Hubble Constant and Hubble Law

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Questions and Answers

What does the Hubble parameter represent in the Hubble law?

The age of the universe

The distance between galaxies

The constant of proportionality (correct)

The speed of light

What is the current expression for the Hubble constant?

$H_0 = 100 km s^{-1} Mpc^{-1}$

$H_0 = 200h km s^{-1} Mpc^{-1}$

$H_0 = 100h km s^{-1} Mpc^{-1}$ (correct)

$H_0 = 50h km s^{-1} Mpc^{-1}$

What does the factor of 'h' represent in the context of the Hubble constant?

The number of galaxies measured

The uncertainty in the value (correct)

The age of the universe in billion years

The speed of light in vacuum

Why was there a factor of 2 uncertainty in the Hubble constant as recently as the 1990s?

Errors in measuring distances and speeds of galaxies Signup and view all the answers

What major error did Hubble make in his original measurements?

Overestimating distances to galaxies Signup and view all the answers

Which of the following is NOT a reason for the uncertainty in measuring the Hubble constant?

Precision of cosmological models Signup and view all the answers

How is the Hubble constant expressed in terms of distance?

km s−1 Mpc−1 Signup and view all the answers

Which of the following statements about Hubble's findings is true?

Hubble's value for the constant was too high initially. Signup and view all the answers

What does the Robertson-Walker metric help determine regarding radiation?

The redshift of radiation Signup and view all the answers

In the equation expressed for a light ray traveling radially, what does ds equal for light?

0 Signup and view all the answers

What is the significance of the variables dte and dtr in the equations?

They are negligible time intervals Signup and view all the answers

What does the right-hand side of the expressions in the document equal for overlapping regions?

The integral of c dt over the specified range Signup and view all the answers

Which of the following equations is used to relate time intervals dte and dtr with light speed?

c dte = c dtr Signup and view all the answers

What does the term 'a' typically represent in the context of the Robertson-Walker metric?

The scale factor of the universe Signup and view all the answers

Which part of the equations corresponds to the path taken by light as it travels from one point to another?

dr Signup and view all the answers

What does the integration over time and distance signify in the context of light traveling in the provided equations?

Total distance traveled over time Signup and view all the answers

What is the formula that relates the velocity of a galaxy to its recession and peculiar velocity?

v = H0 r + vpec Signup and view all the answers

At what distance is parallax measurement considered too small to be useful?

1 Mpc Signup and view all the answers

Which of the following objects can be used as standard candles?

Cepheid variable stars Signup and view all the answers

What is the method used to measure absolute distances in cosmology?

Cosmic distance ladder Signup and view all the answers

What does the observed discrepancy in values of the Hubble constant relate to?

The Hubble tension Signup and view all the answers

What approximate value is often obtained for the Hubble parameter using standard candles?

0.73 ± 0.02 Signup and view all the answers

What does the equation $ t_0 ext{ } hicksim ext{ } \frac{1}{H_0} $ estimate?

The age of the universe Signup and view all the answers

Which factor is NOT a common method for measuring distances to galaxies?

Gravitational lensing Signup and view all the answers

What is the significance of the equation $H^2 = H_0^2 \Omega_{r,0} (1 + z)^4 + \Omega_{m,0} (1 + z)^3 + \Omega_{k,0} (1 + z)^2 + \Omega_{\Lambda,0}$?

It describes the relationship between different components of the universe's density. Signup and view all the answers

In the context of a flat universe with a cosmological constant, what can be inferred about its age compared to a matter-dominated flat universe?

It is always older than the matter-dominated flat universe. Signup and view all the answers

When considering redshift, how is redshift defined mathematically?

Redshift is defined as $z = a_0/a - 1$. Signup and view all the answers

What is the implication of a non-zero cosmological constant on the expansion rate of the universe?

It increases the expansion rate at late times. Signup and view all the answers

How is the age of the universe denoted in the equations provided?

As $t_0$. Signup and view all the answers

What determines the numerical solutions for the age of the Universe?

The curvature of the universe and the cosmological constant. Signup and view all the answers

In which scenario is a matter-dominated open universe older?

When compared to a matter-dominated closed universe. Signup and view all the answers

What does the equation $t_0 = - \int_0^{\infty} \frac{dz}{(z + 1)H(z)}$ represent?

The age of the universe as a function of redshift. Signup and view all the answers

What does the luminosity distance, $d_{lum}$, assume about the flux of photons?

It follows the inverse square law. Signup and view all the answers

In the equation $d_{lum} = r_0 (1 + z)$, what does the term $(1 + z)$ represent?

The effect of redshift on the observed luminosity. Signup and view all the answers

How does redshift affect the energy of each photon according to the content?

The energy decreases as distance increases. Signup and view all the answers

According to the model, what happens to the flux of photons received as redshift increases?

It decreases by a factor of $(1 + z)$. Signup and view all the answers

For objects where $z ilde 1$, how does $d_{lum}$ compare to $d_p$?

The luminosity distance is approximately equal. Signup and view all the answers

In a flat universe ($k = 0$), how is the relationship between $d_{lum}$ and $d_p$ expressed?

$d_{lum} = d_p (1 + z)$ Signup and view all the answers

In a closed universe ($k > 0$), how is $r_0$ related to $d_p$?

$r_0 = ext{sin}(k d_p)$ Signup and view all the answers

What is the overall effect of redshift on the apparent luminosity of distant objects?

It reduces the apparent luminosity. Signup and view all the answers

What does the luminosity distance help to measure?

Cosmological parameters using standard candles Signup and view all the answers

How is the angular diameter distance defined?

Distance an object of known physical extent appears to be Signup and view all the answers

In the equation for angular diameter distance, which variable represents the angle subtended by the object?

dθ Signup and view all the answers

For nearby objects where $z acksim 1$, what is the approximate relationship between the angular diameter distance and dp?

ddiam ≈ dp Signup and view all the answers

What is required for determining the angular diameter distance in the context of standard rulers?

Knowledge of the object's physical extent Signup and view all the answers

Which object is commonly used as a standard candle to provide evidence for dark energy?

Type 1a supernovae Signup and view all the answers

In a flat universe, what does the equation $ddiam \approx dp$ imply about angular diameter distance?

It reflects the true distance for nearby objects Signup and view all the answers

What is a limitation mentioned regarding standard rulers in the universe?

They exhibit the same physical extent across all z Signup and view all the answers

Study Notes

Cosmology - Introduction

Hubble Parameter: Represents the expansion rate of the universe, a time-dependent constant. Its current value (H₀) is typically expressed as 100h km/s/Mpc, where 'h' represents uncertainty.
Hubble Law: States that the recessional velocity (v) of a galaxy is proportional to its distance (r) from us: v = Hr.
Rough Age Estimate: A simplified calculation of the universe's age (t₀) using the Hubble law and the present-day expansion rate (H₀): t₀ ≈ 1/H₀. This estimate is approximate and ignores changing expansion rates.
Observing Limits on Age: Estimating universe's age using various data from: geological data (Earth's age ~ 5 Gyr), decay of uranium isotopes (Milky Way age ~ 7 Gyr), cooling of white dwarfs (~10 Gyr), and globular cluster observations (~10 Gyr).
Accurate Age Calculation: Calculates a more precise age (t₀) incorporating mathematical details of the universe's properties, accounting for the expansion rate at different epochs and the universe's composition. The exact equation involves integrating a function involving the expansion history.

Light Travel and Horizons

Robertson-Walker Metric: A fundamental quantity in general relativity that describes the geometry of spacetime and is used in cosmological calculations.
Red Shift Revisited: Calculations showing how expansion modifies the perception of the wavelength of light from distant objects. It involves concepts like comoving coordinates and relating rates of change of coordinates.
Cosmological Horizon Distance: The maximum distance that light (or any signal) could have traveled since the Big Bang, accounting for the expansion of the universe.
Cosmological Event Horizon: The boundary beyond which objects are too far away for light emitted to ever reach us, accounting for the ongoing expansion of the universe. It's a theoretical concept that changes with time.

Distances

Proper Distance: The spatial distance between two objects at a specific moment in time. Accounts for the expansion effect and involves integration.
Luminosity Distance: Measures an object's apparent distance based on its luminosity and received flux, taking into account how the expansion of space affects the perceived light intensity. It's important for cosmological studies because it factors in the universe's expansion.
Angular Diameter Distance: How the physical size of an object in the universe appears to us, accounting for its redshift and the expansion history of the universe.

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Description

This quiz explores key concepts related to the Hubble constant, its significance in the Hubble law, and historical context regarding its measurements. Test your understanding of the factors influencing its value and the scientific principles underlying cosmological observations.