Question 1: Define dark mass and dark energy and explain their significance in cosmology.

Answer: Dark mass refers to unseen matter that exerts gravitational attraction, contributing to the universe's total mass. Dark energy is a mysterious force causing the accelerated expansion of the universe. Both are significant because they make up most of the universe's total energy content and influence its structure and future evolution.

Question 2: Describe how dark energy affects the expansion of the universe.

Answer: Dark energy causes the universe to expand at an accelerating rate by exerting a repulsive force that counteracts gravity.

Question 1: Using the critical density formula: ρ_c = 3H² / 8πG, where H = 70 km/s/Mpc, calculate the critical density ρ_c in kg/m³. (G = 6.674×10⁻¹¹ Nm²/kg²).

Answer: Convert H to SI units: 70 km/s/Mpc = (70,000 m/s) / (3.086×10²² m) = 2.268×10⁻¹⁸ s⁻¹. Then, ρ_c = (3 × (2.268×10⁻¹⁸)²) / (8π × 6.674×10⁻¹¹) ≈ 8.5×10⁻²⁷ kg/m³.

Question 2: If the current density of dark energy is approximately 70% of the critical density, estimate the mass of dark energy contained within a sphere of radius 1×10²⁶ meters (roughly the size of the observable universe).

Answer: Dark energy density: ρ_de ≈ 0.7 × 8.5×10⁻²⁷ kg/m³ = 5.95×10⁻²⁷ kg/m³. Volume of sphere: V = (4/3)πr³ ≈ 4.19×10⁷⁹ m³. Total mass: M = ρ_de × V ≈ 2.5×10⁵³ kg.

Question 1: Describe an experimental approach that could be used to detect the effects of dark energy on the expansion rate of the universe.

Answer: One approach is to observe distant supernovae and measure their redshifts and brightness. By comparing these observations over time, scientists can determine if the universe's expansion is accelerating, providing indirect evidence of dark energy's effect.

Question 2: Identify two variables that must be controlled in experiments measuring cosmic expansion and explain why.

Answer: Variables such as the distance measurement accuracy and calibration of instruments must be controlled to ensure precise and reliable data on expansion rates.

Question 1: A survey of distant supernovae shows that their observed brightness is lower than expected based on models without dark energy. Explain what this implies about the expansion of the universe.

Answer: This suggests that the universe's expansion is accelerating, which supports the presence of dark energy causing the accelerated expansion.

Question 1: How does research into dark energy contribute to advancements in astrophysical instruments and technology?

Answer: Research drives the development of more sensitive telescopes, detectors, and data analysis techniques, which also benefit other fields like satellite technology and medical imaging.

Question 2: Discuss a potential technological challenge when designing experiments to measure dark energy effects.

Answer: One challenge is achieving the required precision in distance and redshift measurements over vast cosmic scales, which demands highly sensitive instruments and rigorous calibration to minimise systematic errors.