Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 25, Problem 52Q
To determine

(a)

The proof that in the absence of a cosmological constant, the expansion of the universe must slow down.

Expert Solution
Check Mark

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 q0 is used to check whether the expansion of the universe is accelerating or decelerating.

The expansion of the universe is decelerating when q0 has a positive value, the expansion of the universe is accelerating when q0 has a negative value and the expansion rate is constant for q0=0.

Formula Used:

The expression for the deceleration parameter is given by,

q0=12Ω032ΩA

Here, Ω0 is the density parameter and ΩA is the dark energy density parameter.

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 Ω0=1.

The deceleration parameter is calculated as,

q0=12Ω032ΩA=12(1)32(0)=0.5

Since q0 has a positive value, the universe expansion is slowing down.

Conclusion:

Therefore, it is proved that the universe expansion is slowing down in the absence of a cosmological constant.

To determine

(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.

Expert Solution
Check Mark

Answer to Problem 52Q

The value of the deceleration parameter for the universe at present is 0.64, and thus, the universe expansion is speeding up.

Explanation of Solution

Given:

Consider table 25-2 of the book “Universe, Stars and Galaxies 6th Edition”.

The matter density parameter is, Ωm=0.24.

The dark energy density parameter is, ΩA=0.76.

Formula Used:

The density parameter is given by,

Ω0=Ωm+ΩA

The expression for the deceleration parameter is given by,

q0=12(Ωm+ΩA)32ΩA

Here, Ωm is the matter density matter.

Calculation:

The deceleration parameter is calculated as,

q0=12(Ωm+ΩA)32ΩA=12(0.24+0.76)32(0.76)=0.64

Since q0 has a negative value, the universe expansion is .speeding up.

Conclusion:

The value of the deceleration parameter for the universe at present is 0.64, and thus, the universe expansion is speeding up.

To determine

(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.

Expert Solution
Check Mark

Answer to Problem 52Q

The value of the dark energy density parameter is 0.12 and the matter will be dominant in such a universe.

Explanation of Solution

Given:

Consider table 25-2 of the book “Universe, Stars and Galaxies 6th Edition”.

The matter density parameter is, Ωm=0.24.

The other universe is expanding at a constant rate; that is, q0=0.

Formula Used:

The density parameter is given by,

Ω0=Ωm+ΩA

The expression for the deceleration parameter is given by,

q0=12(Ωm+ΩA)32ΩA

Calculation:

The deceleration parameter is calculated as,

q0=12(Ωm+ΩA)32ΩA0=12(0.24+ΩA)32(ΩA)0=0.12ΩAΩA=0.12

Conclusion:

The value of the dark energy density parameter is 0.12 and the matter will be dominant in such a universe.

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