# The Big Bang and Cosmology

The night sky is, for the most part, dark.

This observation has undoubtedly been made many times over, but in the nineteenth century, Heinrich Olbers realized that this simple fact contradicted the existing steady-state model of the Universe. If the Universe is infinitely old and infinitely large (and also homogeneous on large scales), then no matter which way one looks in the night sky, one’s line of sight must eventually find a star and therefore the night sky should be a blazing sphere of light. This is Olbers’s Paradox — he was not the first to draw this conclusion, but he is the most well-known for it.

Even when we consider the fact that less light reaches us from more-distant stars, Olbers’s Paradox is still not resolved. If we picture a series of “shells” of stars, centered on the Earth, we can see that while the light reaching us from each individual star is proportional to $\frac{1}{{d}^{2}}$ as a consequence of the Inverse Square Law, the number of stars per shell is directly related to the surface area of the shell and scales with ${d}^{2}$. Therefore the light reaching us from each shell is the same and the paradox still stands.

Illustration of Olbers’s Paradox (Credit: Htkym / Wikipedia)

Of course, the solution to Olbers’s Paradox is that the Universe is not both infinitely old and infinitely large.

The theory of the Universe beginning with a Big Bang was first proposed by Georges Lemaître in 1927, as part of a solution to the Einstein field equations. (Einstein himself believed in a static universe and had to introduce a “cosmological constant”, Λ, into his equations to compensate.) Edwin Hubble demonstrated concrete proof of an expanding Universe when he noticed that galaxies further from the Earth were moving away at a faster rate; this is now called Hubble’s Law, with recessional velocity equaling Hubble’s constant (H0) times distance. Hubble’s constant is thought to currently be ~ 71 $\frac{km/s}{Mpc}$, but it is worth noting that Hubble’s constant is not truly a constant, as it may change with the expansion of the Universe.

Rough Timeline of the Big Bang / Early Universe

• t = 0 — BANG! (not really an explosion)
• t < ${10}^{-44}$ sec — Planck era, quite literally our idea of it is limited to “?????”
• t = ${10}^ {-36}$ to ${10}^{-34}$ sec — Universe inflates dramatically, increasing in size by 10^(50) times, strong force becomes distinct
• t = ${10}^{-12}$ to ${10}^{-10}$ sec — Electromagnetic and weak forces become distinct
• t = ${10}^{-6}$ to ${10}^{-5}$ sec — hadrons (protons, neutrons, etc.) and leptons (electrons, positrons etc.) form from quarks
• t = 1 sec — annihilation of matter and antimatter has slowed, matter dominates even though they should have been created in equal amounts
• t = ${10}^{2}$ sec — the nuclei of Hydrogen and Helium (and small amounts of Lithium and Beryllium) are formed in what’s called “Big Bang Nucleosynthesis”

A brief history of everything — click to expand to a readable size (Credit: CERN)

About 380,000 years after the Big Bang, the Universe had finally cooled off enough for atoms to form (on the order of 3000 K), thus allowing photons to travel through space without being constantly scattered by free electrons. Due to the ongoing expansion of the Universe, the radiation from this point in time has been cosmologically redshifted to the point where it now falls in the microwave part of the EM spectrum. Thus, we call it the Cosmic Microwave Background Radiation (CMBR). The CMBR was first detected by Arno Penzias and Robert Wilson in the 1960s, as a faint bit of microwave noise coming from, well, everywhere. Data most famously collected by the Cosmic Background Explorer (COBE) and the Wilkinson Microwave Anisotropy Probe (WMAP) shows that this “noise” matches almost exactly with what we would expect from a cosmologically redshifted version of the 3000 K blackbody radiation curve.

The CMBR as observed by Planck — yes, it’s not from WMAP, Planck is more recent and we like it more (Credit: ESA and the Planck Collaboration)

After around 1 billion years, stars and galaxies have finally formed and the universe as we know it has started to take shape. But as we observe the beginnings of the Universe, we also wonder, what will be its eventual fate? To determine this, we must turn to some rather complicated cosmology.

Cosmologists define a density parameter ${\Omega}_{total}$, which is the density of (for lack of a better term) stuff in the Universe — we can’t call it matter because only a fraction of it is matter — as compared to a critical density, ${\rho}_{crit}$. This critical density is just enough for the Universe’s expansion rate to slow down to zero as time approaches infinity. There are three main possibilities:

• ${\Omega}_{total}$ > 1 (ρ > ${\rho}_{crit}$) — a closed Universe, it will eventually reach a maximum size and then start collapsing (“Big Crunch”)
• ${\Omega}_{total}$ = 1 (ρ = ${\rho}_{crit}$) — a flat or critical Universe, the expansion rate of the Universe will approach zero as time goes on
• ${\Omega}_{total}$ < 1 (ρ < ${\rho}_{crit}$) — an open Universe, it will expand forever, but the rate of expansion may be constant or it may be increasing

Different fates of the Universe — orange = closed, green = flat/critical, blue = open, red = open and accelerating (Credit: NASA GSFC)

Data from distant Type Ia supernovae and the CMBR appear to support a model where ρ is very close to ${\rho}_{crit}$, but the Universe is still accelerating. However, this raises another problem — the amount of mass that we can see and measure out in the universe is about 4% of what is required to match ${\rho}_{crit}$. This is where the stuff we referred to earlier comes into play.

First of all, astronomers have noticed that galaxies and clusters appear to contain much more mass than we can actually see. Rather unimaginatively, they named this invisible source of mass dark matter. Even the combined amount of regular matter and dark matter is nowhere near enough to match ${\rho}_{crit}$, but the presence of dark matter still doesn’t explain why the expansion rate of the Universe is increasing. Cosmologists believe that another type of stuff, dark energy, actually creates a “negative pressure” (that is to say, it repels other stuff), thus causing the acceleration.

Distribution of matter and energy in the Universe (Credit: NASA / JPL-Caltech / T. Pyle)

Whew.

We thank you for sticking with us through that, as theoretical cosmology is not exactly our strong suit as astronomy geeks, but we hope you enjoyed our attempt to — quite literally — explain the Universe.

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