cosmic-microwave-backgroundcosmologydragreference framesspecial-relativity
Because the CMB is everywhere and is isotropic, if an object would have a certain velocity, it could have a pressure differential produced by the CMB which would produce drag till it would stop with respect to the CMB.
However, wouldn't this mean that there is a 'universal' reference frame created by the CMB? Wouldn't this be going against special relativity assumptions?
Another way of thinking that might be helpful to you is to take heed that $c$ is not primarily the speed of light. It comes indirectly to mean the observed speed by any observer of any massless particle, and because, as far as we know, light is massless, it comes indirectly to mean the speed of light. But, in its most fundamental form, $c$ is only a parameter that happens to have the dimensions of speed. It doesn't primarily refer to a speed: here's how we go about defining it.
Think about the intuitive Galilean addition of velocities. The combination law is linear. So, assuming a linear combination law, there are some basic symmetries and characterisics of this everyday law you might like to think about. The following might look a bit daunting at first but it really is intuitive and we're not talking about at first anything that gainsays everyday Galilean relativity, so I'd urge you to think about applying these ideas to the simple problem where we have three frames: $F_1$, the street, $F_2$ a bus driving along the street and $F_3$ a person walking down the aisle of the moving bus. In the following, let us call the shift from one frame to another, uniformly relatively moving frame a boost:
Now for the killer question:
Do the conditions 1 through 3 fully define a Galilean transformation? Or, more mundanely, What is the most general form of the matrix $T(v)$ that fulfils conditions 1 through 3?
It turns out that, not only does the Galilean law $v_{1,2}+v_{2,3} = v_{1,3}$ fulfill all the above axioms, but there are a whole family of possible transformations, each parameterised by a parameter $c$, with the Galilean law being the transformation law we get as $c\to\infty$. Such laws are the Lorentz transformations. See the section "From group postulates" in the "Derivations of the Lorentz transformations" Wikipedia page. Notice how one has NOT assumed that $v_{1,2}+v_{2,3} = v_{1,3}$, aside from in the special case of when $v_{1,2} = -v_{2,3}$. It seems likely that Ignatowsky (see Wikipedia page) was one of the first to understand that one could derive relativity from these assumptions alone in 1911, although Einstein actually mentions the group structure of the Lorentz transformations in his famous 1905 paper "On the Electrodynamics of Moving Bodies".
So imagine we had carefully reviewed Galilean relativity as above but we didn't know anything about special relativity. This might well have been how science might have progressed in the late nineteenth century were it not for the Michelson-Morley experiment. We would now understand that our everyday Galilean looking laws might actually arise from a universe wherein we have this weird $c$ parameter that is not infinite but simply very big: this would still be consistent with our everyday addition of velocity laws with a big enough $c$. At this point, we'd only know the form of the Lorentz transformation and that there were a $c$ parameter (maybe infinite) with dimensions of velocity, so we'd like to come up with some experiment to measure whether our universe had a finite $c$ value. It would not be apparent straight away that this velocity parameter were the velocity of anything in particular or indeed whether it even could be the velocity of anything. But, now we say to ourselves, what if something were going at this velocity relative to us? A simple study of the Lorentz transformation would show us that:
So now the Michelson Moreley experiment can be thought of not so much as validating relativity, but rather of showing that light, if made of particles, must be made of massless particles. The Michelson Morely experiment found something whose speed transforms precisely as foreseen by the general Lorentz transformation with a finite $c$, so it would then be a strong hunch (not a proof) that our universe indeed has a finite $c$ and that light is something that travels at this speed. In this context, a positive result of the Michelson Morley experiment (i.e. one showing a dependence of lightspeed on frame) could be thought of either as (i) detecting an aether (medium for light) but equally well (ii) it could be thought of saying that there is no aether but that the light particle has a small mass. Neither result would gainsay our newly found relativity laws.
Of course, many other experiments have since confirmed everything that a relativity grounded on a finite $c$ with $c$ set to the speed of light would foretell, so its quite reasonable to speak of $c$ as the speed of light in relativity. But I hope I have shown that this is not its primary meaning.
Footnote: Unfortunately these ideas don't quite work in more than one dimension. In one dimension, two boosts indeed compose to a boost, but a sequence of boosts in different directions in general compose to one boost together with a rotation. This rotation is called Thompson Precession. So we speak of the Lorentz group as the smallest group of all transformations that can be gotten from a sequence of rotations and boosts, but there is no multidimensional group of boosts, only the "one parameter" one dimensional group of boosts.
Your mistake is to assume that the cosmic microwave background constitutes a universal rest frame, because it doesn't.
In an FLRW universe there is a frame called the comoving frame or proper frame that is particularly mathematically convenient. This is the frame in which the comoving distance between all inhabitants of that frame is constant, so all the "stuff" in the universe is mutually stationary (the comoving frame factors out the Hubble expansion). Given that we expect all the "stuff" in the universe to be created in a similar way we would expect it to be approximately stationary (in a comoving sense) so the sum total of everything, matter and energy, acts as a reference point for the comoving frame.
So there's nothing special about the CMB. If you ignored the CMB and measured the Earth's velocity to all the galaxies we can see then you'd expect to get the same result as measuring the Earth's velocity relative to the CMB. The CMB occupies the same frame as everything else because it was created in basically the same way. The only special thing about the CMB is that gravitational interactions haven't given it various peculiar velocities as has happened for large aggregations of matter.
Best Answer
The CMB does in fact produce a preferential reference frame. Even without pressure, the preferential frame would be the one that equalizes the red and blue shift in all directions. For example Earth's motion around the Sun and the Sun's motion around the galaxy can be extracted from the red and blue shift in CMB data.
This does not contradict relativity, though, because the equations of physics are still valid and take the same form in any reference frame, even ones moving with respect to the CMB. Also, comparing your speed to the CMB requires looking far away, and relativity is based on the idea that your local neighborhood behaves the same regardless of your state of (inertial) motion.
In the same way, when analyzing motion on Earth, it usually makes sense to define our coordinate system so one axis aligns with gravity (i.e. "up and down"), because gravity is one of the main forces at work, and it reduces the number of sines and cosines needed in the equations. But that doesn't mean you could not obtain equally valid answers in a coordinate system with any orientation. And that "up and down" oriented coord system may not be the most natural choice in other situations, like a long way across the globe, or in the middle of space.
EDIT: In terms of "pressure" from the CMB, I think (?) you are referring to the radiation pressure $P$ of the distant source on a moving perfect reflector, as a function of velocity $v$, which Einstein in 1905 derived to be:
$$P=\frac{1}{4\pi}A^2\frac {(1-\frac{v}{c})}{(1+\frac{v}{c})}$$
where $A$ is the EM field amplitude. So this pressure does depend on velocity.