2018년 11월 13일 화요일

HQ3. 숙제 3(Homework Question 3)

[에드엑스 강좌] ANUx -ASTRO4x Cosmology (우주론)

제1부. (요약)공간과 시간(Space and Time)
제2부. (요약)우리 우주의 역학과 기하학(Geometry and Dynamics of our universe)
제3부. 인플레이션(Inflation)
    V3.1 세가지 수수께끼(Three Mystery)
    V3.2 단순성 과 대칭성(Simplicity and Symmetry)
    V3.3 인플레이션(Inflation)
    V3.4 수수께끼의 답 찾기(Solving the Mysteries)
    V3.5 인플레이션의 끝(End of Inflation)
    V3.5b 연대기(Timescales)
    V3.6 로렌스 크라우스와 인터뷰(Lawrence Krauss) #1
    V3.7 로렌스 크라우스와 인터뷰(Lawrence Krauss) #2
    V3.8 로렌스 크라우스와 인터뷰(Lawrence Krauss) #3
    PQ3. 연습문제 3(Practice Question 3)

HQ3. 숙제 3(Homework Question 3)

[HQ3.1] ------------------------------------------------------------

Inflation theory predicts that even the most distant observable parts of the universe should have very similar properties.

Why? Pick one of the answers below which is a crucial part of this explanation. (Note, you only have three submissions)

a] Because of the exponential growth in the size of the universe
b) Because of spontaneous symmetry breaking
c) Because of the Higgs field
d) Because of the unification of the forces of nature
e) Because of the amplification of quantum mechanical fluctuations

Explanation

The exponential growth means that the entire observable universe was once in contact,and hence could even out its properties.

[HQ3.2] ------------------------------------------------------------
Which of the curves in the diagram below would lead to inflation, spontaneous symmetry breaking, and potentially a universe like our own?


Potential curves. A is an inverted mexican hat. B is a mexican hat with a dimple on top. C is a U shaped curve. D is mexican hat shape but asymmetrical, so that one side is lower than the other. E is a flat-bottomed U-shaped curve with a second smaller dip right in the centre of the flat bottom.

Select one answer
a) A
b) B
c) C
d) D
e) E
f] None of the curves correct

Explanation

The curve must be symmetrical (otherwise there would be no symmetry breaking). It must have a flat-topped bump in the middle for the universe to get temporarily stuck on - but nothing that would trap the universe longer term, or inflation would not end and produce a universe like our own.

[HQ3.3] ------------------------------------------------------------
False vacuum has an immense energy density and hence mass. You might therefore think that its gravity would pull the universe back, instead of making it expand exponentially.

Why then does this immense mass cause the universe to grow?

a) Because its huge pressure is enough to overcome the gravity and force an expansion.
b) Because it has negative pressure, which sucks the universe outwards.
c] Because the huge mass causes the gravitational energy to become more and more negative.
d) Because it amplifies quantum-mechanical fluctuations up to galaxy cluster scales.
e) Because the uniformity of the universe means that the gravity pulls outwards, not backwards.

Explanation

The Friedmann equation is an energy conservation one - the more negative the potential energy, the more positive the kinetic energy and hence the faster the expansion. The pressure has no net effect, as it is the same in all directions and hence perfectly balanced (only a pressure gradient can cause acceleration). Similarly, because the universe is so uniform, there is no net force from gravity - forces balance in all directions and hence cause no acceleration.

[HQ3.4] ------------------------------------------------------------
How does the theory of inflation explain the observed fact that our universe has a geometry that is close to being flat?

Select one answer?

a) Because curved regions of space-time have a larger effective density of false vacuum and hence will expand more rapidly.
b) Because the universe can only roll off the top of the mexican hat and hence stop inflation if its geometry is locally flat.
c) Because strongly curved regions will not last long enough for life to evolve
d] Because any smooth curved shape, if enlarged enough, will look flat locally.
e) Because if space was curved, regions of space with different laws of physics would collide, which is not observed.

Explanation

Take any smooth curved shape, and if you make it big enough, it will look flat.

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