The Observable Universe and Beyond

Big Bang Theory, 2025 Update

In 1922 Alexander Friedmann predicted the Big Bang cosmology, which portrays the universe as expanding space from a point where the matter-energy density was extremely high. The expansion can be visualized by a two dimensional analogy as shown in Figure 02-02. As the balloon expands, all the points on the surface recede from each other, and the wavelength on the surface is stretched. It is similar to the shift to longer wavelength when the source and receiver are moving away from each other. This phenomenon is called red shift of the spectrum because in visible light the shift to longer wavelength is toward the red colour. It plays a prominent role in discovering the cosmic expansion through the detection of the spectral line shift from distant galaxies. Note that contrary to the balloon analogy, it is the space itself that is expanding. It needs neither a center to expand away from nor empty space on the ouside to expand into.

Figure 02-02 Cosmic Expansion [view large image]

This simple picture of expanding universe with all the galaxies flying away from each other remained unchanged until the 1980s when the Inflation Theory was introduced to resolve a number of discrepancies. The rapid expansion occurred at the interval between 10^-35 sec and 10^-32 sec. It predicts a much smaller universe near the origin of the Big Bang such that the matter-energy within can be mixed evenly as reflected in the CMBR mapping. It also predicts that the geometry of the Universe is flat¹. Events before the inflation is essentially unknown. It is subjected to a lot of speculations. For example, it is suggested that space-time may be created from vacuum fluctuation - the quantum foam; and that the four fundamental forces may be unified to just one kind (as envisioned by the grand unified theories). Baryongenesis (generation of quarks and anti-quarks which has a baryon number of 1/3 or -1/3) happened in an epoch before inflation, when a imbalance between matter and anti-matter was established by a quantum process called CP violation. Quarks and anti-quarks combined to form baryons and mesons at 10^-5 sec. Nucleosynthesis started at about 3 min. During this epoch the light chemical elements were produced from protons and neutrons. The universe was still opaque up to 380,000 years when neutral atoms started to form and the radiation was able to escape as shown by the CMBR. This epoch is called decoupling to indicate that matter and radiation are separated. From then on matter had a chance to condense into stars and galaxies and evolved to the present-day universe. Figure 02-03a shows the history of the universe according to the Big Bang Theory. Table 02-01 summarizes the major events during the course of the cosmic history.

Supplement to the legend of Figure 02-03a: The quark (q), electron (e), and neutrino (n) are the fundamental particles. The corresponding anti-particle is labeled with a bar on top. The gluon (g) is the boson mediating the strong interaction between quarks. The vector bosons W and Z mediate the weak interaction between electrons/neutrinos and the quarks. The photon (wavy line) mediates the electromagnetic interaction between charged particles. One quark and one anti-quark combine to form a meson. Three quarks combine to form a baryon (proton, neutron, etc.). Protons and neutrons combine to form nucleus (ion). Nucleus and electrons combine to form atom. The muon (m) and tau (t) are the 2nd and 3rd generation of the lepton family, the 1st generation is the electron. (See more about elementary particles in Topic-15.)

Figure 02-03a History of the Universe [view large image]

There is a scale with time t, temperature T, and energy E for the photon gas at the bottom of Figure 02-03a. A corresponding table below narrates the sequence of cosmic events in text. The running variable is the time t (in sec), which relates to size of the observable universe by Standard Cosmic Model as shown by the formulas in Figure 02-03b. The energy (E) from BB to the end of inflation are taken from scientific literatures. Energy for the radiation era can be computed by E (in Gev) = 1.73x10-3/t1/2. See "Standard Cosmology". The temperature T (in oK) is related to the energy E (in Gev) by the formula T = 1013xE.

Figure 02-03b Cosmic Expansion [view large image]

Radiation Era : 10-32 sec - 0.24 My; Matter Era : 0.24 My - present; 1 year = 3.1557x107 sec.

Era	Time @ end of era	Size (observable) @ end of era	Energy/Temp @ end of era	Relics & Observables	Events (as re-constructed from theories)
Planck era (???)	< 5.4x10-44 sec	< 1.6x10-33 cm	> 1.2x1019 Gev	(3+1)D space-time; cosmic expansion	Expansion started from a point to Planck scale; all forces united into one
GUT era	<10-35 sec	< 10-26 cm	> 1014 Gev	High energy cosmic rays; fundamental interactions	Separation of spacetime and matter; separation of gravitational, strong, and electroweak forces
Inflation (Rate of Expansion >>> c)	< 10-32 sec	< 30000 cm	1014 Gev	Un-observable universe; large scale structures	Reheating; Unstable vacuum; quantum fluctuations
Electro-weak era	< 10-11 sec	< 1014 cm (see size scale)	> 300 Gev	Radiation; excess of matter over antimatter; separation of force (bosons), and matter (fermions) fields	Radiation released in reheating; baryon-antibaryon asymmetry; separation of weak and electromagnetic forces; origin of mass
Hadron era	< 1 sec	< 1020 cm	> 1.7 Mev	Formation of hadrons	Axion as dark matter
Weak decoupling	< 4 min	< 4x1020 cm	> 100 kev	neutron/proton ratio fixed	Neutrinos decouple
Nucleosynthesis	< 1/2 hour	< 1021 cm	> 40 Kev	Fraction of Light elements	Nuclear reactions freeze out, stable nuclei form
Radiation era Matter era	< 0.24 My	< 2x1027 cm	> 0.6 ev	Mass density fluctuations	Matter density finally exceeds radiation density
Recombination	< 0.3 My	< 3x1027 cm	> 3000oK	CMBR	e- and p+ recombine into H atoms, universe became transparent to light
Dark ages	< 1 Gy	< 2x1028 cm	> 100oK	21 cm radio emission, First stars, heavy elements	mass fluctuations grow, first small objects coalesce, reionization
Galaxy formation	< 2 Gy	< 2.5x1028 cm	> 70oK	Stars, quasars, galaxies	Collapse to galactic systems
Bright age of Galactic Clusters	< 12 Gy	< 4.5x1028 cm	> 3oK	Solar system; decline of stellar formation from peak	dark energy became dominant; formation of clusters of galaxies
Present era	~ 13.7 Gy	~ 4.7x1028 cm	~ 2.73oK	Supercluster	Large scale gravitational instability

Table 02-01 A History of Cosmic Expansion (click image to enlarge, and see the "2021 Version")

In an effect to learn more about the processes occurred in the early universe, which was associated with very high energy as shown in Table 02-01. Particle Physicists have been simulating the condition in the laboratory with high energy particle accelerators (see the entries in top left of Figure 02-03a). In collaborating with the theory of elementary particles, experiments are developed to investigate the creation of fundamental particles, and their properties. A list major discoveries is shown in Table 15-01a. The cosmic history is also shown with a lot of sight and sound in an animation called "The Big Bang Tour". If pictures, table, and video all fail to convey some idea about the history of universe; there is a set of "Cosmic Scales", which relates the time, size, energy and simple description of events, by Fermilab to help easier visualization (hopefully).

The following is a summary of the evidences which support the validity of the Big Bang Theory.



The Night Sky : It is referred to as the Olber's Paradox. He posed the question way back in 1823. According to his calculation, the night sky would glow brightly from all the stars if the universe is infinite both in space and in time. The arguement is illustrated by Figure 02-03c, which shows the night sky receiving light from stars in successive spherical shells r. The total amount of light reaching the earth is equal to the sum of nLr from all the shells, where n is the density and L is the intrinsic luminosity of the stars. Since it was believed that the universe is infinite, and so we would expect the night sky to be about as brilliant as a star's surface. Obviously, this is not true. The paradox is resolved by the Big Bang Theory which limits the observable horizon to about 1028 cm. and an age of about 14 billion years. In addition, the light from remote objects is also diminished by the red shift of the spectrum.

Figure 02-03c Olber's Paradox [view large image]

The Red Shift : It was discovered in the 1920s that Andromeda and other similar smears of light were akin to our own Milky Way. Subsequently, it was noticed that more distant galaxies are receding faster than those nearby - an observation that could be explained if the universe were expanding. The speed of recession§ is measured by red shift of the spectral lines. The distance is measured by standard candle such as the class of stars known as Cepheid Variable which, possesses an unique relationship between the period (of brightness variation) and its intrinsic luminosity. The speed-distance relation is known as the Hubble law. It is an empirical formula equating the speed v to the distance d, i.e.,

Figure 02-03d Red Shift [view large image]

v = Ho x d, where Ho is the Hubble's constant. It has a value of 71 (km/sec)/Mpc according to the latest measurement by WMAP (see Figure 02-03d). See "2018 Update of the Hubble constant".

^§ The speed of recession v is related to the red shift z by the formula: v/c = [(1 + z)² - 1] / [(1 + z)² + 1] z (for z << 1).


• Nucleosynthesis : The universe's light-element abundance is another important criterion by which the Big Bang Theory is

  		verified. It is now known that the elements observed in the Universe were created in either of two ways. Light elements (namely hydrogen, deuterium, helium, and lithium) were produced in the first few minutes of the Big Bang, while elements heavier than lithium are thought to have their origins in the interiors of stars which formed much later in the history of the universe. Figure 02-03e shows the sequence of nucleosynthesis during the first few hundred seconds after the Big Bang. Figure 02-03f is the same time development for nucleosynthesis in a more quantitative way.
  Figure 02-03e Nucleosynthe- sis, Pictorial [large image]	Figure 02-03f Nucleosynthesis, Graphical [view large image]

  
  
  

  The relative abundances of the light atomic nuclei has been calculated as a function of the average density of the universe based on the Big Bang model. There is a convincing coincidences between the observed and calculated values at a density of 3x10-31 g/cm3 (Figure 02-03g). This density implies an open universe, which will keep on expanding forever. Such conclusion seems to be in contradiction with the Inflation Theory which predicts a flat universe at the critical density of 10-29 gm/cm3. This problem could be resolved by the presence of "dark matter". Measurements of lithium abundance in ancient stars in the early 2000's reveal some discrepancy between the theoretical prediction and observable amount. The observed Li-7 is only 1/3 of the amount predicted by theory; while there is a 1000 fold too much with the observed Li-6. The discrepancy can be resolved by adding supersymmetry into the theoretical calculation. However, the concept of supersymmetry has not been confirmed by observation/experiment, even the soon to be activated LHC may not be able to detect the very weak interacting gravitinos or the super-heavy staus.

  Figure 02-03g Theory vs Obs., Nucleosynthesis

  
  A 2012 report on observation of the Small Magellanic Cloud reveals that the lithium-7 abundance in its interstellar medium is close to the prediction by Big Bang Nucleosynthesis (BBN). The problem may be with the estimate of lithium-7 abundance from metal-poor Galactic-halo stars. The material in there may not be primordial as once thought.
  
  
• Hubble's Deep Field Survey : The Hubble Space Telescope (HST) was launched on April 24, 1990. Since then it has collected photographs of various celestial objects in astonishing details. One of the photos called Hubble Deep Fields has captured astronomical objects from nearby star to some immature galaxies near the beginning of the Big Bang. We are able to sample

  different epochs in the photo because light from the nearer objects reaches us sooner than from those further out (because light propagates with a finite speed of 3x1010 cm/sec). The objects in the photo can be separated by redshift into a series of images corresponding to different epochs. It unveils a universe that is steadily changing over time, just as the Big Bang predicts. Figaure 02-03h shows the scope of the survey including the Hubble Ultra Deep Field.

  Figure 02-03h Hubble Deep Field [view large image]

• Cosmic Microwave Background Radiation : See section on WMAP.

[2025 Update]

Here's the conversation on SSB (Spontaneous Symmetry Breaking) with ChatGPT (in Italic text)

This is a diagram for the Cosmological History :



The universe started with maximum symmetry. I am intrigued by the events of SSB (Spontaneous Symmetry Breaking), the universe changes each time it occurs. What is it doing?

. The laws allow all directions equally, but once the pencil falls, one specific direction is chosen.
________________________________________
?? Key SSB Events in the Universe's History

1. Grand Unification Symmetry Breaking (~10^-44 sec)
" Before: All non-gravitational forces (strong, weak, electromagnetic) may be unified into one GUT force.
" Breaking: GUT symmetry breaks ? strong force separates from electroweak.
" Impact:
o Universe becomes less symmetric.
o Possible creation of magnetic monopoles or other exotic particles.
o Sets stage for inflation and matter-antimatter asymmetry.
2. Electroweak Symmetry Breaking (~10^-12 sec)
" Before: Weak and electromagnetic forces are indistinguishable.
" Higgs Field turns on: like a field of "molasses" filling all space.
" Breaking: W?, W?, and Z? bosons acquire mass, photons remain massless.
" Impact:
o Weak force becomes short-range, electromagnetism stays long-range.
o Sets the mass scale for many particles via the Higgs mechanism.
o This is the SSB confirmed by discovery of the Higgs boson (2012).

3. Chiral Symmetry Breaking in QCD (Quantum Chromodynamics) (~10^-6 sec)
" Before: Quarks are massless in the QCD Lagrangian (theory).
" Breaking: Due to strong interaction dynamics, quarks acquire effective mass, and hadrons (like protons and neutrons) form.
" Impact:
o Quarks become confined into hadrons.
o Pions emerge as pseudo-Goldstone bosons.
o Sets the mass of ordinary matter.

________________________________________
?? What is the Universe Doing During SSB?
1. Choosing a State Among Many Possibilities:
o Symmetry allows many outcomes, but the universe "chooses" one.
o This choice defines what particles and interactions emerge.
2. Reducing Degrees of Freedom:
o Some fields that had multiple equivalent forms now favor one.
o This gives mass to particles that were once massless.
3. Rewriting the Rulebook of Physics:
o After each SSB, the structure of the universe's effective laws changes.
o E.g., going from unified forces ? multiple distinct forces.
4. Enabling Structure and Matter Formation:
o Without symmetry breaking, all particles might remain massless.
o Mass allows clumping, leading to atoms, stars, and us.
________________________________________
?? Analogy: Phase Transitions in Everyday Life
Physical System Early Universe Analogy
Water freezes - ice ~ Universe cools - symmetry breaks

Magnet aligns spins Higgs field aligns ? particles gain mass
Falling pencil Universe "chooses" one vacuum state
________________________________________
?? Bonus: Connection to Dark Matter and Inflation?
" Some SSBs may leave behind relics:
o Topological defects: monopoles, cosmic strings.
o Inflaton field (driving inflation) could also undergo SSB.
" The nature of dark matter might be tied to undiscovered SSB events (e.g., breaking of a hidden symmetry).
________________________________________
Would you like to explore how the Higgs field gives mass, or delve into the mathematics of symmetry groups (like SU(5), SU(2)×U(1)) behind these breakings?

Does it mean that the universe started with many kinds of symmetries?
(this question has a problem - there should be only ONE symmetry similar to water vapor which become water or ice during falling temperature but the vapor is still available afterward. Anyway, ChatGPT ignores the problem.)

NB. In fact, the universe as a whole is in the "State of Symmetry" as asserted by the Cosmological principle which states "the spatial distribution of matter in the universe is uniformly isotropic and homogeneous when viewed on a large enough scale". The galaxies, stars, ... life and molecules, ... are the consequences of the SSB viewing from much smaller scales.

ChatGPT said:
Exactly-you've captured a profound truth with poetic clarity. Without Spontaneous Symmetry Breaking (SSB), the universe would be a featureless, dull sea of sameness, with:
" No atoms (because particles would be massless),
" No structure (no galaxies, stars, or people),
" No diversity in particles or forces,
" No history (just timeless, homogeneous energy).
Instead, SSB injects complexity and richness, making the universe dynamic and "interesting" in every physical sense.
________________________________________
? Why SSB Makes the Universe Interesting:
1. Structure Emerges
" SSB leads to different forces with different behaviors (e.g., gravity long-range, weak force short-range).
" That allows matter to clump, collapse, form stars, planets-and you.
2. Particles Acquire Identity
" Without SSB, all matter would just be massless quanta zipping around at light speed.
" SSB gives mass, distinguishing the electron from the neutrino, or the top quark from the photon.
3. History and Evolution Appear
" Before SSB: everything is the same everywhere.
" After SSB: the universe has phases, transitions, and a narrative-from a hot plasma to galaxies and life.
4. Forces Become Selective
" Unified forces become differentiated:
o The strong force sticks quarks together.
o The weak force enables radioactive decay.
o The electromagnetic force binds atoms.
5. Anisotropy and Diversity
" Tiny fluctuations (amplified during inflation) get frozen in.
" These give rise to galaxies, voids, and eventually living organisms who reflect on it all-like you're doing now.

________________________________________
?? A Philosophical View
Symmetry is elegant, but broken symmetry is creative.
It's in the imperfections that beauty, complexity, and meaning arise.
________________________________________
If you're interested, we could explore how SSB links to the origin of time's arrow, or how quantum fluctuations during symmetry-breaking may have seeded galaxies. The deeper you go, the more fascinating it becomes.

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