Dark Energy Cont.
How Do You Measure This, Exactly?
Observable distortions of the distant universe due to weak gravitational lensing (cosmic mirage) are predictable given a cosmological model. LSST will do this in a variety of ways. Because of the redshift-distance effect of the Hubble expansion, LSST's multi-color deep imaging survey will provide distances to galaxies out to redshift 3. We can subdivide these galaxies into many redshift or distance bins and then perform lensing tomography: measure how the cosmic mirage effect changes with distance. If the galaxies can be separated into n multiple redshift bins, then we can create n shear maps. The most interesting statistical properties of these maps are the shear-shear correlation functions. These n(n+1)/2 unique shear power spectra can be written as projections of the matter power spectrum along the line of sight out to some redshift. The resulting tens of shear cross correlations vs redshift are very powerful independent probes of the expansion history (see the figure). It is clear that the unparalleled survey area of LSST allows a significant detection of the power spectra over a wide range of angular scales, from degree scales to arcminute scales. Jointly, these correlations contain enough information to determine cosmological parameters, including dark energy parameters..
Weak lensing has high information content. If we know distances to source galaxies, the mass distribution and cosmic geometry can be measured as a function of redshift. Weak lensing thus has sensitivity to the evolution of dark energy. The light deflection by a foreground mass is given by a product of the mass inside the impact radius and a dimensionless ratio of distances. Both of these terms are affected by dark energy and other cosmological parameters. Combining lensing data with CMB data enables separate direct investigations of the growth of dark matter structure and multiple probes of the geometry from z~1 to the present.
Testing the Foundation
Combining many new observations of our universe (multiple cosmic shear probes over a wide range of cosmic look-back times with the LSST, distant supernova data, and studies of the cosmic microwave background at high angular resolution with the Wilkinson MAP satellite and the upcoming Planck satellite) will lead to precision cosmology. More importantly, the combination holds the promise of testing the entire foundation of the theory.Ê What if different tests of dark energy yield conflicting results? Then we may be onto something even more interesting: a hint that we do not fully understand the nature of spacetime-gravity. Thus, LSST will play a key role in probing new physics beyond the standard model.
How can gravity be repulsive?
Consider a little region within a larger massive medium. In Newtonian gravity, the gravitational force exerted by this little region is proportional to its mass density. Since this density is always positive, the force never changes sign and classical gravity is always attractive. Any relativistic generalization of the gravitational force must not only involve the energy density (instead of the mass density) but also the momentum density (since energy and momentum can be transformed into each other by changing the reference frame). Within Einstein's framework of General Relativity, the gravitational force exerted by an element of an isotropic medium is proportional to the sum of its energy density and three times its local pressure (which measures the momentum flow).
A medium can have a negative pressure: a common example is a rubber ball that is forced to expand beyond its equilibrium radius. If this negative pressure is large enough (greater in magnitude than a third of the energy density), it can thus produce a repulsive gravitational force! In particular, vacuum energy where the pressure is equal and opposite to the energy density (Einstein's cosmological constant is an example) will produce such repulsive force. If such vacuum energy is dominant, it would generate an accelerated expansion of the universe. Another important example is the case of a particle field that is highly out of equilibrium. This is the mechanism believed to have produced the inflation in the early universe.
