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
- Suppose that the universe were full of spherical objects, each of mass m and radius r, with the objects distributed uniformly throughout the universe as in the previous problem. (Assume nonrelativistic objects.) Given the density of these spherical objects (as you would have found in the previous problem), how far would you be able to see in meters, on average, before your line of sight intersected one of them? Values (note, different from the above problem): m = 3 kg r = 0.03 m Answer must be in scientific notation and include zero decimal places (1 sig fig).arrow_forwardIf some unknown cause of red shift—such as light becoming “tired” from traveling long distances through empty space—isdiscovered, what effect would there be on cosmology?arrow_forwardIf the average density of the Universe is small compared with the critical density, the expansion of the Universe described by Hubble's law proceeds with speeds that are nearly constant over time. Calculate t since the big bang, assuming H = 22.0 km/s/Mly.arrow_forward
- According to thermodynamic equilibrium, which should be the most abundant and least abundant quarks during the period from 10-13 s to 10 -3 s?arrow_forwardThe critical mass density needed to just halt the expansion of the universe is approximately 10-26 kg/m3. Convert this to eV/c2.m3 .arrow_forwardBecause of the cosmological expansion, a particular emission from a distant galaxy has a wavelength that is 2.00 times the wavelength that emission would have in a laboratory. Assuming that Hubble’s law holds and that we can apply Doppler-shift calculations, what was the distance (ly) to that galaxy when the light was emitted?arrow_forward
- Suppose the Universe is dominated by a strange substance with an equation of state w = -0.7. This substance fills the Universe in a uniform way, and is the only dynamically important constituent. Suppose further that in some time interval the Universe doubles in (linear) size, i.e. the scale factor doubles. By what factor has the energy density of this substance changed during this time interval, i.e., what is εfinal/εinitial? The energy density substance dilutes in proportion to a to some power p, i.e. ε(a) ∝ aparrow_forwardSome of the familiar hydrogen lines appear in the spectrum of quasar 3C9, but they are shifted so far toward the red that their wavelengths are observed to be 3.0 times as long as those observed for hydrogen atoms at rest in the laboratory. (a) Show that the classical Doppler equation gives a relative velocity of recession greater than c for this situation. (b) Assuming that the relative motion of 3C9 and Earth is due entirely to the cosmological expansion of the universe, find the recession speed that is predicted by the relativistic Doppler equation.arrow_forwardAn electron jumps from n=3 to n=2 in a hydrogen atom in a distant galaxy, emitting light. If we detect that light at a wavelength of 3.00 mm, by what multiplication factor has the wavelength, and thus the universe, expanded since the light was emitted?arrow_forward
- Assume the average density of the Universe is equal to the critical density. (a) Prove that the age of the Universe is given by 2/(3H). (b) Calculate 2/(3H) and express it in years.arrow_forwardThe Klein-Gordon equation at background level for a scalar field φ is given by (found in image below) where H is the Hubble parameter, V the potential of the scalar field, and V′ = dV/dφ.Assume a flat Friedmann-Robertson-Walker universe, dominated by the scalar field.i) State the conditions for slow-roll inflation. Write down the Friedmann equation and theKlein-Gordon equation valid for slow-roll inflation.ii) For a scalar field potential V =1/2m^2φ^2, where m is the mass of the field, calculate thetime evolution of the field φ in the case of slow-roll inflation.arrow_forwardWhat two major limitations prevent us from building high-energy accelerators that are physically small?arrow_forward
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
- Stars and Galaxies (MindTap Course List)PhysicsISBN:9781337399944Author:Michael A. SeedsPublisher:Cengage LearningFoundations of Astronomy (MindTap Course List)PhysicsISBN:9781337399920Author:Michael A. Seeds, Dana BackmanPublisher:Cengage Learning