Cosmology and the History of the Universe Notes

What is the scientific study of the universe as a whole called?

Cosmology

What do astronomy and astrophysics focus on?

Objects within the universe, such as stars, planets, and galaxies

What aspects of the universe do cosmologists study?

The birth, evolution, and ultimate fate of the entire universe

What type of science is being used when discussing the age or size of the universe?

Cosmology

What type of science is being used when studying the life cycle of a star?

Astronomy or astrophysics

What paradox arises from the question "Why is the night sky dark?"

Olbers' Paradox

Why is it paradoxical to say the night sky is dark because the Sun isn't shining?

Because if the universe were infinite and filled with stars, the sky should be infinitely bright, even at night

Why doesn't distance alone explain the dark night sky in an infinite universe?

Because even dim stars, if infinite in number, would add up to infinite brightness

Why doesn't interstellar dust resolve Olbers' Paradox?

Because over time, dust would absorb starlight, heat up, and re-radiate the same energy, still making the sky bright

What deeper implication does Olbers' Paradox suggest about the universe?

That the universe is not infinite, not eternal, or both—it must have had a beginning, and is possibly expanding

Who formally posed the question, "If the universe is infinite and full of stars, why is the night sky dark?"

German astronomer Heinrich Olbers

What key limitation of the universe helps resolve Olbers' Paradox?

The universe has a finite age, meaning it had a beginning

What is the universe's speed limit that affects what we can see?

The speed of light

Why don't we see stars beyond a certain distance?

Their light hasn't had time to reach us since the Big Bang

How do Einstein's theories help resolve Olbers' Paradox?

Special and General Relativity revealed the finite speed of light and a finite age for the universe

What would we observe if the universe were infinitely old and static?

A sky that is infinitely bright, even at night

What defines the boundary of the observable universe?

The maximum distance light has traveled since the universe began

If the universe were only 100 years old, how far away could we see?

Only up to 100 light-years away

What shape does the observable universe take for any observer?

A sphere centered on the observer, with radius equal to the universe's age in light-years

Is Earth at the center of the universe?

No, but it appears to be at the center of our observable universe, just as any other location appears to be at the center of its own observable universe

Why can't we see stars beyond a certain distance?

Their light hasn't had time to reach us since the Big Bang

What is the observable universe?

The region of the universe from which light has had time to reach us since the Big Bang

What determines the size of the observable universe?

The age of the universe and the speed of light

What is the cosmic horizon?

The outer edge of the observable universe—the most distant light we can possibly detect

How does the cosmic horizon resemble a black hole's event horizon?

Both are boundaries beyond which no information can reach us—we are trapped inside the cosmic horizon, just as nothing escapes from inside a black hole's event horizon

How does the observable universe change over time?

It expands outward by about one light-year per year as more distant light reaches us

What surprising insight does General Relativity suggest about the universe?

The entire universe might be mathematically similar to a black hole turned inside out

What would the sky look like if the universe were infinite and eternal?

It would be infinitely bright, as every line of sight would end on a star

Why isn't the night sky infinitely bright?

Because the universe is not eternal—it has a finite age, and light travels at a finite speed

What is the current radius of our observable universe?

About 14 billion light-years, corresponding to the universe's age

Why do we see a finite number of stars, even if the universe is infinite?

We can only observe stars whose light has had time to reach us—those inside our cosmic horizon

What is the key resolution to Olbers' Paradox?

The finite age of the universe and the finite speed of light ensure the sky is dark at night, as we can see only a finite amount of starlight

What did Einstein's equations reveal about the universe?

That spacetime had a beginning—a singularity of infinite curvature

What is the Big Bang?

The origin of spacetime itself, not an explosion in preexisting space

How does General Relativity describe the Big Bang?

As the emergence of space and time from a point of infinite density and curvature

How does this understanding of the Big Bang resolve Olbers' Paradox?

It shows the universe has a finite age, limiting how far light has traveled and explaining why the night sky is dark

Why is it incorrect to imagine an empty universe before the Big Bang?

Because spacetime did not yet exist—there was no "before."

What does General Relativity say about the origin of time?

Time began with the Big Bang; there was no earlier moment

What does the Big Bang mark?

The temporal and spatial origin of our universe—the beginning of spacetime itself

What does General Relativity predict should happen to the universe's expansion due to gravity?

It should gradually slow down because all matter attracts gravitationally

What determines the ultimate fate of the universe's expansion?

The universe's average mass density compared to a critical value

What happens if the density is greater than the critical value?

Expansion reverses, spacetime collapses, ending in the Big Crunch

What happens if the density is less than the critical value?

Gravity is too weak to stop expansion, and the universe expands forever

What happens if the density equals the critical value?

Expansion continues forever, but the rate of expansion slows over time

What geometry corresponds to greater than critical density?

Closed geometry-curved like a sphere

What geometry corresponds to less than critical density?

Open geometry—curved like a saddle

What geometry corresponds to exactly critical density?

Flat geometry—like Euclidean space

What determines the geometry of the universe?

The universe's average mass density compared to the critical density

What is the geometry of a universe with density greater than the critical value?

Closed geometry

What is a concrete example of closed geometry?

A sphere or ellipsoid

What are the properties of closed geometry?

Triangle angles > 180°, circle circumferences < 2πr, parallel lines converge

What is the geometry of a universe with density less than the critical value?

Open geometry

What is a concrete example of open geometry?

A hyperboloid (saddle-shaped surface)

What are the properties of open geometry?

Triangle angles < 180°, circle circumferences > 2πr, parallel lines diverge

What is the geometry of a universe with density equal to the critical value?

Flat geometry

What is a concrete example of flat geometry?

A place (Euclidean geometry)

What are the properties of flat geometry?

Triangle angles = 180°, circle circumferences = 2πr, parallel lines stay parallel

Does a flat universe mean no gravity?

No. A flat universe refers to the large-scale geometry, not local gravitational curvature caused by stars, galaxies, or black holes

Can local gravitational effects exist in all three geometries?

Yes. Local distortions occur in closed, open, and flat universes

What does the mass of normal matter (luminous stars) suggest about the geometry of the universe?

It suggests an open universe, which would expand forever

How does dark matter affect the universe's geometry?

Dark matter could potentially make the universe flat or closed, depending on its distribution and amount

What role does dark matter play in the universe's expansion?

Dark matter's gravitational effects could halt expansion and lead to a Big Crunch (closed geometry) or continue expansion indefinitely (flat geometry)

What is the current understanding of dark matter?

Its composition remains a mystery, but it's known to make up about 27% of the universe's mass-energy content

How much dark matter is there compared to normal matter?

There is about 10 times more dark matter than normal (luminous) matter

Is dark matter needed for gravitational dynamics at the star system scale?

No, the gravitational interactions in the Solar System (e.g., between the Sun and planets) are fully explained by normal matter alone

What would happen if there were no dark matter in the universe?

Galaxies and clusters of galaxies would not remain bound and the universe would expand indefinitely

Why did most physicists, including Einstein, reject the idea that the universe had a beginning?

Most physicists believed the universe was static and eternal, leading Einstein to initially reject the implications of his own General Theory of Relativity, which suggested a universe with a beginning

What was the cosmological constant, and why did Einstein introduce it?

The cosmological constant was a "fudge factor" Einstein introduced to counteract the solutions of General Relativity that implied the universe had a beginning. It was meant to keep the universe static

What important discovery did Edwin Hubble make in 1929?

The universe is expanding, based on the observation that the light from distant galaxies was redshifted, indicating they were moving away from us

What does the redshift of light from distant galaxies indicate?

The redshift indicates that these galaxies are moving away from us, which provides evidence for the universe's expansion

Why do some galaxies like the Milky Way and Andromeda exhibit blueshift?

Blueshift occurs when galaxies within the same galactic group or cluster are falling toward each other due to gravitational attraction, as opposed to the general expansion of the universe

How do local gravitational forces affect the general expansion of the universe?

Local gravitational forces, such as between galaxies in the same cluster, can cause galaxies to move toward each other, which can result in blueshift. However, the general trend of cosmic expansion causes galaxies to recede overall

According to General Relativity, what is the nature of cosmic expansion?

Cosmic expansion is not the motion of galaxies themselves, but the expansion of spacetime, which carries galactic groups and clusters away from each other, leading to recessional motion and redshifted light

Why did Einstein call the introduction of the cosmological constant his "biggest blunder"?

Einstein referred to the cosmological constant as his "biggest blunder" after Hubble's discovery of the expanding universe showed that the universe was not static, as Einstein had once thought, but expanding over time

Who are the six key figures credited with the development of the Big Bang model?

The six key figures are:

Edwin Hubble: For his observations of cosmic expansion.

Albert Einstein: For deriving the concept of a universe with a beginning.

Alexander Friedmann, Howard Robertson, Arthur Walker, and Georges Lemaître: For developing the mathematical details of the expansion

What is one of the key triumphs of the Big Bang model?

The prediction of cosmic expansion, which was confirmed through Hubble's observations

Why do all galaxies beyond the Local Group appear to be moving away from us, but we are not at the center of the universe?

While every observer in the universe appears to be at the center of their observable universe, there is no true "center" of the universe. The expansion of spacetime causes all galactic groups and clusters to move away from each other, giving the illusion that each observer is at the center of expansion

How can the concept of spacetime expansion be understood using the analogy of ants on a balloon?

Imagine ants on the surface of a balloon. As air is added, the balloon inflates, causing the ants to move farther apart. From each ant's perspective, all others appear to be moving away, so each believes it is at the center of expansion. Similarly, galaxies seem to move away from each other as spacetime expands, but there is no actual "center."

In the analogy of ants on a balloon, what does the stretching of the balloon's surface represent in cosmology?

The stretching of the balloon's surface represents the expansion of spacetime, which carries galactic groups and clusters away from each other. No matter where an observer is, they perceive the same expansion

How does spacetime expansion cause galaxies to appear to move away from each other?

As spacetime stretches, galactic groups and clusters appear to move away from each other. This causes the redshift of light, with light from distant galaxies becoming increasingly stretched as it travels toward us

Why is there no true center to the universe's expansion?

There is no true center because every galactic group or cluster perceives itself to be at the center of the universe's expansion. The universe expands uniformly, and each observer sees galaxies moving away from them, giving the illusion of centrality

What does Hubble's Law state about the recessional speed of galaxies?

The recessional speed (v) of galaxies is proportional to their distance (d) from us, expressed as v = H₀d, where H₀ is the Hubble constant (approximately 70 km/s per megaparsec)

What causes galaxies to recede from each other according to Hubble's Law?

The stretching of spacetime causes galaxies to recede from each other. This leads to the redshift of light, as the wavelength of light is stretched while it travels through expanding space

What is cosmological redshift and how does it differ from other types of redshifts?

Cosmological redshift refers to the stretching of light's wavelength as it travels through expanding spacetime, causing galaxies to appear redshifted. This is different from kinematic redshift, which results from the motion of galaxies relative to each other, and gravitational redshift, which occurs due to the influence of strong gravity on light

If intelligent civilizations existed in every galactic group, what would they observe regarding other galaxies?

They would observe redshifted light from other galaxies, indicating that the galaxies are receding due to the expansion of the universe, a phenomenon explained by cosmological redshift

Why can cosmological redshift be interpreted as kinematic redshift in terms of recessional speed?

Cosmological redshift can be interpreted as kinematic redshift because it appears that all galaxies beyond our Local Galactic Group are moving away from us. This allows us to calculate their recessional speeds using the Hubble law, which links speed to distance

How does the analogy of cars in a parking lot explain Hubble's Law?

The analogy involves two circles of cars:

First circle: Cars moving at 60 mph and 60 miles away, covering 60 miles after one hour, implying they started moving away an hour ago.

Second circle: Cars moving at 120 mph and 120 miles away, covering 120 miles after one hour, implying they also started moving away an hour ago

What does the direct proportionality between recessional speed and distance support regarding the universe's history?

The direct proportionality between recessional speed and distance supports the idea that the universe began with a Big Bang. The expansion of the universe leads to galaxies moving away from each other, consistent with the Big Bang model

What does the analogy of circles of cars moving away from us at increasing speeds help illustrate about Hubble's Law?

The analogy shows that if cars are moving away from us at increasing speeds, we would conclude they all started moving away from us at the same time, based on the proportional relationship between speed and distance. This illustrates Hubble's Law, where the recessional speeds of galaxies are directly proportional to their distance from us, implying that all galaxies started moving away from us at the same time: the Big Bang

Why does Hubble's Law imply that there is no center to the universe's expansion?

According to Hubble's Law, every point in the universe appears to be at the center of its own observable universe. The stretching of spacetime causes all galactic groups or clusters to move away from each other. Therefore, any point in the universe would observe galaxies receding from it, making it seem like the center of the expansion. There is no actual center of the universe's expansion

How does the Hubble constant relate to the recessional speed of galaxies?

The Hubble constant (approximately 70 km/s per megaparsec) means that for each megaparsec of distance, galaxies move away at an additional 70 km/s. For example:

A galaxy 1 megaparsec away moves at 70 km/s.

A galaxy 2 megaparsecs away moves at 140 km/s.

The recessional speed increases proportionally with distance, indicating an expanding universe

How can we estimate the age of the universe using the Hubble constant?

By solving for the Hubble constant in the equation v=H0d, we find that the reciprocal of the Hubble constant gives an estimate for the age of the universe. This is known as the Hubble time. It represents the time that galactic groups and clusters have been expanding since the Big Bang

What does the Hubble time represent, and how is it calculated?

The Hubble time is the reciprocal of the Hubble constant. It serves as an estimate of the universe's age by providing the time that has passed since all galaxies began moving away from each other at the moment of the Big Bang. Given that the Hubble constant is approximately 70 km/s per megaparsec, the Hubble time can be used to estimate the age of the universe

Why is the reciprocal of the Hubble constant important for estimating the age of the universe?

The reciprocal of the Hubble constant is important because it gives an estimate of the time that has passed since the Big Bang. Since the Hubble law relates recessional speed and distance, the Hubble time can be used as a rough approximation of how long the universe has been expanding, providing an estimate for its age

How is the Hubble time calculated and what is its value?

The Hubble time is calculated by taking the reciprocal of the Hubble constant (roughly 70 km/s per megaparsec) and performing a unit conversion. This results in an approximation of 14 billion years, which gives the age of the universe. It represents the time since galaxies began expanding from the Big Bang

What does a larger Hubble constant indicate about the age of the universe?

It indicates a shorter expansion time for the universe, meaning the universe has been expanding for a shorter amount of time. The reciprocal relationship between the Hubble constant and the Hubble time means that if the constant is large, the universe's age will be smaller

Why do cosmologists still refer to the Hubble constant even though it may not truly be constant?

The Hubble constant is still used because its variations occur over millions of years, meaning it remains approximately constant over human timescales. Therefore, it's reasonable to refer to it as the Hubble constant, even though it might change gradually over time.

What is the highest rung of the Cosmological Distance Ladder?

The Cosmological Distance Ladder is used to measure the distance to very distant galaxies such as quasars by interpreting their cosmological redshift as a kinematic redshift and calculating their recessional speed

How are distances to nearby galactic groups and clusters measured?

Distances to nearby galactic groups and clusters are measured using methods such as the Tully-Fisher relation, Faber-Jackson relation, and the Type Ia supernova method, which provide ways to determine galaxy distances based on their luminosity and other properties

How is the Hubble constant determined?

By measuring the redshift of galaxies and determining their recessional speeds, then using these measurements along with distance measurements from nearby galactic groups and clusters to calculate its value (approximately 70 km/s per megaparsec)