User interface language: English | Español

Date May 2017 Marks available 2 Reference code 17M.3.HL.TZ1.17
Level Higher level Paper Paper 3 Time zone Time zone 1
Command term Calculate Question number 17 Adapted from N/A

Question

Recent evidence from the Planck observatory suggests that the matter density of the universe is ρm = 0.32 ρc, where ρc ≈ 10–26 kg\(\,\)m–3 is the critical density.

The graph shows the variation with time t of the cosmic scale factor R in the flat model of the universe in which dark energy is ignored.

M17/4/PHYSI/HP3/ENG/TZ1/17.a

On the axes above draw a graph to show the variation of R with time, when dark energy is present.

[1]
a.

The density of the observable matter in the universe is only 0.05 ρc. Suggest how the remaining 0.27 ρc is accounted for.

[1]
b.i.

The density of dark energy is ρΛc2 where ρΛ = ρc – ρm. Calculate the amount of dark energy in 1 m3 of space.

[2]
b.ii.

Markscheme

curve starting earlier, touching at now and going off to infinity

[1 mark]

a.

there is dark matter that does not radiate / cannot be observed

 

Unexplained mention of "dark matter" is not sufficient for the mark.

[1 mark]

b.i.

ρΛ = 0.68ρc = 0.68 × 10−26 «kgm−3»

energy in 1 m3 is therefore 0.68 × 10−26 × 9 × 1016 ≈ 6 × 10−10 «J»

[2 marks]

b.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Additional higher level option topics) » D.5 – Further cosmology (HL only)
Show 22 related questions

View options