**HUBBLE DIAGRAM AND ITS CONSTRAINTS ON COSMOLOGY**

*Bradley Schaefer*

A Hubble Diagram is presented based on 172 distance measures involving 52 Gamma-Ray Bursts out to redshifts of 6.3. The observed shape of the Hubble Diagram is a measure of the expansion history of the Universe, which will include the effects of the 'Dark Energy' that dominates over matter. Gamma-Ray Bursts can be seen to high redshift, and this uniquely allows for tests as to whether the Dark Energy changes with time. If Einstein's Cosmological Constant is a good representation of cosmology, then the equation of state of the Dark Energy won't change in time over the age of the Universe. The observed Hubble Diagram can be compared with the shape predicted by various models, including the model where the Cosmological Constant is a constant. The result is that the Cosmological Constant is rejected at a moderate confidence level. That is, apparently, Dark Energy changes with time. As with all such results, a consensus final conclusion can only be reached after the result is duplicated by independent experiments. To this end, over the next two years, the satellites Swift and HETE will discover another ~50 bursts that can be placed on the Hubble Diagram and this will serve as an independent test of the claim. The result also highlights the Gamma-Ray Burst Hubble Diagram as a new front-line technique to measure Dark Energy and the high-redshift Universe.

As I relay in the earlier part of the thread containing responses to the Evolving Dark Enery of Sean Carroll's, certain insights that had been gained along the way raise the issue of how such a dark energy would have influenced, how we gain information from the luminousity of standard candles, and how we would gain from that information.

**Lubos Motl**:

The corresponding equation of state would give "w" (the pressure/energy_density ratio) smaller than "-1" (much like in models of phantom energy) which would violate the dominant energy condition - and potentially allow superluminal signals. This sounds highly suspicious. Gamma ray bursts had to be used for the analysis - and they are sufficiently poorly understood - and independent experimental astrophysical sources at Harvard also recommend you to ignore the news.

Of course we are going to want to know why Lubos.

This set the stage for me in wonder about gravitonic concentrations, and how these woudl have been indicators of the strengths and weakeness, which would influence this information gained. I guess, it is in understanding better how such information could be "skewed" that I am looking at the answers given as a further response by Brad is illucidated upon.

So what is "dark energy" in relation to what gravitonic considerations might have on how we see such expasnion process say to us, the unievrse is indeed expanding.

It is always interesting to me to see how the cosmological values contained in the universe could have ever held to "GR curvature indicators" and that such values if held in regard to Einsteins and Riemann's spherical relations, then how indeed could we have siad that the nature of the universe is

As mentioned earlier, the value of is a measurement for the density of the universe. The definition of is such that,

where is the critical density of the universe. A critical density is associated with an "Einstein de Sitter Universe" for which equals 1. It has the property that the curvature is zero, the universe is spatiallyflat. Light will travel in a straight line and the angles of a triangle add to 180 degrees (space is Euclidean). The other possibilities are an open universe ( ) in which space will expand forever, and a closed universe ( ) in which gravity will halt the expansion and force the universe to contract, eventually leading to a "big crunch". The consequence could possibly be an oscillating universe, which gives a kind of continuity to the model. Figure 2 illustrates the three cosmological models.

Figure 2:The three cosmological models of the universe: open (), closed ( ) and flat ( )

Part of my exercise is to see the underlying geoemtries that are evolving thriugh time as we keep our universe in perspective. Do we know where this center is? And if so can we see whwere such expansiotry calculations would have given some indication? Are we always looking to the furthest edge so that we can help understand this red shifting that is going on tohelp us determine this value of the open uinverse?

Well within context of all this, the move to a higher lensing implications is most puzzling becuase it will shape the nature and kinds of infomration that is needed in order to make these determinations about unibverse values. Thus being inclined to pass by such galaxies in the forming state, as influencing the viability of the information given to us. So to me "Luminousity" is very important here as to the ejection of infomration that may reach us, and information that will held in context of those galaxy formations. So it is as if we are giving, an image in mind of these holes geoemtrically induced, along side of matter formation from causes that would influence the very nature of the repsonses we get.

**Critical density**

**Sean Carroll**:

Last time we talked about dark energy and its equation-of-state parameter, w. This number tells you how quickly the dark energy density changes as the universe expands; if w=-1, the density is strictly constant, if w>-1, the density decreases, and if w<-1, the density actually increases with time. (In equations, if a is the scale factor describing the relative size of the universe as a function of time, then the density goes as a-3(1+w).) For comparison purposes, cosmological "matter" (slowly-moving massive particles) has w=0, and "radiation" (relativistic particles, including photons) has w=1/3

So if we are to look for this center how would we find the valuation of what began?

You would have needed to see a time when

**critical density**would have said to you that the infomration that is being propelled from the center, and here, critical density would have partaken of this value, because gravity would have been very strong? Strong enough that for any infomration to be propelled from that center, to have continued on to this day as a expansitory consideration. So that we may still hold it in considertaion as to exactly what this universe is doing now.

Once you have then held the unierse in a certain way you have to ask these question based on what you understood by implicating Lagrange points in your assesment of how the univere became the way it is. YOur lensing has created these holes for light to travel, and in those spaces, satelittes have found easier ways to have manueverd without expending a lot of energy.

We can still tap the greater reserviors of energy and radiation, to help these vehicles continue their journeys. But it is more then that, that we might have sent this vehicle to collect the stardust to help shape our perspective on what constituted that beginning of the universe, as we sent our probes out for further material in which to judge?