Author: Prof. A.W. Peet, University of Toronto
![[my avatar]](../images/avatars/an32sq.png)
Creative Commons licence: BY-NC-SA 4.0 Int'l
Last updated: 2014-06-14
On average, the universe is expanding. Almost all other stars/galaxies are moving away from ours. Sources that are further away are moving away from us faster. Hubble encoded this in an equation: $$ v=H_0\, D\,. $$ This is possible because the very fabric of spacetime itself is expanding. But gravitationally bound objects -- like galaxies and solar systems -- do not expand with the fabric of spacetime. Their gravity binds them together.
Once you have looked at the Hubble equation for awhile, a scary thought appears to you. What if the galaxy was far enough away that the recessional speed became greater than the speed of light? What would this mean? Does it mean that signals are actually being transmitted faster than the speed of light in violation of Einstein’s fundamental speed limit!?
No. You can rest easy. There is another way to interpret Hubble’s Law that gives a much better understanding of how our expanding universe operates. Actually, galaxies which appear to go faster than light are galaxies we cannot see. The light from them simply cannot reach us any more. We call the patch of spacetime containing things with which we could in principle communicate the causal patch. It has a finite size because our universe has lived for only a finite amount of time (about 13.7 billion years). We can only see out to our cosmological horizon, and physics within the horizon is completely consistent with causality. We are simply out of causal contact with all stuff that is outside our cosmological horizon. The principle of causality is safe.
Let me outline and address a few possible misconceptions about the Big Bang. The “Big Bang” refers to evolution of the universe rather than its (speculative) origins. Also, the Big Bang is not an expansion into space: instead, the Big Bang made space. Big Bang nucleosynthesis (BBN), which created hydrogen helium and lithium, does not depend on what theory you use to make sense of the Planck epoch. Astrophysicists have a good handle on how to compute relative abundances of different elements and isotopes. But we honestly don’t know if the universe started infinitely small and infinitely hot, or as something completely different-looking. Theoretical cosmologists are working hard on this question and most of what is known today is still very controversial.
So what is the edge of our knowledge comfort zone
right now? We are experimentally confident about the history of the universe presented last week starting from baryogenesis and electroweak symmetry breaking. The LHC will be able to help clarify these physics issues significantly. The parts of the story about inflation (the universe’s huge early growth spurt) and the Planck epoch -- the really early universe -- are still considered speculative. Astrophysicists and physicists will continue looking for indirect ways to test ideas experimentally, but we may well end up fundamentally limited in our ability to know about the universe. Finding those limits is still very much a work in progress.
Einstein’s static universe was one early contender for a theory of the entire cosmos. Another contender was Lemaître and Gamow’s Big Bang Nucleosynthesis (BBN) model. Their associates Alpher and Herman predicted the cosmic microwave background radiation (CMBR) from this theory. The CMBR was discovered in 1964 by Penzias and Wilson, who got a Nobel Prize for their discovery. (One of their early hypotheses for the effect they were seeing was .... pigeon crap. LOL!) The CMBR later turned out to be the most perfect blackbody known in the entire universe. The temperature of the CMBR today is very cold: approximately 2.725 Kelvin.
![[some complicated curves displaying element abundance (c.f. hydrogen) for deuterium, helium-3, helium-4, depicted on the vertical axis, as sensitive functions of the density of ordinary matter (c.f. photon density), depicted on the horizontal axis]](images/BBN.jpg)
The image below shows the COBE data compared against theory. The experimental errors on the observatinoal data points are so small that you cannot see them with this image resolution! Theory and experiment fit perfectly.
![[COBE power spectrum]](images/cobespectrum.jpg)
Early astrophysicists established the Cosmological Principle: the fact that the universe looks isotropic (same in all directions) and homogeneous (the same here as over there). Suppose that we model the universe by assuming that space grows with time t via a simple scale factor a(t). The people who first wrote down the Einstein equations and solved them were Friedman Robertson and Walker. These cosmologies (spacetimes approximating our universe) are known as FRW universes.
So what do Einstein’s equations say about the evolution of the scale factor $a(t)$ with time? They give the scale factor velocity $\dot{a}(t)$ in terms of the Newton constant $G_N$, the energy density $\rho$, and the curvature $\kappa$: $$ \left({\frac{\dot{a}}{a}}\right)^2 = {\frac{8\pi G_N}{3}}\rho - {\frac{\kappa}{a^2}} \,, $$ and they give the scale factor acceleration $\ddot{a}(t)$ in terms of $G_N, \rho$ and the pressure $p$: $$ {\frac{\ddot{a}}{a}}= - {\frac{4\pi G_N}{3}} \left( \rho +3p \right) \,. $$ The Hubble parameter is $$ H = {\frac{\dot{a}}{a}} $$ The density parameter $\Omega$ obeys $$ \Omega = {\frac{8\pi G_N}{3H^2}}\rho = 1 + {\frac{\kappa}{H^2 a^2}} $$
The only point of showing you these equations is to motivate why knowing the curvature of space $\kappa$ is so important: it points the way to predicting the future evolution of the universe! Positive curvature (like a basketball) has $\kappa$=+1; negative curvature (like a Pringle) has $\kappa$=-1; flat has $\kappa$=0.
![[cartoons of surfaces with spatial curvatures which are positive (sphere), negative (saddle) and zero (flat)]](images/kappa.jpg)
Inflation was invented in 1965 by Zeldovich and independently by Alan Guth in 1980. One of the motivations was the observed isotropy of the CMBR. It is surprising that the CMBR would be so uniform, because the particle horizon at recombination was only about two degrees on our sky. It was unclear to astrophysicists of the day what mechanism would cause wider regions to have (approximately) the same temperature. Our universe has also been measured to be extremely close to flat. In addition, we have seen zero magnetic monopoles so far, but they are objects that are typically predicted in GUTs (grand unified theories). The solution to each of these problems, and a few more besides, is inflation.
Dark matter is defined as matter which doesn’t shine. It gravitates but does not interact with photons. It gravitates just the same as regular matter, so can be weighed the same way. Dark matter might be composed of superparticles, but this is speculative.
Dark energy is a lot more mysterious. It corresponds to having a constant energy density, i.e., a constant amount of energy per unit volume of space. The weirdest thing about dark energy is that it gravitates like it has negative pressure, which seems physically crazy in the sense that we don’t yet know of any substance that behaves like this! Despite decades of work by the world’s smartest physicists, nobody yet has a sensible theory of what dark energy is. People have some partial ideas, but they all have logical holes in them. If you can crack the puzzle of dark energy, then you will surely win the admiration of your colleagues worldwide as well as a Nobel Prize.
Einstein’s equations are very well tested indeed. Weighing the universe using them gives a pretty spectacular result:
![[pie chart of the universe showing approximate percentages composing our cosmos. Over 70% is dark energy, about 25% is dark matter, and less than 5% is made of regular particles like hydrogen, helium, stars, heavy elements, and neutrinos.]](images/piechart.jpg)
Why is this pie chart surprising? Well, it says that 95% of the universe is composed of completely foreign stuff that we have not yet seen in the lab!
These results come from combining multiple techniques: CMBR, Type Ia supernovae, Large Scale Structure, Hubble, gravitational lensing, etc. No single technique is king. It is the combination of data-gathering experiments that makes current understanding of cosmological parameters so precise compared to twenty years ago.
What kinds of apparatus did humans use to weigh the CMBR?
![[pictures of the experiments of Penzias and Wilson, COBE, and Planck, alongside all-sky images of the cosmic microwave background radiation obtained using those three pieces of equipment]](images/CMBRexpts.jpg)
Penzias and Wilson discovered the CMBR using a ground-based detector. COBE was the first CMBR satellite, put in orbit in 1990. Its results were incredibly important and extremely influential. It discovered anisotropy in the CMBR at the level of one part in 100,000. John Mather and George Smoot, PIs for the project, won the Nobel Prize.
Other CMBR experiments were also important, including balloon-borne experiments like Boomerang. The Wilkinson Microwave Anisotropy Probe (WMAP, a NASA satellite) produced first results in 2003. WMAP gave us a much more detailed picture of small deviations from the perfect blackbody spectrum. Planck (an ESA satellite) was launched in May 2009. There are many other CMBR experiments as well. At any rate, the age of precision cosmology is here.
Figuring out expansion of the universe (à la Hubble, etc.) is not straightforward, because you cannot measure the distance of stars/galaxies independently of their brightness. A very few astronomical objects are sufficiently well understood to be called standard candles. Type Ia supernovae are a class of such objects, which all form from similar-mass white dwarfs. Observing the light curves (the graph of the luminosity versus time) of many exploding Type Ia supernovae across the sky was enough to constrain cosmological parameters already in the late 1990s. Combining the discovery of the CMBR with SNIa information produced the discovery of dark energy. This was earth-shaking for the astronomy and physics communities.
The best theoretical fit to current astronomical observations is a model sometimes abbreviated as ΛCDM. This includes (1) a cosmological constant (dark energy); (2) cold dark matter, which moves slowly enough to be non-relativistic, and (3) regular matter that we know and love. The physics of dark energy dominates the accelerated expansion of our large universe at this stage in its evolution. But dark energy dynamics did not dominate in the early universe.
You can check out how varying the composition of the universe today affects its future by accessing this cool NASA web tool at http://map.gsfc.nasa.gov/resources/camb_tool/cmb_plot.swf.
![[cartoon graph showing how expansion of the universe differs with time depending on how much of the total density is made of matter (dark and regular) as compared to dark energy]](images/possibleUs.jpg)