Cosmic Expansion and Wavelength Effects

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Questions and Answers

What happens to the wavelength of light from distant galaxies as the universe expands?

  • It decreases.
  • It varies randomly.
  • It increases proportionally. (correct)
  • It remains constant.

What does the ratio $\frac{l_0}{l}$ represent in the context of cosmological redshift?

  • The distance of a galaxy from Earth.
  • The age of the universe.
  • The scale factor of the universe at different times. (correct)
  • The speed of recession of a galaxy.

How much larger is the current scale factor $R_0$ compared to the scale factor 750 million years ago?

  • 5.3% larger. (correct)
  • 15.7% larger.
  • 1% larger.
  • 10% larger.

What is the cosmological redshift?

<p>The increase in wavelength of light due to the expansion of the universe. (B)</p> Signup and view all the answers

What does a measured wavelength ratio of approximately 8.6 imply about the volume of space?

<p>The volume of space is about 640 times larger than it was. (D)</p> Signup and view all the answers

What determines the actual value of the recession speed ($v$) of a galaxy?

<p>The density of the universe, the value of $H_0$, and the expansion history. (D)</p> Signup and view all the answers

Why can the recession speed of some galaxies exceed the speed of light?

<p>Due to the expansion of space itself, not relative motion. (D)</p> Signup and view all the answers

What is meant by saying, 'the universe isn’t expanding into emptiness'?

<p>There is no surrounding space for the universe to expand into. (D)</p> Signup and view all the answers

What does the expansion of the universe signify about its characteristics?

<p>The scale factor of the universe is increasing. (D)</p> Signup and view all the answers

What is dark energy theorized to act like in the context of the universe's expansion?

<p>An antigravity force that causes universal repulsion. (A)</p> Signup and view all the answers

What proportion of the universe's average energy density is attributed to dark energy?

<p>68.5% (B)</p> Signup and view all the answers

How does the average density of matter in the universe compare to the density of dark energy?

<p>It is less than dark energy. (A)</p> Signup and view all the answers

What conclusion can be drawn if the average energy density of the universe is equal to the critical density?

<p>The universe is infinite and expanding forever. (D)</p> Signup and view all the answers

What is the current estimated age of the universe?

<p>13.8 billion years (C)</p> Signup and view all the answers

What is the significance of the average energy density being precisely equal to critical density?

<p>It shows the universe is infinite and barely unbounded. (D)</p> Signup and view all the answers

Which percentage best represents the average energy density of conventional matter in the universe?

<p>4.9% (D)</p> Signup and view all the answers

What could happen if the average energy density becomes slightly larger than the critical density?

<p>The universe would become finite and contract. (B)</p> Signup and view all the answers

What role does gravitational attraction play in the universe's expansion?

<p>It can slow down the expansion depending on its strength. (A)</p> Signup and view all the answers

Flashcards

Cosmological redshift

The increase in wavelength of light from distant galaxies as the universe expands.

Scale factor (R)

A dimensionless quantity representing the ratio of the current size of the universe to its size at a specific time in the past.

Infinite universe

The universe has no boundaries; there's nothing outside of it.

Wavelength (l)

The distance between two corresponding points of a wave.

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Expanding universe

The universe's scale grows larger over time.

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Hubble constant (H0)

The rate of expansion of the universe at the present time.

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Observable universe

The portion of the universe that we can observe due to the limitations of time and distance.

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Critical Density

The exact density needed for the universe's expansion to neither stop nor accelerate.

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Dark Energy

A mysterious force that speeds up the expansion of the universe.

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Recession velocity

The speed at which distant galaxies appear to be moving away from us due to the expansion of the universe.

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Wavelength Ratio

The measurement of the increase/decrease of wavelengths with respect to the expansion of the universe.

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Dark Matter

Mysterious matter that accounts for a significant portion of the universe's mass.

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Recession speed greater than light speed

Objects can appear to recede faster than light in the expanding universe, because it's not an object moving. Space itself is expanding.

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Conventional Matter

The ordinary matter that makes up stars, planets, and us.

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Big Crunch

A hypothetical scenario where the universe stops expanding and starts contracting.

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Universe's Energy Density

Average amount of energy per volume of space in the universe.

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Age of the universe

The calculated age of the universe, approximately 13.8 billion years.

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Unbounded universe

The universe has no edges or limits.

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Study Notes

Wavelength and Scale Factor in an Expanding Universe

  • Wavelength of light from distant galaxies increases as the universe expands
  • λ₀ / λ = R₀ / R (λ₀ = current wavelength, λ = wavelength at any time, R₀ = current scale factor, R = scale factor at any time)
  • Cosmological redshift: increase in wavelength with time and increasing scale factor
  • Farther objects have greater redshift due to longer travel time and more significant change in R
  • Current largest measured wavelength ratio for galaxies ~ 8.6, implying a significant increase in space volume

Recession Speed and Relativity

  • Recession speed can exceed the speed of light for very distant objects
  • Does not violate special relativity because recession speed is not from object's motion relative to space coordinates
  • Expansion of space itself causes objects coordinates to move apart rapidly
  • Observable universe is limited by the light travel time

Infinite and Unbounded Universe

  • Universe is infinite, without edges
  • Expansion is the increase of the universe's scale factor
  • Not expanding into an empty space

Critical Density and Dark Energy

  • Gravitational attraction slows expansion
  • Dark energy acts as an antigravity, causing universal repulsion
  • Dark energy density is ~ 68.5% of critical density (ρcc2)
  • Matter density is ~ 31.5% of critical density
  • Dark energy contributes substantially to the universe's expansion acceleration, resulting in continuous expansion.

Universe's Average Energy Density

  • Average energy density of the universe equals ρcc2 (within observational error)
  • Implies an infinite and unbounded universe (nearly)
  • If energy density were slightly larger, universe would be finite
  • Observational error in average energy density is currently <1%, needing improvement to confirm unboundedness.

Matter Composition of the Universe

  • Ordinary matter (4.9%)
  • Dark matter (26.8%)
  • Dark energy (68.3%)

Significance of ρcc2

  • Universe is infinite and unbounded (to within observational error)

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