat pump and in the heating mode when the outside air is below 35, the unit cycles like crazy. Keeps me up at night. Is this correct? I have tried two different thermostats with the same result.

Yes it is defrosting. You need a cut out of some type. The company that installed your unit needs to come back and adjust or add a cut out for the outside unit.

Thanks,

The contractor indicated it was caused by the thermostat and the fact that when the temp is cold, then the unit goes off and soon as one degree change occurs, the unit comes back on. THen it meets the required temp and then it goes off. Sounded like bull.

YES BS for sure. If the unit cannot keep up due to a frost on the coil condition it will go to defrost too much. You need to do as suggested and use a temp cut off.

There could also be other problems like a low refrigerant charge but you will need a pro to check that out.