Can an object move faster than light in an accelerated frame of reference? In an accelerated frame attached to an accelerating rocket the Lorentz contraction of the rest frame is steadily increasing, which means that distant galaxies are getting closer and closer. Does this mean that the galaxies are moving faster than light (towards the rocket) in the accelerated frame?
 A: When you move from one inertial frame to another, or, to put it another way, when you are in an accelerating reference frame, the coordinates of objects can indeed move faster than c. If you are standing so that the Sun is directly to your right, and you swivel round so the Sun is directly to your left, in your accelerating frame of reference the Sun has moved around you faster than the value of c.
If you accelerate from rest in a straight line, distances in your original rest frame will be shortened as a consequence of length contraction, so that an object sufficiently far away will appear to be moving towards you faster than c. However, the light from that distant object will also seem to be approaching you faster than c, so the distant object is still not 'really' moving faster than light- the effect is just an artefact of your continually changing reference frame. See, for example, https://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
A: 
Does this mean that the galaxies are moving faster than light (towards the rocket) in the accelerated frame?

In a coordinate-independent sense nothing with mass can ever move faster than light. However, in non-inertial frames it is possible for things with mass to move faster than c. In such frames the speed of light is not restricted to c, so moving faster than light and moving faster than c are not the same.
