Posted on **09/08/2012 1:36:57 PM PDT** by **neverdem**

IU mathematician offers unified theory of dark matter, dark energy, altering Einstein field equations

BLOOMINGTON, Ind. -- A pair of mathematicians -- one from Indiana University and the other from Sichuan University in China -- have proposed a unified theory of dark matter and dark energy that alters Einstein's equations describing the fundamentals of gravity.

Shouhong Wang, a professor in the IU College of Arts and Sciences' Department of Mathematics, and Tian Ma, a professor at Sichuan University, suggest the law of energy and momentum conservation in spacetime is valid only when normal matter, dark matter and dark energy are all taken into account. For normal matter alone, energy and momentum are no longer conserved, they argue.

While still employing the metric of curved spacetime that Einstein used in his field equations, the researchers argue the presence of dark matter and dark energy -- which scientists believe accounts for at least 95 percent of the universe -- requires a new set of gravitational field equations that take into account a new type of energy caused by the non-uniform distribution of matter in the universe. This new energy can be both positive and negative, and the total over spacetime is conserved, Wang said.

It is curved spacetime, along with a new scalar potential field representing the new energy density, and the interactions between the two that form the foundation for the new gravitational field equations.

"Many people have come up with different theories for dark energy," Wang said. "Unfortunately, the mystery remains, and in fact, the nature of dark energy is now perhaps the most profound mystery in cosmology and astrophysics. It is considered the most outstanding problem in theoretical physics.

"The other great mystery concerning our universe is that it contains much more matter than can be accounted for in our visible stars. The missing mass is termed as dark matter, and despite many attempts at detecting dark matter, the mystery remains and even deepens."

The researchers postulate that the energy-momentum tensor of normal matter is no longer conserved and that new gravitational field equations follow from Einstein's principles of equivalence and general relativity, and the principle of Lagrangian dynamics, just as Einstein derived his field equations. Wang said the new equations were the unique outcome of the non-conservation of the energy-momentum tensor of normal matter.

When Einstein developed his theory, dark energy and dark matter had not yet been discovered, so it was natural for him to start his theory using the conservation law of energy and momentum of normal matter, Wang added.

"The difference between the new field equations and Einstein's equations is the addition of a second-order covariant derivative of a scalar potential field," he said. "Gravity theory is fundamentally changed and is now described by the metric of the curved spacetime, the new scalar potential field and their interactions."

Tensors provide a concise framework for solving general relativity problems and the energy-momentum tensor quantifies the density and current of energy and momentum in spacetime. The second-order covariant derivative would be the geometric analog of a second order derivative in calculus which measures how the rate of change of a quantity is itself changing.

Associated with the scalar field is a scalar potential energy density consisting of positive and negative energies and representing a new type of energy caused by the non-uniform distribution of matter in the universe. The scalar potential energy density varies as the galaxies move and matter redistributes, affecting every part of the universe as a field.

Wang said negative energy produces attraction while the positive energy produces a repelling force fundamentally different from the four forces -- gravity, electromagnetism, the weak interaction and the strong interaction -- recognized in physics today.

"Most importantly, this new energy and the new field equations offer a unified theory for both dark energy and dark matter, which until now have been considered as two totally different beasts sharing only 'dark' in name," he said. "Both dark matter and dark energy can now be represented by the sum of the new scalar potential energy density and the coupling energy between the energy-momentum tensor and the scalar potential field."

The negative part of this sum represents the dark matter, which produces attraction, and the positive part represents the dark energy, which drives the acceleration of expanding galaxies, he said.

"In a nutshell, we believe that new gravity theory will change our view on energy, gravitational interactions, and the structure and formation of our universe," Wang said.

Kevin Zumbrun, chair of the Department of Mathematics at IU Bloomington, said the new unified theory looked sound in principle.

"It is speculative at the cosmological level, since one must match with experiment, but the math is solid," he said. "It's a new and elegant angle on things, and if this does match experiment, it is a huge discovery. Quite exciting!"

Wang said the new field equations also lead to a modified Newtonian gravitational force formula, which shows that dark matter plays a more important role in a galactic scale at about 1,000 to 100,000 light years, but is less important in the larger scale, where dark energy will be significant (more than 10 million light years).

"This unified theory is consistent with general characterizations of dark energy and dark matter, and further tests of the theory up to measured precisions of cosmic observations are certainly crucial for an eventual validation of the theory," Wang added.

The full research paper, "Gravitational Field Equations and Theory of Dark Energy and Dark Matter,"(PDF) is available at the open access online preprint archive arXiv, and the work was supported by funding from the U.S. Office of Naval Research and the National Science Foundation.

**For more information please contact Steve Chaplin, IU Communications, at 812-856-1896 or stjchap@iu.edu. Tweeting IU Science: @Indiana Science; blogging IU science news at Science at Work.**

To: **neverdem**

Darn, they beat me to it.

2
posted on **09/08/2012 1:41:23 PM PDT**
by beethovenfan
(If Islam is the solution, the "problem" must be freedom.)

To: **neverdem**

Thanks for this. My daughter, an undergraduate astrophysics major, will be interested in this...I will send it on. I am not smart enough to understand this stuff... I’m a biology guy.

To: **neverdem**

Is it possible that gravity is not what we have thought it was?

Or more likely, that there is more to it ?

To: **neverdem**

Ya heard it here first: gravity is as about strong as the electromagnetic force, but it is counter by a nearly as strong repulsive force from dark energy.

/seriously, been playing with the math

5
posted on **09/08/2012 1:52:19 PM PDT**
by piytar
(The predator-class is furious that their prey are shooting back.)

To: **neverdem**

Ya heard it here first: gravity is as about strong as the electromagnetic force, but it is counter by a nearly as strong repulsive force from dark energy.

/seriously, been playing with the math

6
posted on **09/08/2012 1:53:22 PM PDT**
by piytar
(The predator-class is furious that their prey are shooting back.)

To: **neverdem**

PING

To: **winodog**

As admitted amateur who is nontheless fascinated by all this stuff, have always believed that one day it will be shown that gravity is NOT a property of matter, but that matter is a property of gravity.

To: **piytar**

Yeah, right. I’m sure that you are playing with high level tensor analysis (sarc). And I’m also sure that nobody is impressed by your lame attempt to sound smart.

To: **fhayek**

Interesting theory.

To: **fhayek**

My physics prof at UBC back in ‘62 was Friedrich Kaempfer, leading proponent of the opposing graviton theory, positing gravitational particles.

I’m not able to have a dog in this fight, however, not “’aving me Latin”, as it were..

12
posted on **09/08/2012 2:38:09 PM PDT**
by headsonpikes
(Mass murder and cannibalism are the twin sacraments of socialism - "Who-whom?"-Lenin)

To: **pelican001**

Yup, dimensionality was always fun - a “quartad” being of rank 4 and having 51 components was even more fun!

To: **neverdem**

Just don't mix them together...

To: **pelican001**

Whoa, did I strike some sore spot there? Graudate degree in engineerig focused on QM, moved to other things. Still play.

Why so hostile?

15
posted on **09/08/2012 3:17:30 PM PDT**
by piytar
(The predator-class is furious that their prey are shooting back.)

To: **pelican001**

I will admit my tensor analysis sucks. Had a hard time with eignstates at first. Playing with a lower level set of issues, mostly pinned on why current theories estimate vacuum energy to be MUCH stronger than it apparently is. (See From Eternity to Here by Carrol for a great layman’s discussion.)

Why did that offend you so much?

16
posted on **09/08/2012 3:27:31 PM PDT**
by piytar
(The predator-class is furious that their prey are shooting back.)

To: **neverdem**

the addition of a second-order covariant derivative of a scalar potential field,

17
posted on **09/08/2012 3:27:51 PM PDT**
by Chode
(American Hedonist - *DTOM* -ww- NO Pity for the LAZY)

To: **neverdem**

For those who allatime go off their nut about Liberal Arts, this particular mathematics department is part of the Indiana University College of Arts and Sciences ~ their core majors in that college are: http://college.indiana.edu/programs/ ~ interesting that the top end Chinese mathematicians are edging out into cosmology

To: **winodog**

I will consider believing in dark energy/matter when physicists prove to my satisfaction that they haven't just underestimated the mass of the black hole at the center of every galaxy.

Of course this is simplistic but it explains all the missing matter in the universe.

Of course this is simplistic but it explains all the missing matter in the universe.

To: **neverdem**

Wow! Now to design a predictive theory.

The scalar potential field is kind of revolutionary, as it seems to assert what I'll term a pre-actual physical reality. Maybe what John Bell described as “information.”

This Ma and Wang theory (sounds so very wrong in Amelican Engrish) may want for a “neutral” as well as the “positive/negative” manifestations. Not only for dark matter. For, as we know, in quantum mechanics the results of key experiments differ when the fact of observation is introduced. Vide Schrodinger’s Cat.

20
posted on **09/08/2012 6:11:17 PM PDT**
by Unknowing
(Now is the time for all good men to come to the aid of their country.)

To: **neverdem**

Well, sure .. if you throw in a second-order covariant and crosscircuit-to-B then anything is possible!

The difference between classical physicists and contemporary physiciasts is that contemporary physicists actually *DO* believe in the Easter Bunny.

To: **mikrofon**

Quick! Somebody do a search to see if there are any Zefram Cochranes recently borne!

22
posted on **09/08/2012 6:50:26 PM PDT**
by VanShuyten
("a shadow...draped nobly in the folds of a gorgeous eloquence.")

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