University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Chapter 44, Problem 44.13DQ
To determine
To explain: Why the cosmological principle requires that
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Explain why the cosmological principle requires that H0 must have the same value everywhere in space, but does not require that it be constant in time.
a)Define the term “standard candle” as used in cosmology.
b)The flux is defined asf(Dlum) = L/4πD^2lumwhere L is the absolute luminosity and Dlum is the distance to the radiation source (youmay assume z ≪ 1).Assume that we have measured the flux to be f = 7.234 10^−23 Wm^−2 and the absoluteluminosity is given by L = 3.828 x10^26W. Calculate the luminosity distance D lum to the objectin Mpc.
Consider a cosmological spacetime in which the line element is given by
ds? = a²(t)(-dt + dr² + dy² + dz²),
where a(t) > 0 is the scale factor. Two light rays tangent to l = (1,1,0, 0)
and l = (1,0, 1,0) are received at time t =
u" = (a-'(to), 0, 0, 0). Compute the observed angle between the correspond-
ing images.
to by someone with 4-velocity
Chapter 44 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 44.1 - Each of the following particles can be exchanged...Ch. 44.2 - Prob. 44.2TYUCh. 44.3 - From conservation of energy, a particle of mass m...Ch. 44.4 - Prob. 44.4TYUCh. 44.5 - Prob. 44.5TYUCh. 44.6 - Is it accurate to say that your body is made of...Ch. 44.7 - Prob. 44.7TYUCh. 44 - Prob. 44.1DQCh. 44 - Prob. 44.2DQCh. 44 - When they were first discovered during the 1930s...
Ch. 44 - The gravitational force between two electrons is...Ch. 44 - Prob. 44.5DQCh. 44 - Prob. 44.6DQCh. 44 - Prob. 44.7DQCh. 44 - Prob. 44.8DQCh. 44 - Prob. 44.9DQCh. 44 - Does the universe have a center? Explain.Ch. 44 - Prob. 44.11DQCh. 44 - Prob. 44.12DQCh. 44 - Prob. 44.13DQCh. 44 - Prob. 44.1ECh. 44 - Prob. 44.2ECh. 44 - Prob. 44.3ECh. 44 - Prob. 44.4ECh. 44 - Prob. 44.5ECh. 44 - Prob. 44.6ECh. 44 - Prob. 44.7ECh. 44 - An electron with a total energy of 30.0 GeV...Ch. 44 - Deuterons in a cyclotron travel in a circle with...Ch. 44 - The magnetic field in a cyclotron that accelerates...Ch. 44 - Prob. 44.11ECh. 44 - Prob. 44.12ECh. 44 - Prob. 44.13ECh. 44 - Prob. 44.14ECh. 44 - Prob. 44.15ECh. 44 - Prob. 44.16ECh. 44 - Prob. 44.17ECh. 44 - Prob. 44.18ECh. 44 - What is the mass (in kg) of the Z0? What is the...Ch. 44 - Prob. 44.20ECh. 44 - Prob. 44.21ECh. 44 - Prob. 44.22ECh. 44 - Prob. 44.23ECh. 44 - Prob. 44.24ECh. 44 - Prob. 44.25ECh. 44 - Prob. 44.26ECh. 44 - Prob. 44.27ECh. 44 - Prob. 44.28ECh. 44 - Prob. 44.29ECh. 44 - Prob. 44.30ECh. 44 - Prob. 44.31ECh. 44 - Prob. 44.32ECh. 44 - Prob. 44.33ECh. 44 - Prob. 44.34ECh. 44 - Prob. 44.35ECh. 44 - Prob. 44.36ECh. 44 - Prob. 44.37ECh. 44 - Prob. 44.38ECh. 44 - Prob. 44.39PCh. 44 - Prob. 44.40PCh. 44 - Prob. 44.41PCh. 44 - Prob. 44.42PCh. 44 - Prob. 44.43PCh. 44 - Prob. 44.44PCh. 44 - Prob. 44.45PCh. 44 - Prob. 44.46PCh. 44 - Prob. 44.47PCh. 44 - Prob. 44.48PCh. 44 - Prob. 44.49PCh. 44 - Prob. 44.50PCh. 44 - Prob. 44.51PCh. 44 - The K0 meson has rest energy 497.7 MeV. A K0 meson...Ch. 44 - DATA While tuning up a medical cyclotron for use...Ch. 44 - Prob. 44.54PCh. 44 - Prob. 44.55PCh. 44 - Consider a collision in which a stationary...Ch. 44 - Prob. 44.57PPCh. 44 - Prob. 44.58PPCh. 44 - Prob. 44.59PP
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- What are the basic observations about the universe that any theory of cosmology must explain?arrow_forwardThe average lifetime of a pi meson in its own frame of reference is 2.6 × 10−8 s. If the meson moves with a speed of 0.95c, what is (a) its mean lifetime as measured by an observer on Earth and (b) the average distance it travels before decaying, as measured by an observer on Earth?arrow_forwardConsider a cosmological spacetime in which the line element is given by ds? = a°(t)(-dt + da² + dy° + dz?), where a(t) > 0 is the scale factor. Two light rays tangent to l4 = (1, 1, 0,0) and = (1,0, 1,0) are received at time t = to by someone with 4-velocity u" = (a-'(to), 0, 0, 0). Compute the observed angle between the correspond- ing images.arrow_forward
- Consider the following line element, ds^2 = −dt^2 + a^2(t) (dx^2 + dy^2) + b^2(t) dz^2, where a(t) and b(t) are distinct functions. State whether or not this line element obeys the Cosmological Principle, if applied to describe the universe on large scales. Justify your answer.arrow_forwarda) Define the term “standard candle” as used in cosmology b). The flux is defined as f(Dlum) = L /4πD2lum , where L is the absolute luminosity and Dlum is the distance to the radiation source (you may assume z ≪ 1). Assume that we have measured the flux to be f = 7.234 10−23Wm−2 and the absolute luminosity is given by L = 3.828 1026W. Calculate the luminosity distance Dlum to the object in Mpc. c). Calculate the distance modulus µ for the object of the previous subquestion. Show that the distance modulus µ can be written as given in imagearrow_forwardQuestion A7 Consider the following line element, ds² = - dt² + a² (t) (da² + dy²) + b² (t) dz², where a(t) and b(t) are distinct functions. State whether or not this line element obeys the Cosmological Principle, if applied to describe the universe on large scales. Justify your answer.arrow_forward
- What mechanism can simultaneously solve both the flatness and horizon problems in cosmology?arrow_forwarda) Briefly explain what is meant by "particle horizon" and "event horizon" in cosmology. b) Calculate the physical particle horizon, RH (t), at time t. Assume a flat FRW universe which is dominated by a fluid that gives rise to scale factor evolution a(t) = ao ()*, to where n is a constant with 0arrow_forwardThis a question on Cosmology: Suppose that you have a flat universe that has matter and dark energy with wd = -2/3 & Ωd,0 =0.7 At the time when light with z = 1 was emitted from a distant galaxy what was the ratio Ɛd /Ɛm ?arrow_forwardName: Hubble Distances Redshift z parameter The relativistic redshift is parametrized by z and given by Δ In terms of the scale factor, 2= X do - de de 1+z= ao a (2) Problem 01. Find the redshift z for a Hydrogen spectral line originally at 656 nm which has been observed at a wavelength of 1.64 μm. Astro 001 Fall 2022 Problem 02. How much smaller was the universe when this light was emitted? U₁ = DHO Using the redshift to measure the velocity, we find D~ (1) 0.1 Hubble's Law Hubble's Law states that the recession velocity of a redshifted galaxy is given by the product of the distance and the Hubble constant. (3) ZC Ho where c = 3 x 108 m/s and Ho = 2.3 x 10-18 s in standard units. The standard measurement of the Hubble constant is Ho = 71 (km/s)/Mpc. Problem 03. What is the distance in Mpc and ly to the galaxy measured in problem 01? 1 pc = 3.26 ly.arrow_forwardAssume a flat Friedmann-Robertson-Walker universe, and that the density parameters for matter,radiation, and the cosmological constant are given today by Ωm,0 = 0.4, Ωrad,0 = 0.01, and ΩΛ,0 =0.59, respectively.a) Calculate the redshifts for matter-radiation and matter-dark energy equality. b) State what effect the lower ratio of ΩΛ,0/Ωm,0, compared to the standard Λ-CDM cosmology,has on structure formation.arrow_forward(a) Calculate the approximate age of the universe from the average value of the Hubble constant, H0 = 20km/s ⋅ Mly . To do this, calculate the time it would take to travel 1 Mly at a constant expansion rate of 20 km/s. (b) If deceleration is taken into account, would the actual age of the universe be greater or less than that found here? Explain.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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