Concept explainers
(a)
The proof that in the absence of a cosmological constant, the expansion of the universe must slow down.
Answer to Problem 52Q
The proof that the expansion of the universe must slow down in the absence of a cosmological constant is as stated below.
Explanation of Solution
Given:
The deceleration parameter
The expansion of the universe is decelerating when
Formula Used:
The expression for the deceleration parameter is given by,
Here,
Calculation:
For the case when there is no cosmological constant, the dark energy density parameter is zero.
Consider table 25-2 of the book “Universe, Stars and Galaxies 6th Edition”. The density parameter is
The deceleration parameter is calculated as,
Since
Conclusion:
Therefore, it is proved that the universe expansion is slowing down in the absence of a cosmological constant.
(b)
The value of the deceleration parameter for the universe at present and to check whether the universe expansion is speeding up or slowing down.
Answer to Problem 52Q
The value of the deceleration parameter for the universe at present is
Explanation of Solution
Given:
Consider table 25-2 of the book “Universe, Stars and Galaxies 6th Edition”.
The matter density parameter is,
The dark energy density parameter is,
Formula Used:
The density parameter is given by,
The expression for the deceleration parameter is given by,
Here,
Calculation:
The deceleration parameter is calculated as,
Since
Conclusion:
The value of the deceleration parameter for the universe at present is
(c)
The value of dark energy density parameter for a universe that has the same value of matter density parameter as our universe but the expansion of the universe is neither speeding up nor slowing down and to check whether matter or dark energy will be dominant in such a universe.
Answer to Problem 52Q
The value of the dark energy density parameter is
Explanation of Solution
Given:
Consider table 25-2 of the book “Universe, Stars and Galaxies 6th Edition”.
The matter density parameter is,
The other universe is expanding at a constant rate; that is,
Formula Used:
The density parameter is given by,
The expression for the deceleration parameter is given by,
Calculation:
The deceleration parameter is calculated as,
Conclusion:
The value of the dark energy density parameter is
Want to see more full solutions like this?
Chapter 25 Solutions
Universe: Stars And Galaxies
- 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_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_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_forward
- Edwin Hubble observed that the light from very distant galaxies was redshifted and that the farther away a galaxy was, the greater its redshift. What does this say about very distant galaxies? When Hubble first estimated the Hubble constant, galaxy distances were still very uncertain, and he got a value for H of about 600 km/s per Mpc. What would this have implied about the age of the universe? What problems would this have presented for cosmologists?arrow_forwardSuppose that the universe were full of spherical objects, each of mass m and radius r . If the objects were distributed uniformly throughout the universe, what number density (#/m3) of spherical objects would be required to make the density equal to the critical density of our Universe? Values: m = 4 kg r = 0.0407 m Answer must be in scientific notation and include zero decimal places (1 sig fig --- e.g., 1234 should be written as 1*10^3)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
- What mechanism can simultaneously solve both the flatness and horizon problems in cosmology?arrow_forwardThe visible section of the Universe is a sphere centered on the bridge of your nose, with radius 13.7 billion light-years. (a) Explain why the visible Universe is getting larger, with its radius increasing by one light-year in every year. (b) Find the rate at which the volume of the visible section of the Universe is increasing.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_forwardThe expanding universe is carrying distant objects away from each other at a rate proportional to their separations. We use the Doppler effect observed in spectra of distant galaxies and quasars to calculate recession speeds. For the most distant objects recession speeds approach c, and therefore, the relativistic Doppler shift expression must be used. We define the redshift, z, as the fractional change in wavelength. a) The most distant quasar currently known is ULAS J1120+0641, discovered with the UK Infrared Telescope on Mauna Kea. It has a redshift of 7.1. Calculate its radial velocity in terms of v/c. b) Determine the distance to this quasar. c) At what wavelength would the Ha line (656.28 nm) be observed for this quasar?arrow_forwardThe geometry of spacetime in the Universe on large scales is determined by the mean energy density of the matter in the Universe, ρ. The critical density of the Universe is denoted by ρ0 and can be used to define the parameter Ω0 = ρ/ρ0. Describe the geometry of space when: (i) Ω0 < 1; (ii) Ω0 = 1; (iii) Ω0 > 1. Explain how measurements of the angular sizes of the hot- and cold-spots in the CMB projected on the sky can inform us about the geometry of spacetime in our Universe. What do measurements of these angular sizes by the WMAP and PLANCK satellites tell us about the value of Ω0?arrow_forwardHubble's law can be stated in vector form as v = HR. Outside the local group of galaxies, all objects are moving away from us with velocities proportional to their positions relative to us. In this form, it sounds as if our location in the Universe is specially privileged. Prove that Hubble's law is equally true for an observer elsewhere in the Uni- verse. Proceed as follows. Assume we are at the origin of coordinates, one galaxy cluster is at location R, and has velocity v, = HR relative to us, and another galaxy cluster has position vector R, and velocity v, = HR, Suppose the speeds are nonrelativistic. Consider the frame of reference of an observer in the first of these galaxy clusters. (a) Show that our velocity relative to her, together with the position vector of our galaxy cluster from hers, satisfies Hubble's law. (b) Show that the position and velocity of cluster 2 rel- ative to cluster 1 satisfy Hubble's law.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning