Dark Matter

Dark Matter is the polar opposite of Innocence in the D. Gray Man anime and manga and serves as the power source for both the Noah family and it's Akuma servants, and now also the Third Exorcists of the Black Order. A dark and terrible force, it appears as a black haze that invokes fear and dread in those that see it.

Akuma
All Akuma are created from a skeleton of Dark Matter, which seems to serve to bind the souls as well as giving them a form. After a level 0 Akuma, a new born one which is just the revived soul in the Dark Matter skeleton, kills its first victim, the person who called them back, the skeleton forces itself into its victim's skin and takes their form. As an Akuma evolves, so does the Dark Matter that comprises it. As the Dark Matter evolves, the soul within the Akuma deteriorates. The later Akuma evolutions are described as having souls in such states, that it makes onlooker physically revolted and sick to look at them. If an Akuma is killed by anything other than Innocence, then the soul powering the Akuma is consumed by the Dark Matter and lost forever.

Akuma have shown a variety of abilities as they and the Dark Matter comprising them evolves. Level 1s have a common Akuma Blood Virus bullet ability in which they fire bullets containing a poison which even a small amount rapidly deteriorates and kills the victim. Level 2s have the most variety in abilities, from mystical powers, to elemental control to physical morphing and enchanced combat strenght. Level 3s seem to bring the variety back into a more grouped area of powers, where they use the pure power of dark matter in an energy form itself to create unique abilities. Level 4s have shown no real unique abilities amoungst individuals as yet but they do have several shared abilities; they can create and fire Akuma Blood Virus bullets; use an Akuma scream capable of knocking even a General-level exorcist down to their knees and fire dark matter energy bolts. It could be the dark matter is mostly turned internally in their newest evolution, perhaps going some way to explaining the sheer increases that make them so strong and tough to destroy, even for general level exorcists.

The Noah Family
The Noah Family use Dark Matter to give them their unique supernatural abilities and all of their powers are based off it. Because of this, they are both vulnerable to Innocence and yet also Innocence is vulnerable to them; the Noah are capable of easily destroying innocence shards with their bare hands. The seperate, unique abilties of the Noah with the Dark Matter are as follows:
 * Millennium Earl: able to use Dark Matter to create new Akuma and to create very large explosions
 * Tryde: Unknown abilities.
 * Tyki Mikk (Joyd): Can create butterflies known as Tease to do his bidding. Also he has the 'Choose' ability, allowing him to touch or not touch whatever he wants, making him intangible or tangible as he desires. This allows him to pluck organs from peoples' bodies and pass harmlessly through buildings at will. Since 'awakening' with his true Noah surfacing, he can create ribbons of Dark Matter to bind and impale his oppoents and to fire blasts of Dark Matter energy. It seems the Dark Matter also grants him the extreme increases in speed, strenght, endurance and power.
 * Cyril Kamelot (Desires): His powers are as yet not fully explained but he has been shown to control the bodies of multiple people to his desires, matching him in name with deed. He has been shown controlling their movements and being able to cause their bones and limbs to break using simply his mind.
 * Wisely (Wisdom): The full extent of his powers have yet to be seen. The Dark Matter allows him to read peoples minds, crush their heads and move their bodies somewhat through the art of telekenesis. He is also able to project peoples' consciousnesses into others mind to observe their memories, like he did with Allen Walker by showing him Yu Kanda's memories of childhood.
 * Fiddler (Eclipse): Unknown abilities. It has been mentioned though he controls the powers of darkness, to an extent to impress the Millennium Earl himself.
 * Mercym (Mercy): Unknown abilities.
 * Skin Boric (Wrath): The Dark Matter gives him passive increases in both strenght and endurance. In his awakened Noah form, Dark Matter forms golden armour over his being, further increasing his offensive and defensive strenght. As an awakened Noah, he can create Dark Matter lightning easily in a variety of forms, in blasts, energy rings and chains. His lightning acts a form of self defense, for to even strike him is to be harmed. Skin Boric's powers are pure destruction; when fully charged and awakened, he can unleash attacks that utterly destroy the surrouding area and severely wound powerful exorcists like Yu Kanda.
 * Road Kamelot (Dreams): Road is able to use the Dark Matter to warp reality, creating pocket dimensions in which she traps oppoents. She is able to control every ascept of these dimensions, hence making her a tough oppoent to beat. With this same reality warping ability, she can freely move between dimensions without the use of Noah's Ark, the only Noah able to do so. She has also shown high speed regeneration abilities.
 * Jasdevi (Bondomu): Jasdevi is unique as he is often spends his time as his split selves, Jasdero and David. In the form of the twins, they possess the power of materialization, being able to materialize what they want simply by thinking of it at the same time and by using their toy guns as the medium for their powers. As Jasdevi, he has the power of materialization but does not need the guns as mediums. In this form he simply has to think of something for it to become real. This goes from anything from creating simple blasts of Dark Matter energy, to pentacles to act as shields and traps to imaging his own body is the strongest body possible, granting him immense increases in speed, power and endurance.
 * Lulu Bell (Lust): Lulu Bell can change her form to be whatever she wants it to be, no matter how impossible. She has show to be able to change it to water, to reconstruct it's shape to fit her needs and to change into common animal forms, her favourite being a black cat.
 * Mightra (Talent): Unknown Abilities.
 * The Pianist: Unknown Abilities. In the past however he nearly defeated and killed the Millennium Earl, hinting he has incredibly powerful abilities.

Third Exorcists
Recently, it was revealed that the Black Order too has the means to use the Dark Matter as a weapon; the Third Exorcist Programs combines humans with Akuma cells, genetically altering them to use Akuma abilities based on the Dark Matter. They are able to use these powers to devour Akuma, the only other real way to destroy them besides Innocence. What happens to the souls of those Akuma destroyed in this way is yet to be known. It is also yet to be shown if the Third Exorcists are able to use the Dark Matter in more exotic and individual power and abilities like the Noah and the more evolved Akuma can.

Trivia

 * Exactly what Dark Matter is is unknown. It has been said to be a dark and terrible force and use of it by characters in the manga and anime invoke fear and dread in those that observe it, however this may be just their natural reactions. Perhaps if it is anything, then it is the energy of evil itself.
 * Dark Matter and Innocence are polar opposites and are the weakness of each other.
 * Dark Matter is an unrestrained force and unlike Innocence, there does not seem to a limit to how much of it there is (Innocence is divided into 109 fragments while the dark matter is a power spread amongst the millions of Akuma and the Noah family). However, it could be the power of the Innocence is as great as that of Dark Matter but rather is far more concentrated.
 * The Akuma and the Noah Family all have diverse, unique powers based off the Dark Matter. It remains to be seen if the Third Exorcists too have unique abilities due to their hybrid nature.