What is phantom matter and how is it different from dark matter? What is phantom matter and how is it different from dark matter? I have googled the term "Phantom Matter" and the results were mostly research papers which assume that the readers already know the term. 
P.S. Please help me tag; I don't have a clue what this is really about.
 A: Firstly note that cosmologists tend to use the terms matter and energy interchangeably because what matters is normally the energy density and matter is counted as energy using the well known expression $E = mc^2$. But, as Julian says in a comment, it's more common to speak of phantom energy rather than phantom matter.
To understand what phantom energy is consider the following:
Suppose you have a cube of side $a$, so the volume of the cube is $a^3$. If we have regular matter like a gas inside the cube then the density is inversely proportional to the volume so it's proportional to $a^{-3}$:
$$ \rho_{matter} \propto \frac{1}{V} \propto a^{-3} $$
But this is not a universal law. For example in the very early history of the universe the energy density was dominated by radiation not matter. As the universe expanded it affected the energy density in two ways: firstly the density fell as $a^{-3}$ like matter, but secondly the expansion red shifted the radiation. The net result is that the energy density fell as:
$$ \rho_{radiation} \propto a^{-4} $$
Finally, the energy density of a cosmological constant, which is one of the suggested sources of dark energy, is constant as the universe expands so the energy density is independant of $a$:
$$ \rho_{cc} \propto a^0 $$
But suppose you had some stuff that has an energy density proportional to a positive power of $a$:
$$ \rho_{phantom} \propto a^n $$
where $n > 0$. This means that as the universe expands the energy density increases instead of decreasing, and this makes the expansion faster. The result is that the expansion rate increases exponentially and the universe is destroyed in a Big Rip. This stuff is called phantom energy.
As for what phantom energy is, at the moment phantom energy is just a cute idea for theorists to play with and there are no concrete suggestions for what it consists of. But then we don't know what dark energy consists of either.
Note that dark matter scales just like ordinary matter i.e. $\rho \propto a^{-3}$. As Julian mentions in a comment above, phantom energy is unrelated to dark matter though it could be a form of dark energy.
