Universe
Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
bartleby

Concept explainers

Question
Book Icon
Chapter 25, Problem 53Q

(a)

To determine

The value of qz at z=0.5, if the value of the deceleration parameter varies with time. It is given that the formula for the deceleration parameter at a redshift, z, for a flat universe, is qz=1232[ΩΛΩΛ+(1ΩΛ)(1+z)3]. Here, ΩΛ is the dark energy density parameter. Use the value of ΩΛ from table 25-2.

(a)

Expert Solution
Check Mark

Answer to Problem 53Q

Solution:

0.22

Explanation of Solution

Given data:

The value of the redshift is 0.5.

Using table 25-2, the value of ΩΛ is found to be 0.76.

The formula for the deceleration parameter at redshift z is qz=1232[ΩΛΩΛ+(1ΩΛ)(1+z)3].

Formula used:

The given formula is written as,

qz=1232[ΩΛΩΛ+(1ΩΛ)(1+z)3]

Here, ΩΛ is the dark energy density parameter and qz is the deceleration parameter at the redshift, z.

Explanation:

Recall the provided formula.

qz=1232[ΩΛΩΛ+(1ΩΛ)(1+z)3]

Substitute 0.5 for z and 0.76 for ΩΛ.

qz=1232[.76.76+(1.76)(1+.5)3]=1232[.761.57]=0.50.7261=0.22

Conclusion:

Therefore, the value of qz is 0.22.

(b)

To determine

The value of qz at z=1, if the value of the deceleration parameter varies with time. It is given that the formula for the deceleration parameter at the redshift, z, for a flat universe, is qz=1232[ΩΛΩΛ+(1ΩΛ)(1+z)3]. Here, ΩΛ is the dark energy density parameter. Use the value of ΩΛ from table 25-2.

(b)

Expert Solution
Check Mark

Answer to Problem 53Q

Solution:

0.074

Explanation of Solution

Given data:

The value of the redshift is 1.

Using table 25-2, the value of ΩΛ is found to be 0.76.

Formula used:

The provided formula is written as:

qz=1232[ΩΛΩΛ+(1ΩΛ)(1+z)3]

Here, ΩΛ is the dark energy density parameter and qz is the deceleration parameter at the redshift, z.

Explanation:

Recall the provided formula.

qz=1232[ΩΛΩΛ+(1ΩΛ)(1+z)3]

Substitute 1 for z and 0.76 for ΩΛ.

qz=1232[.76.76+(1.76)(1+1)3]=1232[.762.68]=0.50.4253=0.074

Conclusion:

Therefore, the value of qz is 0.074.

(c)

To determine

An explanation for the result that shows that the expansion of the universe was decreasing at z=1. The expansion of the universe has changed from deceleration to acceleration between z=1 and z=0.5. It is given that the formula for the deceleration parameter at the redshift, z for a flat universe, is qz=1232[ΩΛΩΛ+(1ΩΛ)(1+z)3]. Here, ΩΛ is the dark energy density parameter.

(c)

Expert Solution
Check Mark

Explanation of Solution

Given data:

The values of the redshift are 1 and 0.5.

Using table 25-2, the value of ΩΛ is found to be 0.76.

Formula used:

The provided formula is written as:

qz=1232[ΩΛΩΛ+(1ΩΛ)(1+z)3]

Here, ΩΛ is the dark energy density parameter and qz is the deceleration parameter at the redshift, z.

Explanation:

The value of qz at z=.5 is 0.22, which is calculated in part (a) and value of qz at z=1 is 0.074, which is calculated in part (b). From this, it can be seen that the value at redshift .5 is negative and at redshift 1 is positive.

A positive value of qz indicates that the expansion of the universe is decelerated, which is at redshift 1. On the other hand, the value qz is negative at redshift 0.5, so the expansion of the universe is accelerated. So, it can be said that the universe must have accelerated between the redshifts, 1 and 0.5.

Conclusion:

Therefore, the universe accelerated between redshift 1 and 0.5.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Name: 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.
At time t=0s, there are No unstable pions. What fraction of pions decay after travelling a distance of 25 m? Assume the pions travelling at 0.86c and their average lifetime is 20.0 ns. Select the correct answer choice: (a) 85.9% (b) 91.6% (c) 99.2% (d) 89.2%
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
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Text book image
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning