What are the explanations for dark energy?

1) One explanation for dark energy is that it is a property of space. Albert Einstein was the first person to realize that empty space is not nothing. Space has amazing properties, many of which are just beginning to be understood. The first property that Einstein discovered is that it is possible for more space to come into existence. In another version of Einstein's gravity theory, the version that contains a cosmological constant, he makes a second prediction: "empty space" can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands. As more space comes into existence, more of this energy-of-space would appear. As a result, this form of energy would cause the Universe to expand faster and faster. Unfortunately, no one understands why the cosmological constant should even be there, much less why it would have exactly the right value to cause the observed acceleration of the Universe. 

And so one can say that dark energy is simply the "cost of having space": that is, a volume of space has some intrinsic, fundamental energy. This is the cosmological constant. Since energy and mass are related by E = mc², Einstein's theory of general relativity predicts that it will have a gravitational effect. It is sometimes called a vacuum energy because it is the energy density of empty vacuum. In fact, most theories of particle physics predict vacuum fluctuations that would give the vacuum this sort of energy.

3) Another explanation for dark energy is that it is a new kind of dynamical energy fluid or field, something that fills all of space but something whose effect on the expansion of the Universe is the opposite of that of matter and normal energy. Some theorists have named this "quintessence," after the fifth element of the Greek philosophers. But, if quintessence is the answer, we still don't know what it is like, what it interacts with, or why it exists. So the mystery continues.

4) Einsteins theory of gravitation is not correct ----A last possibility is that Einstein's theory of gravity is not correct. That would not only affect the expansion of the Universe, but it would also affect the way that normal matter in galaxies and clusters of galaxies behaved. This fact would provide a way to decide if the solution to the dark energy problem is a new gravity theory or not: we could observe how galaxies come together in clusters. But if it does turn out that a new theory of gravity is needed, what kind of theory would it be? How could it correctly describe the motion of the bodies in the Solar System, as Einstein's theory is known to do, and still give us the different prediction for the Universe that we need? There are candidate theories, but none are compelling. So the mystery continues.

The thing that is needed to decide between dark energy possibilities - a property of space, a new dynamic fluid, or a new theory of gravity - is more data, better data.

What Is Dark Matter?

Abell 2744: Pandora's Cluster Revealed One of the most complicated and dramatic collisions between galaxy clusters ever seen is captured in this new composite image of Abell 2744. The blue shows a map of the total mass concentration (mostly dark matter).

In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy. Its existence is inferred from gravitational effects on visible matter and gravitational lensing of background radiation, and was originally hypothesized to account for discrepancies between calculations of the mass of galaxies, clusters of galaxies and the entire universe made through dynamical and general relativistic means, and calculations based on the mass of the visible "luminous" matter these objects contain: stars and the gas and dust of the interstellar and intergalactic medium. Many experiments to detect dark matter through non-gravitational means are underway.

Estimated distribution of dark matter and dark energy in the universe By fitting a theoretical model of the composition of the Universe to the combined set of cosmological observations, scientists have come up with the composition that we described above, ~70% dark energy, ~25% dark matter, ~5% normal matter.

Observations show that there is far too little visible matter in the Universe to make up the 25% required by the observations. Second, it is not in the form of dark clouds of normal matter, matter made up of particles called baryons. W/e know this because we would be able to detect baryonic clouds by their absorption of radiation passing through them. Third, dark matter is not antimatter, because we do not see the unique gamma rays that are produced when antimatter annihilates with matter. Finally, we can rule out large galaxy-sized black holes on the basis of how many gravitational lenses we see. High concentrations of matter bend light passing near them from objects further away, but we do not see enough lensing events to suggest that such objects to make up the required 25% dark matter contribution.

A small proportion of dark matter may be baryonic dark matter: astronomical bodies, such as massive compact halo objects, that are composed of ordinary matter but which emit little or no electromagnetic radiation. The vast majority of dark matter in the universe is believed to be nonbaryonic, and thus not formed out of atoms. It is also believed that it does not interact with ordinary matter via electromagnetic forces; in particular, dark matter particles do not carry any electric charge. The nonbaryonic dark matter includes neutrinos, and possibly hypothetical entities such as axions, or supersymmetric particles. Unlike baryonic dark matter, nonbaryonic dark matter does not contribute to the formation of the elements in the early universe ("Big Bang nucleosynthesis") and so its presence is revealed only via its gravitational attraction. In addition, if the particles of which it is composed are supersymmetric, they can undergo annihilation interactions with themselves resulting in observable by-products such as photons and neutrinos ("indirect detection").

Nonbaryonic dark matter is classified in terms of the mass of the particle(s) that is assumed to make it up, and/or the typical velocity dispersion of those particles (since more massive particles move more slowly). There are three prominent hypotheses on nonbaryonic dark matter, called Hot Dark Matter (HDM), Warm Dark Matter (WDM), and Cold Dark Matter (CDM); some combination of these is also possible. The most widely discussed models for nonbaryonic dark matter are based on the Cold Dark Matter hypothesis, and the corresponding particle is most commonly assumed to be a neutralino. Hot dark matter might consist of (massive) neutrinos. Cold dark matter would lead to a "bottom-up" formation of structure in the universe while hot dark matter would result in a "top-down" formation scenario.

Baryonic matter could still make up the dark matter if it were all tied up in brown dwarfs or in small, dense chunks of heavy elements. These possibilities are known as massive compact halo objects, or "MACHOs".

But the most common view is that dark matter is not baryonic at all, but that it is made up of other, more exotic particles like axions or WIMPS (Weakly Interacting Massive Particles).

The tug of war between dark matter and dark energy

"...If the expansion of the universe is the result of a battle between dark energy speeding things up and dark matter slowing things down, then the history of cosmic expansion will have a record of which entity was winning at various points. Because light takes time to get to us, we can see into the past by observing distant objects. In the recent past (say, the last five billion years) we see acceleration. But if we could look far enough into the past, then the balance should tip — the dark matter should be denser when the universe was a smaller place, while the dark energy, if it resembles the cosmological constant, should hold steady. This would make the universe slow down. Mr. Riess led a group that carried out these observations with the Hubble Space Telescope. In 2004 and in 2007, his team showed that the change from deceleration to acceleration really happened: the predictions for a dark energy/dark matter universe match the observations..." from NYtimes article from Robert Kirshner

NOTE: The Nobel Prize in Physics 2011 was divided, one half awarded to Saul Perlmutter, the other half jointly to Brian P. Schmidt and Adam G. Riess "for the discovery of the accelerating expansion of the Universe through observations of distant supernovae".