The Big Bang and Expansion of The Universe

This topic is part of the HSC Physics course under the section Origins of The Elements.

HSC Physics Syllabus

investigate the processes that led to the transformation of radiation into matter that followed the ‘Big Bang’
investigate the evidence that led to the discovery of the expansion of the Universe by Hubble (ACSPH138)

The 'Big Bang' and Evidence for The Expansion of The Universe

This video will discuss the processes following the inception of the universe according to the Big Bang theory. The video will also discuss the evidence that led to the discovery of the expansion of the universe including

Hubble's observation of galaxies
cosmic background microwave radiation
analysis of primordial elements

The 'Big Bang' Theory

The Big Bang Theory or model is the most popular understanding of the origin of the universe. It is supported by various experimental evidence and astronomical observations.

The model proposes that the universe originates from a point where energy is concentrated in a singularity. Following its inception, several things happened as discussed below in chronological order.

1. Creation and separation of fundamental forces

There are four fundamental forces in the current universe: gravitational force, electromagnetic force, strong and weak nuclear force. All four forces were created at the beginning of the Big Bang

Gravitational force first separated from strong-electro-weak force (this group of three forces is termed Grand Unified force) during which the temperature cools to 10³²

Shortly after (less than one second), strong nuclear force separated from electro-weak force during which the temperature cools to 10²⁷

Radiation is more abundant than matter (besides fundamental particles, no other matter exists at this stage)

2. Inflation of the universe occurred shortly after the formation and distinction of fundamental forces.

The expansion led to the release of energy which allows the universe to cool rapidly but more importantly create matter. The initial phase of expansion occurred over a very short interval of time (magnitude of 10^-43 seconds), during which the size of the universe expanded by a factor of 10²⁵.

Scientists believe that this rapid inflation is critical to prevent the universe from collapsing back into a black hole (due to its immense density and high level of energy).

3. Formation of particles and antiparticles

Formation of fundamental particles - quarks, leptons and antiparticles (antiquarks and antileptons) were created from radiation.

Particles and anti-particles have the mass but are always opposite in one of the fundamental characteristics of particles such as charge and magnetic moment.

Leptons separate into electrons, neutrinos and antiparticles e.g. positron.

Quarks and antiquarks form protons, neutrons and antiparticles e.g. antiproton.

Initially, the production of particles and antiparticles from radiation was always in pairs such that they were formed in equal ratios. Due to the high energy state of the universe, newly formed particles and their antiparticles quickly underwent annihilation to form gamma photons.

4. Formation of matter – Baryogenesis

The continuous outward expansion and cooling of the universe caused the number of collisions between particles and antiparticles to decrease. As a result, the conversion of matter into radiation decreased.

At the same time, for reasons unknown to physicists, the production of particle and antiparticle eventually became unbalanced. A greater number of particles started to form more often than their antiparticles.

This increased the ratio of particles to antiparticles. The excess particles led to baryogenesis where quarks combined to form subatomic particles such as protons and neutrons. The composition of subatomic particles will be covered in the standard model of matter.

5. Big Bang Nucleosynthesis

The collision between protons and neutrons resulted in the formation of hydrogen-2 nuclei (H-2). However, due to the high temperature of the universe, these nuclei were not stable and quickly decomposed to reproduce protons and neutrons.

H-2 nuclei only stopped decomposing when the temperature of the universe was low enough.

Deuterium nuclei collided with neutrons to form tritium nuclei (H-3).

Tritium nuclei collided with protons to form He-4.

Although lithium-3 (Li-3) nuclei were sometimes formed during this process, their relatively low nuclear stability resulted in their disintegration. Hence, He-4 nuclei are considered as the heaviest element to have been formed during the Big Bang nucleosynthesis.

As more nuclei are formed, the universe continued to cool. The process of nucleosynthesis stopped when the temperature became insufficient for further collision between protons and neutrons to occur.

6. Matter decoupled from radiation – Recombination

Recombination marked the point in time when the universe cooled to approximately 3000 K.

There are several events that occurred at recombination:

The temperature of the universe was low enough for electrons to be captured by nuclei to form atoms.

Photons were able to propagate through the universe without interacting with matter. The transmission of these photons can be observed today in the form of low energy microwave photons (Cosmological Background Microwaves).

Matter became more abundant than radiation. As a result, the density of matter of the universe became greater than the density of radiation.

7. Formation of stars and galaxies

A billion years following the Big Bang, stars and galaxies started to form. Elements heavier than helium were formed by nuclear fusion reactions in stars and supernova explosions.

Around 8 billion years after the Big Bang, the Solar system and the Sun were created. Throughout this time, the universe continued to expand and the temperature continued to decrease. The temperature of the universe today is around 3 K.

Change in matter, radiation and temperature

Throughout the events that followed the Big Bang, there was a constant exchange between radiation and matter. However, in the beginning, matter quickly converted back into radiation via particle-antiparticle annihilation. The decrease in temperature of the universe eventually hindered annihilation and hence caused radiation to transform into matter.

Figure shows the decrease in density of matter and radiation as the Universe expands and cools. As matter becomes more dominant than radiation, its density eventually 'crosses over' to become greater than that of radiation. Knowledge of dark energy is not required for HSC Physics.

The prominence and popularity of the Big Band theory and more importantly the expansion of the universe is due to a diversity of experimental evidence and astronomical observations. The primary one is the work done by Edwin Hubble.

Edwin Hubble’s discovery of the expansion of the universe

Hubble used the largest telescope at the time to obtain long spectral exposures of nearby and distant galaxies. Specifically, he used the Doppler shift of hydrogen absorption lines to determine the galaxies' velocities relative to Earth. Hubble discovered that almost all spectral lines were red-shifted. This observation was observed in all directions and suggested that the galaxies were moving (receding) away from Earth.

Since galaxies were shown to have recessional velocities relative to Earth, Hubble argued that the universe was expanding at a velocity that is more significant than the relative velocity of a galaxy.

Hubble then measured the luminosity of stars in these galaxies as well as their brightness. Using inverse square law (`I_1r_1^2=I_2r_2^2`), he measured the distance of each galaxy from Earth.

What is Hubble's Law?

By plotting this distance against the recessional velocity of each galaxy relative to Earth, Hubble discovered a proportional relationship between the two. This relationship is known as Hubble's law:

$$v=H_0D$$

where v is the velocity of a galaxy relative to Earth (or The Milky Way), H₀ is Hubble’s constant and d is the distance of a galaxy away from Earth.

Hubble's law states that the recessional velocity of a galaxy relative to Earth is proportional to its distance from Earth. In other words, the further away a galaxy is, the faster it is moving away from Earth, suggesting that the expansion of the universe becomes faster the further away it is from Earth.

Hubble's discovery of the expansion of the universe supports the Big Bang model as it suggests that the universe started from a single point back in time.

What is Hubble Time?

Hubble's constant in Hubble's law is related to the age of the universe (time since its inception). Specifically, the inverse (reciprocal) of the gradient of the graph above is an approximation of the age of the universe. The estimation derived from Hubble’s law is around 13.7 billion years with an error of 1% when compared to the actual value.

The Expansion of the Universe is Accelerating

In 1995, new observational evidence suggested that Hubble's description was incomplete. Scientists discovered that the expansion of the universe is not just continuing at a constant rate, but is actually accelerating. This discovery was surprising because, according to the laws of gravity, the expansion of the universe was expected to slow down over time due to the gravitational attraction between galaxies.

The key evidence for the accelerating expansion came from studying Type Ia supernovae in distant galaxies. Type Ia supernovae are "standard candles" in astronomy, meaning they have a known intrinsic brightness. By comparing the observed brightness of these supernovae to their known intrinsic brightness, astronomers can determine their distance from Earth.

Scientists found that the light from these distant supernovae was dimmer than expected. This implied that the supernovae were farther away than predicted by a constant expansion rate, suggesting that the rate of expansion of the universe has increased over time.

Instead of a straight line, the velocity-distance graph becomes a curve. At greater distances, the curve flattens out, indicating lower velocities than would be expected from a linear relationship. This flattening reflects the fact that we are observing these galaxies as they were in the past, when the expansion rate was slower.

Cosmic Background Microwave Radiation (CBMR)

Penzias and Wilson were adapting radio-antennae for astronomy research whereby they encountered background noise in the form of radiation. After troubleshooting they figured this was not a systematic error but resulted from radiation of primitive cosmic origin.

Cosmic background microwaves are the remnants of gamma radiation that was described by the Big Bang model in the beginning of the universe. As the universe cooled and expanded, the wavelength of gamma radiation increased (due to cosmological red shift), causing gamma photons to become the observed microwaves at present day.

The temperature of the universe is about 2.7 K which, when substituted into Wien’s displacement law, corresponds to a peak wavelength of about 0.2 cm. This wavelength lies within the microwave spectrum.

Cosmic background microwave radiation supports the Big Bang model and the expansion of the universe.

Analysis of Primordial Elements

The Big Bang nucleosynthesis created various isotopes of hydrogen and helium. The amount of each isotope became fixed when the temperature of the universe became insufficient for meaningful collisions between particles to occur. As a result, the mass ratio of hydrogen and helium nuclei can be predicted and compared to the present value.

The Big Bang model predicts that majority of matter in the universe is due to hydrogen and helium isotopes. Only a small amount by mass is due to elements heavier than helium as these were synthesised in stars which only formed a billion years after the Big Bang.

It is estimated that the current universe, by mass, consists of 23-26% helium, 73-75% hydrogen and the rest is heavier elements. These values are consistent with predictions by the Big Bang model. It also provides evidence for the Big Bang nucleosynthesis – the condition was sufficient for nuclear fusion to occur to produce hydrogen and helium isotopes.

This discovery provides evidence against the theory that the production of nuclides mostly occur in stars via nuclear fusion.

Next section: Spectra of Stars