Cosmological FactsHubble's Law
For a galaxy a distance d away from us and receding at a speed v it is observed that
where H is Hubble's Constant, which is about 65 km/s per megaparsec. That is, for every megaparsec the speed of recession increases by about 65 km/s.v = H dAbundances
The matter in the universe consists largely of hygrogen, helium, deuterium and lithium. The observed proportions of these elements in the universe is
Element Nuclear Structure Abundance (%) Hydrogen 1 proton 77 Helium-4 2 proton, 2 neutrons 23 Deuterium 1 proton, 1 neutron 10-3 Helium-3 2 protons, 1 neutron 10-3 Lithium 3 protons, 4 neutrons 10-8 Cosmic Microwave Background (CMB) Radiation
The CMB is observed to have a perfect thermal radiation spectrum corresponding to a temperature of 2.7 K. Indeed, it is the most perfect thermal spectrum known. The microwave radiation comes to us from all directions and is observed to be uniform across the entire sky to one part in ten thousand. This is one of the most extraordinary discoveries of our times. See COBE home page.
The Big BangThe best current explanation of the cosmological facts is that the universe began a finite time ago in a titanic explosive event, called the Big Bang, which can be called the creation of the universe.
Age of the Universe t
Before we can talk sensibly about the age of the universe we need to agree on what we mean by this phrase.
One of the first people to determine the age of the universe was Bishop Ussher, who defined the age of the universe as the time since its creation by God. He determined that the universe was created on Sunday, 23 October, 4004 BC. As we shall see shortly, modern estimates are somewhat earlier than this!
We shall define the age of the universe as the time since its creation at the big bang. Let's try to estimate that time period. Consider a galaxy that is a distance d from us and assume (to keep the mathematics simple) that over the age of the universe t the galaxy's recession speed v was constant.
At the big bang, the energy that would eventually become the galaxy was next to the energy that eventually led to us. The age of the universe would be the time it has taken the "galaxy" to move from our immediate vicinity to its current position. Since we know the galaxy's speed, and we assume it has remained constant since the beginning, we can estimate this time as follows
or, when we use Hubble's Law v = Hd ,t = d/vThat is, an approximate value for the age of the universe is just the inverse of the Hubble constant. A more accurate calculation must take account of the fact that the gravity arising from all forms of matter and energy in the universe acts like a break which decelerates the universal expansion. This calculation was first performed by Lemaitre, who obtained:t = 1/Has the age of the universe.t = (2/3) x (1/H)Thequantity 1/H is called the Hubble Time, which according to Lemaitre's calculation is greater than the age of the universe.
Why is this so? Well, if the expansion has been decelerating since the big bang, because of the breaking effect of gravity, then recession speeds must have been greater in the past; that is, galaxies must have receded faster, on average, than they do at present. Consequently, every galaxy must have arrived at its present location, relative to us, sooner than the Hubble time, which is the age we inferred by assuming the recession speed never changed.
If we take Hubble's Constant to be 50 km/sec per megaparsec we predict an age of about 15 billion years, a time it should be note considerably longer than that estimated by Bishop Ussher.
Critical Density and Spacetime
Today we prefer to think of space and time as a single entity called spacetime. The latter is made of 3 space plus 1 time dimension--that is, it is a 4-dimensional volume! Moreover, according to Einstein, this volume can be warped!
Unfortunately, our human intuition is incapable of imagining such a thing; our understanding of higher dimensions is based upon our intuition about 2-dimensional surfaces. General relativity predicts that the 4-dimensional volume can curve in different ways depending upon the density of matter and energy in the universe. In the simplest models of the universe, there are three possible ways in which space can bend:
Open Universe--In this case the global geometry of space has negative curvature. Unfortunately, this is quite impossible to imagine. Negative curvature arises if the matter and energy density is less than a critical value of about 3 Hydrogen atoms/cubic meter. There is then not enough matter to slow down the expansion sufficiently and the universe will expand forever.Cosmic Horizon--How far can we see?
Closed Universe--In this case the global geometry of space has positive curvature. This curvature is akin to the curvature of a sphere. The universe would have a finite volume but no boundary, just like the surface of a sphere. Positive curvature arises if the density is greater than the critical density. Then there is enough matter eventually to halt the expansion and cause the universe to contract and finally collapse in a titanic implosion called (inevitably) the Big Crunch.Flat Universe--The global geometry of space has zero curvature, just like the geometry of a flat plane. Flat geometry arises if the density is exactly equal to the critical density. In this case, the universe will expand forever but will reach a zero expansion speed in the infinite future. Most cosmologists believe the global geometry of the universe is flat.
We see the universe because of the radiation that comes to us at the speed of light. So in 15 billion years the maximum distance that the radiation can travel is 15 billion light years. The light from objects further out than 15 billion light years has not had enough time to reach us and so these objects cannot be seen at present. However, as the universe ages we will be able to see further and further into space. The maximum distance to which we can see, at any given time, is called our Cosmic Horizon. The cosmic horizon defines the Visible Universe.