Title: Second-order Gauge Invariant Cosmological Perturbation Theory; -- Einstein equations in terms of gauge invariant variables -- Authors: Kouji Nakamura

Along the general framework of the gauge invariant perturbation theory developed in the papers {K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid, 113 (2005), 481.}, we formulate the second order gauge invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We derive the all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that the second order vector and tensor modes may be generated due to the mode-mode coupling of the linear order scalar perturbations. We also briefly discuss the main progress of this work by the comparison with some literatures.

Title: Why Does Gravity Ignore the Vacuum Energy? Authors: T. Padmanabhan

The equations of motion for matter fields are invariant under the shift of the matter lagrangian by a constant. Such a shift changes the energy momentum tensor of matter by T^a_b --> T^a_b + ho \delta^a_b. In the conventional approach, gravity breaks this symmetry and the gravitational field equations are not invariant under such a shift of the energy momentum tensor. I argue that until this symmetry is restored, one cannot obtain a satisfactory solution to the cosmological constant problem. I describe an alternative perspective to gravity in which the gravitational field equations are (Gab -\kappa Tab) n^an^b =0 for all null vectors n^a. This is obviously invariant under the change T^a_b --> T^a_b + ho \delta^a_b and restores the symmetry under shifting the matter lagrangian by a constant. These equations are equivalent to Gab = \kappa Tab + Cgab where C is now an integration constant so that the role of the cosmological constant is very different in this approach. The cosmological constant now arises as an integration constant, somewhat like the mass M in the Schwarzschild metric, the value of which can be chosen depending on the physical context. These equations can be obtained from a variational principle which uses the null surfaces of spacetime as local Rindler horizons and can be given a thermodynamic interpretation. This approach turns out to be quite general and can encompass even the higher order corrections to Einstein's gravity and suggests a principle to determine the form of these corrections in a systematic manner.

Physical particles may seem very different from the space-time they inhabit, but what if the two are one and the same thing?

Lee Smolin is no magician. Yet he and his colleagues have pulled off one of the greatest tricks imaginable. Starting from nothing more than Einstein's general theory of relativity, they have conjured up the universe. Everything from the fabric of space to the matter that makes up wands and rabbits emerges as if out of an empty hat. It is an impressive feat. Not only does it tell us about the origins of space and matter, it might help us understand where the laws of the universe come from. Not surprisingly, Smolin, who is a theoretical physicist at the Perimeter Institute in Waterloo, Ontario, is very excited.

"I've been jumping up and down about these ideas" - Lee Smolin.

This promising approach to understanding the cosmos is based on a collection of theories called loop quantum gravity, an attempt to merge general relativity and quantum mechanics into a single consistent theory.

Nowadays many of the most sensitive measurements in science depend on some quantum phenomenon which very subtly can often be exploited to gain maximum precision. In an experiment conducted at the Università di Firenze (University of Florence) the quantum phenomenon in question is called Bloch oscillation. This weird effect occurs when particles subject to a periodic potential -- such as electrons feeling the regular gridlike electric force of a crystalline lattice of atoms -- are exposed to an additional static force, say, an electric force in a single direction; what happens is that the electrons do not, as you would expect, all move in the direction of the force, but instead oscillate back and forth in place.

In a new experiment conducted by Guglielmo Tino and his Florence colleagues, the particles are supercold strontium atoms held in a vertically oriented optical trap formed by criss-crossing laser beams, while the static force is merely the force of gravity pulling down on the atoms. What are the unique features of this experiment? First of all, although Bloch oscillations have been observed before, they have never been sustained for as long as 10 seconds, which is the case here. Experiments that mix gravity and quantum mechanics are rare. Furthermore, even though the cloud of Sr atoms in use do not exist in the form of a Bose-Einstein condensate (BEC), the atoms do absorb the trapping laser light in a coherent way; that is, they absorb the light in a stimulated (not random) way. They quickly re-emit the light and then absorb still another photon. The number of photons per atom transferred in this way -- in the thousands rather than tens -- is the largest ever for a physics experiment. Finally, close observation of the Bloch oscillations allows you to measure the strength of the static force, gravity, with high precision -- in this case to measure gravity with an uncertainty of a part in a million. With planned improvements to the apparatus, the researchers will be able to bring the atoms to within a few microns of a test mass and will measure g with an uncertainty of 0.1 parts per million. With these conditions, one can probe theories which say that gravity should depart from the Newtonian norm, perhaps signifying the existence of unknown spatial dimensions.

According to Tino unlike gravity-measuring experiments which use torsional balances or cantilevers, the Florence approach measures gravity directly and over shorter distances. The atom-trap setup should also prove useful for future inertial guidance systems and optical clocks.

If there is a mathematician eagerly waiting for the Large Hadron Collider near Geneva to start up next year, it is Alain Connes of the Collège de France in Paris. Like many physicists, Connes hopes that the Higgs particle will show up in detectors. The Higgs is the still missing crowning piece of the so-called Standard Model--the theoretical framework that describes subatomic particles and their interactions. For Connes, the discovery of the Higgs, which supposedly endows the other particles with mass, is crucial: its existence, and even its mass, emerges from the arcane equations of a new form of mathematics called noncommutative geometry, of which he is the chief inventor.

Connes's idea was to extend the relation between geometric space and its commutative algebra of Cartesian coordinates, such as latitude and longitude, to a geometry based on noncommutative algebras. In commutative algebra, the product is independent of the order of the factors: 3 x 5 = 5 x 3. But some operations are noncommutative. Take, for example, a stunt plane that can aggressively roll (rotate over the longitudinal axis) and pitch (rotate over an axis parallel to the wings). Assume a pilot receives radio instructions to roll over 90 degrees and then to pitch over 90 degrees toward the underside of the plane. Everything will be fine if the pilot follows the commands in that order. But if the order is inverted, the plane will take a nosedive. Operations with Cartesian coordinates in space are commutative, but rotations over three dimensions are not.

Title: Holographic entanglement entropy of de Sitter braneworld Authors: Yukinori Iwa****a, Tsutomu Kobayashi, Tetsuya Shiromizu, Hirotaka Yoshino

Researchers study the holographic representation of the entanglement entropy, recently proposed by Ryu and Takayanagi, in a braneworld context. The holographic entanglement entropy of a de Sitter brane embedded in an anti-de Sitter (AdS) spacetime is evaluated using geometric quantities, and it is compared with two kinds of de Sitter entropy: a quarter of the area of the cosmological horizon on the brane and entropy calculated from the Euclidean path integral. They show that the three entropies coincide with each other in a certain limit. Remarkably, the entropy obtained from the Euclidean path integral is in precise agreement with the holographic entanglement entropy in all dimensions. They also comment on the case of a five-dimensional braneworld model with the Gauss-Bonnet term in the bulk.

A team of scientists working at the National High Magnetic Field Laboratory has uncovered an intriguing phenomenon while studying magnetic waves in a pigment known commonly as Han purple. The researchers discovered that when they exposed crystals of the pigment to high magnetic fields at very low temperatures, it entered a rarely observed state of matter. At the threshold of that matter state - the "quantum critical point" - the waves actually lost a dimension.

Theoretical physicists have postulated that this kind of dimensional reduction might help explain some mysterious properties of other materials (high temperature superconductors and metallic magnets known as "heavy fermions" for example) near the absolute zero of temperature, but until now, a change in dimension had not been experimentally observed. The experiment was performed at the magnet lab's DC Field Facility at Florida State University by Neil Harrison from the Pulsed Field Facility and Suchitra Sebastian from Stanford University, in collaboration with a team of scientists from these institutions.

Title: How Many Universes Do There Need To Be? Authors: Douglas Scott, J.P. Zibin

In the simplest cosmological models consistent with General Relativity, the total volume of the Universe is either finite or infinite, depending on whether or not the spatial curvature is positive. Current data suggest that the curvature is very close to flat, implying that one can place a lower limit on the total volume. In a Universe of finite age, the "particle horizon" defines the patch of the Universe which is observable to us. Based on today's best-fit cosmological parameters it is possible to constrain the number of observable Universe sized patches, N_U. Specifically, using the new WMAP data, we can say that there are at least 10 patches out there the same volume as ours. Moreover, even if the precision of our cosmological measurements continues to increase, density perturbations at the particle horizon size limit us to never knowing that there are more than about 10^5 patches out there.

An exotic theory, which attempts to unify the laws of physics by proposing the existence of an extra fourth spatial dimension, could be tested using a satellite to be launched in 2007.

Such theories are notoriously difficult to test. But a new study suggests that such hidden dimensions could give rise to thousands of mini-black holes within our own solar system – and the theory could be tested within Pluto’s orbit in just a few years.

Black holes of various masses are thought to have sprung into existence within 1 second of the big bang, as elementary particles clumped together at extreme energies. But Einstein's theory of general relativity predicts the smallest of these "primordial" black holes should have already evaporated, through a quantum process called Hawking radiation. But according to some alternative theories that attempt to unify gravity with quantum mechanics, such as string theory, small black holes could still exist. That is because these theories propose extra spatial dimensions, which alter the way gravity behaves on small scales. The theory of general relativity holds that there are three spatial dimensions plus time.

"That (extra spatial dimension) changes the rate at which black holes radiate, so you can slow down the evaporation quite substantially" - Charles Keeton, a physicist at Rutgers University in New Jersey, US.

New theory of gravity challenges Einstein's general relativity

Scientists at Duke and Rutgers universities have developed a mathematical framework they say will enable astronomers to test a new five-dimensional theory of gravity that competes with Einstein's General Theory of Relativity.

Charles R. Keeton of Rutgers and Arlie O. Petters of Duke base their work on a recent theory called the type II Randall-Sundrum braneworld gravity model. The theory holds that the visible universe is a membrane (hence "braneworld") embedded within a larger universe, much like a strand of filmy seaweed floating in the ocean. The "braneworld universe" has five dimensions -- four spatial dimensions plus time -- compared with the four dimensions -- three spatial, plus time -- laid out in the General Theory of Relativity. The framework Keeton and Petters developed predicts certain cosmological effects that, if observed, should help scientists validate the braneworld theory. The observations, they said, should be possible with satellites scheduled to launch in the next few years.

"This would upset the applecart. It would confirm that there is a fourth dimension to space, which would create a philosophical shift in our understanding of the natural world." - Arlie O. Petters.

The scientists' findings appeared May 24, 2006, in the online edition of the journal Physical Review D. Keeton is an astronomy and physics professor at Rutgers, and Petters is a mathematics and physics professor at Duke. Their research is funded by the National Science Foundation.

The Randall-Sundrum braneworld model -- named for its originators, physicists Lisa Randall of Harvard University and Raman Sundrum of Johns Hopkins University -- provides a mathematical description of how gravity shapes the universe that differs from the description offered by the General Theory of Relativity. Keeton and Petters focused on one particular gravitational consequence of the braneworld theory that distinguishes it from Einstein's theory. The braneworld theory predicts that relatively small "black holes" created in the early universe have survived to the present. The black holes, with mass similar to a tiny asteroid, would be part of the "dark matter" in the universe. As the name suggests, dark matter does not emit or reflect light, but does exert a gravitational force. The General Theory of Relativity, on the other hand, predicts that such primordial black holes no longer exist, as they would have evaporated by now.

"When we estimated how far braneworld black holes might be from Earth, we were surprised to find that the nearest ones would lie well inside Pluto's orbit" - Charles R. Keeton.

"If braneworld black holes form even 1 percent of the dark matter in our part of the galaxy -- a cautious assumption -- there should be several thousand braneworld black holes in our solar system" - Arlie O. Petters.

But do braneworld black holes really exist -- and therefore stand as evidence for the 5-D braneworld theory? The scientists showed that it should be possible to answer this question by observing the effects that braneworld black holes would exert on electromagnetic radiation travelling to Earth from other galaxies. Any such radiation passing near a black hole will be acted upon by the object's tremendous gravitational forces -- an effect called "gravitational lensing."

"A good place to look for gravitational lensing by braneworld black holes is in bursts of gamma rays coming to Earth" - Charles R. Keeton.

These gamma-ray bursts are thought to be produced by enormous explosions throughout the universe. Such bursts from outer space were discovered inadvertently by the U.S. Air Force in the 1960s. Keeton and Petters calculated that braneworld black holes would impede the gamma rays in the same way a rock in a pond obstructs passing ripples. The rock produces an "interference pattern" in its wake in which some ripple peaks are higher, some troughs are deeper, and some peaks and troughs cancel each other out. The interference pattern bears the signature of the characteristics of both the rock and the water. Similarly, a braneworld black hole would produce an interference pattern in a passing burst of gamma rays as they travel to Earth, said Keeton and Petters. The scientists predicted the resulting bright and dark "fringes" in the interference pattern, which they said provides a means of inferring characteristics of braneworld black holes and, in turn, of space and time.

"We discovered that the signature of a fourth dimension of space appears in the interference patterns. This extra spatial dimension creates a contraction between the fringes compared to what you'd get in General Relativity" - Arlie O. Petters.

Petters and Keeton said it should be possible to measure the predicted gamma-ray fringe patterns using the Gamma-ray Large Area Space Telescope, which is scheduled to be launched on a spacecraft in August 2007. The telescope is a joint effort between NASA, the U.S. Department of Energy, and institutions in France, Germany, Japan, Italy and Sweden. The scientists said their prediction would apply to all braneworld black holes, whether in our solar system or beyond.

"If the braneworld theory is correct, there should be many, many more braneworld black holes throughout the universe, each carrying the signature of a fourth dimension of space."