History of the Universe

Reading: Chapter 26, Cosmology and Chapter 27, The Early Universe

The Big Bang theory for the Universe is in good shape. The Universe is expanding, is bathed in a low temperature sea of background radiation (the CMBR), and has a chemical composition (primrily hydrogen and helium) which can be understood in terms of the Big Bang theory. There are issues for sure, but the basic Big Bang is secure.

A potential problem is that the Universe is inferred to be 13.7 billion years old based on observations of the Cosmic Microwave Background Radiation (CMBR) and our current best version of the Big Bang Theory . The ages of the oldest stars in our Galaxy (the Milky Way galaxy) are found from studies of globular cluster stars which are estimated to have ages to lie between 11 and 18 billion years with 95 % confidence that they must be older than ~11 billion years. If, in fact, globular clusters are found to have ages closer to the upper end of their estimated ages, then significant alterations will need to be made to our current thoughts about the Universe.

Overview of the History of the Universe

TIMELINE FOR THE UNIVERSE

Today, the Universe is bathed in the 2.7 Kelvin CMBR. This suggests that when the Universe was younger (and smaller) that it was hotter. In fact, if we were to run the clock backward, we would encounter almost unimaginably extreme conditions at early times. We would find that at the earliest times in the Universe, the Universe was dominated by radiation. As the Universe expanded and cooled, eventually matter dominated the evolution of the Universe. The crossover occured around 50,000 years after the Big Bang. As the Universe continued to expand and cool, Dark Energy took over and dominated the evolution of the Universe. This crossover occured around 4 billion years ago. We are currently in the Dark Energy era. Note, however, that at early times, Dark Energy is less important than matter and radiation and so may be ignored in the discussion of the Early Universe. In the sections below, we discuss the evolution of the Universe in more detail.

Friedman Models and the Future of the Universe

The principal distinction between the models is the manner in which the Universe eventually winds-up its evolution. The early times are fairly similar. This simplifies our discussion. Before I continue, let me define some quantities which have appeared in some earlier plots, but which were not discussed in detail.
The ultimate fate of an expanding Universe is determined by the interplay of;

the mutual gravitational attraction of mass in the Universe
the repulsive nature of Dark Energy

The above two plots show the behavior of the Friedman models in two forms. The left figure shows how universes look in terms of how the redshifts of distant galaxies depend on their distances (this is the Hubble Law for small redshift, z). The right plot shows how the scale factor R(t) changes with time for the different universes.
Initially, the Universe was driven to expand by some unknown impetus. The current rate at which the Universe expands is measured by the Hubble constant H_o. The expansion is slowed by the gravitational attraction of material contained in the Universe. If the amount of material is large enough then the expansion of the Universe will be halted and the Universe will eventually stop expanding and start to contract! In this sense, one can define an escape speed for the Universe. If the Universe exceeds this escape speed, it will expand forever.

There is then some critical amount of material in the Universe (which determines how strongly gravity slows the expansion). For this precise amount of mass, the Universe assumes a critical form where it is neither open nor closed, but is flat. This amount of mass leads to the definition of the Critical Density.

The critical density is given by

where H (=H_o) is the Hubble constant and G is the gravitational constant. Note that the faster the expansion (the greater the Hubble constant H_o, the larger the critical density.) For the currently accepted Hubble constant value, H_o ~ 22 km per second per million light years, the critical density is around 9x10^-30 grams per cubic centimeter. This critical density which controls the evolution of the Universe is very rarefied; the density of air in this room is around 10^-6-10^-5 grams per cubic centimeter.
We define the quantity known as Omega as
For a flat Universe, the total material in the Universe takes the form

where the material density is composed of two parts, the matter density composed of the dark matter and normal matter, and the Dark Energy component. Here, the Omegas are the fractions of the critical density contained in the matter component and Dark Energy component, respectively. For an open universe, the measured density is less than the critical density and the sum of the Omegas is less than l and for a closed universe, the measured density is greater than the critical density and the Omegas are greater than 1.
The determination of H_o and the Omegas are crucial for the determination of the ultimate fate of the Universe and will be addressed in the next Topic. We now discuss how the Universe evolved from the time of the Big Bang to the current time.
TIMELINE FOR THE UNIVERSE
In the following, we discuss each era in the evolution of the Universe in more detail. The history is uncertain in the beginning, but after 10^-11 seconds, things are on very solid ground as by this time conditions in the Universe are such that much of the relevant physics may be probed in Terrestrial laboratories.

0 ===> 10^-43 seconds, the Planck Era
The Planck era when the four forces of the Universe -- the gravitational, electro-magnetic, strong (nuclear), and weak forces -- may have been unified. This is the era of quantum gravity -- the time when a theory which encompasses both quantum mechanics and gravity must be used. The size of the current Universe at this time is less than 10^-50 centimeters.

10^-43 ===> 10^-32 seconds, Era of the GUTs and On to Inflation

Era of the Grand Unified Theories (GUTs) when gravity separates from the other three forces (i.e., gravity becomes an interaction distinct from the other forces). This ended after around 10^-32 seconds had elapsed after the Big Bang. At this time the Universe had a temperature of 10²⁷-10²⁸ Kelvin. Inflation begins at the end of this stage -- inflation is driven by some as of now, unknown repulsive force. We describe inflation in the next section.

10^-32 ===> 1 second, Inflation, the Quark Epoch, and On to Element Production, Nucleosynthesis
The strong (nuclear) force becomes a distinct interaction at the beginning of this stage and inflation stops at the beginning of this stage. During inflation, the Universe increases in size by a huge factor -- perhaps by as much as a factor of 10^10¹²!!! Some models say that the size of the current Universe increased from 10^-50 centimeters to roughly the size of a grapefruit during inflation. A region as small as the Planck length (~ 10^-33 cm) would expand enough to encompass the currently observable Universe.

Pair Production and Annihilation
After inflation, the Universe continues to expand. The Universe is still exceedingly hot, T > 10¹⁵ Kelvin and very energetic. The high-energy radiation carries very large energies. This has important consequences. In his Special Theory of Relativity, Einstein showed that there is an equivalence between mass and energy,
This means that high-energy radiation can transform into massive particles, if the radiation is energetic enough. Interestingly, the production always produces pairs of massive particles, one an ordinary particle and the other its anti-matter twin. In the inverse process, matter particles and their anti-matter twins will annihilate to produce energy (radiation)! When the Universe is very hot, pair production of quarks and leptons occurs.

Something odd happens during this time, however, because for an unknown reason more matter quarks and leptons are produced than anti-matter quarks and anti-matter leptons, even though they should always be created in matter/anti-matter pairs. The slight excess of matter over anti-matter leads to the outcome that there is matter in our Universe today.

After inflation the Universe is dominated by a quark-gluon plasma. What are quarks and gluons? To the right is a schematic picture of what is known as a baryon. Baryons are a class of fundamental particles which includes protons and neutrons; protons and neutrons are composed of three quarks held together by the intermediary particles known as gluons. When the Universe is very hot and energetic, the quarks and gluons are free and are not tied up in baryons.

As the Universe expands it cools. After around around ~ 10^-11 seconds hve elapsed, the temperature is around ~ 10¹⁵ Kelvin and the weak nuclear force and the electromagnetic force become distinct (a further symmetry breaking. We now have a universe dominated by the four known forces of the Universe, the gravitational force, the strong nuclear force, the weak nuclear force, and the electromagnetic force. From this time on, we are rather secure in our understanding of the Universe. The conditions in the Universe from here onward are attainable in Terrestrial laboratories and so amenable to detailed experimental study.
Around 10^-6 seconds after the birth of the Universe, quarks and gluons combine to form baryons (neutrons and protons). This marks the end to the Quark Epoch. The production of baryons continues until the temperature drops below 10¹³ Kelvin where the Universe is no longer energetic enough to produce baryonic matter/anti-matter pairs. Unfortunately, there is no barrier to annihilations of matter/anti-matter pairs and the annihilation process continues quite efficiently. As noted earlier, we are lucky in that there was a slight asymmetry between matter and anti-mattter quarks and leptons which allows some matter baryons to survive the annihilation! The production of the matter baryons is referred to as baryogenesis while the existence of the slight excess of matter over anti-matter referred to as the Matter-Anti-Matter Asymmetry Problem.
Because electrons are less massive than baryons, the similar event for electrons and their anti-matter twins, the positrons, occurs later, around ~1 second after the birth of the Universe when the temperature has dropped below 1 billion Kelvin.

1 second ===> 100 seconds, Nucleosynthesis and the Nuclear Epoch

Big Bang Nucleosynthesis
The final symmetry breaking has already occured by this time (at time 10^-11seconds); quarks and gluons have combined to form protons; protons and electrons combined to form neutrons; and the stage is set for the formation of the elements in a process referred to as nucleosynthesis. In nucleosynthesis, hydrogen, helium, a little lithium and the hydrogen isotope deuterium are produced in the few minutes after 1 second has elapsed into evolution of the Universe. The top panel shows how helium nuclei are produced from four hydrogen nuclei (protons). The middle panel shows how the larger, more massive element Carbon may be produced. This chain almost never completes in the early Universe because the intermediate step where Beryllium forms leads to a bottleneck. Beryllium decays (breaks apart into helium nuclei) after 6.710^-17 seconds, way too fast for it capture another helium nucleus. The bottom panel shows paths to form some lighweight elements through the capture of hydrogen nuclei (protons).

In Big Bang Nucleosynthesis, only hydrogen, helium, lithium and the hydrogen isotope deuterium are produced in significant amounts (see the figure to the left). The amount of helium produced in the Big Bang is insensitive to the mass contained in baryons in the Universe, but the amount of deuterium is very sensitive to the mass in baryons in the Universe. Based on current measurements of the primordial abundances of hydrogen, helium, and deuterium, we infer that the amount of normal matter which can be contained in the Universe is 3-4 % of the critical density (the gray bar in the figure to the left)!
After the finish of the era of nucleosynthesis, the Universe continues to expand and cool but no new chemical elements are created until stars form and die.

380,000 years ===> Formation of CMBR
Recombination
The Universe becomes cool and rarefied enough for electrons and protons to form neutral hydrogen atoms. This occurs around when the temperature of the Universe has dropped to around 3,000 Kelvin (z ~ 1,000). Because neutral hydrogen atoms are not efficient absorbers of radiation, the Universe becomes transparent to radiation. Before the Era of Recombination , the Universe was opaque to radiation, that is, the Universe was "foggy" in that light could not travel very far which meant that our view of the Universe was limited. What are the consequences of this?

After Recombination, we can get unimpeded view of the distant Universe. So, as the Universe gets older, we can see further and further into the past. However, we cannot see forever because at some point the Universe becomes opaque; we can only see up to Recombination. This is what we see when we observe the Cosmic Microwave Background Radiation, the CMBR. This ia analogous to the situation we encounter when we see the light from a cloud in the sky. We see the clear space between the cloud and us, but we cannot see into the dense, opaque part of the cloud.

10⁶ ===> 10⁹ years, Stars, Galaxies, and Large-Scale Structure Formation

Protogalaxies begin to form. This may be annoying since the clumps of matter and the clumps of the clumps of overdense matter should distort the CMBR. The reason is that if these clumps are formed by the attraction of gravity, then such large overdensities take a fairly long time to form (recall the discussion of the free-fall time). This means that at the time of recombination, the ovedensities need to be large. Currently, the largest structures in the Universe are consistent with the imperfections seen in the CMBR. If we see much larger structures, then there will be trouble.

1 billion years ===> 3 billion years
Quasars and some radio galaxies become detectable

3 billion years ===> 13.7 billion years and Dark Energy Era
Solar System, planets, life, ...

13.7 billion years ===> End

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