Cosmology — OCR A-Level Physics

The parsec (pc) is a cosmological distance unit defined using parallax: one parsec is the distance at which one astronomical unit subtends an angle of one arcsecond. It equals about 3.09 × 10¹⁶ m, or about 3.26 light-years. The light-year (ly) is the distance light travels in a vacuum in one year, about 9.46 × 10¹⁵ m. To convert, multiply parsecs by 3.26 to get light-years, or multiply light-years by 0.307 to get parsecs. For example, a star at 10 pc is about 32.6 ly away, or about 3.09 × 10¹⁷ m. Parsecs are preferred for stellar distances because they connect directly to parallax angle measurements.

The abbreviation (pc) stands for the parsec, the distance unit used throughout OCR A Level Physics A cosmology. One parsec is defined as the distance at which one astronomical unit subtends an angle of one second of arc, so 1 pc ≈ 3.09 × 10¹⁶ m, about 3.26 light-years. Because the definition is built from a parallax angle, the parsec links directly to stellar parallax and to the equation d = 1/p. In multiple-choice questions you may be asked to identify the parsec from its definition, to convert between parsecs, metres and light-years, or to choose the correct order of magnitude for a stellar or galactic distance. Always check whether the value given is in pc, kpc or Mpc before selecting an answer.

Stellar parallax is the apparent shift in a nearby star's position against more distant background stars as the Earth moves from one side of its orbit to the other. The parallax angle p is half the total angular shift measured over six months, with the baseline equal to 1 astronomical unit. The effect is tiny: even the nearest stars have parallaxes below one second of arc, which is why space missions are needed for accurate measurement. In multiple-choice questions you may be asked to identify the baseline, the definition of the parallax angle, why the measurement is taken six months apart, or why the method fails for very distant stars.

The equation d = 1/p gives the distance d in parsecs to a star when its parallax p is measured in seconds of arc. The relationship is inverse: a larger parallax means a nearer star, and a smaller parallax means a more distant star. For example, a star with p = 0.1″ lies at d = 1/0.1 = 10 pc, while Proxima Centauri with p ≈ 0.77″ lies at about 1.3 pc. In multiple-choice questions you may be asked to calculate d from p, to find p from d, to convert the result to metres or light-years, or to recognise that the equation only works when p is in seconds of arc.

The Cosmological principle states that, on sufficiently large scales, the universe is homogeneous and isotropic, and that the laws of physics are universal. Homogeneous means the distribution of matter and energy is the same everywhere, so no location is special. Isotropic means the universe looks the same in every direction from any observation point. Universal laws mean the same physical principles apply throughout space and time, allowing astronomers to interpret distant spectra and light curves using laboratory physics. In multiple-choice questions you may be asked to distinguish homogeneity from isotropy, to identify evidence such as the smooth cosmic microwave background, or to explain why the principle underpins cosmological models.

The Doppler effect is the change in observed frequency and wavelength when a source of waves moves relative to an observer. For electromagnetic radiation, a source moving away from the observer has its observed wavelength stretched, producing a red shift; a source moving towards the observer has its wavelength compressed, producing a blue shift. The size of the shift depends on the relative speed along the line of sight. In cosmology, nearly all distant galaxies show red shift, which is evidence that they are receding. You should be able to identify the direction of motion from the sign of the shift and distinguish red shift from blue shift in spectra.

The Doppler equation for electromagnetic radiation relates the fractional change in wavelength or frequency to the relative speed of the source and observer. It is expressed as \(\frac{\Delta \lambda}{\lambda} \approx \frac{\Delta f}{f} \approx \frac{v}{c}\), where \(\Delta \lambda\) is the change in wavelength, \(\lambda\) is the emitted wavelength, \(\Delta f\) is the change in frequency, \(f\) is the emitted frequency, \(v\) is the relative speed along the line of sight, and \(c\) is the speed of light. This approximation is valid for speeds much less than \(c\) (\(v \ll c\)). For a receding source, the observed wavelength increases (red-shift) and frequency decreases. For an approaching source, wavelength decreases (blue-shift) and frequency increases. You must be able to calculate \(v\), \(\Delta \lambda\), or \(\Delta f\) using this relationship.

Hubble’s law states that the recessional speed v of a galaxy is approximately proportional to its distance d from the observer: v ≈ H₀ d, where H₀ is the Hubble constant. The constant has units of s⁻¹, often quoted as km s⁻¹ Mpc⁻¹. The law applies to galaxies that are receding, which is almost all galaxies beyond the Local Group. You should be able to use the equation to find v, d or H₀, and understand that the linear relationship is evidence for an expanding universe. The approximation sign indicates that the relationship is not exact for very large distances or very high speeds.

The model of an expanding universe states that space itself is expanding, causing galaxies to move apart from one another. This is supported by the observation of galactic red shift: light from distant galaxies is shifted towards longer wavelengths, indicating that they are receding. Hubble’s law shows that recessional speed is proportional to distance, which is consistent with a uniform expansion. The red shift is not due to galaxies moving through space but to the expansion of space between them. You should be able to explain how red shift data supports the expanding universe model and distinguish it from alternative explanations.

The Hubble constant H₀ links a galaxy's recession speed v to its distance d through v = H₀d, so H₀ is the gradient of a v–d graph. Its usual unit is km s⁻¹ Mpc⁻¹: a galaxy 1 Mpc away recedes at H₀ km s⁻¹. Because 1 Mpc = 3.09 × 10¹⁹ km, the km cancels when you divide, giving H₀ in s⁻¹. For example, 70 km s⁻¹ Mpc⁻¹ becomes 70 ÷ (3.09 × 10¹⁹) s⁻¹ ≈ 2.3 × 10⁻¹⁸ s⁻¹. The reciprocal 1/H₀ then has units of seconds and gives a rough age of the universe, about 4.4 × 10¹⁷ s or 1.4 × 10¹⁰ years. Always convert megaparsecs to kilometres before dividing, and keep the negative index on s⁻¹.

The Big Bang theory states that the universe began from an extremely hot, dense state about 1.4 × 10¹⁰ years ago and has been expanding and cooling ever since. It is not an explosion of matter into pre-existing space; rather, space-time itself expands, carrying galaxies apart. Evidence includes Hubble's law, the cosmic microwave background radiation at 2.7 K, and the observed abundances of light elements such as hydrogen and helium. A useful check is that the theory predicts a hot, dense early universe, so a faint uniform microwave glow should fill the sky, which is exactly what Penzias and Wilson detected in 1965.

The cosmic microwave background radiation (CMBR) is a faint, almost perfectly uniform microwave signal coming from every direction in space. Its spectrum matches that of a black body at about 2.7 K, which is the cooled remnant of the hot early universe. In the Big Bang model, the young universe was opaque and hot; after about 380 000 years it cooled enough for electrons and protons to combine into hydrogen, so radiation could travel freely. That radiation has since been stretched by the expansion of space-time to microwave wavelengths, giving the 2.7 K temperature today. Penzias and Wilson detected it accidentally in 1965, and it is now mapped in detail by satellites such as COBE and Planck.

In the standard cosmological model, the Big Bang marks the origin of space-time itself, not an explosion of matter inside a pre-existing space. Immediately after the origin, space-time began to expand, and it continues to expand today. Galaxies are not flying through space away from a centre; rather, the space between them stretches, so distant galaxies recede faster, in line with Hubble's law. A useful analogy is a rising raisin cake or a balloon with dots: as the surface stretches, every dot moves away from every other, and no dot is the centre. This expansion also stretches the wavelength of light travelling through space, producing cosmological redshift and cooling the CMBR to 2.7 K.

The Hubble constant H₀ describes how fast the universe expands: recession speed v = H₀d, so H₀ has units of s⁻¹ (km s⁻¹ Mpc⁻¹). If expansion has been roughly uniform, the time since galaxies were coincident is the distance divided by the speed, giving t ≈ H₀⁻¹. This is an estimate, not an exact age, because gravity and dark energy change the expansion rate over time. Worked method: convert H₀ to SI. For H₀ = 70 km s⁻¹ Mpc⁻¹, 1 Mpc = 3.09 × 10²² m, so H₀ = 70 000 m s⁻¹ ÷ 3.09 × 10²² m = 2.27 × 10⁻¹⁸ s⁻¹, and t ≈ 1 ÷ (2.27 × 10⁻¹⁸ s⁻¹) ≈ 4.4 × 10¹⁷ s ≈ 1.4 × 10¹⁰ years.

After the Big Bang the universe expanded and cooled, passing through a sequence of stages. In the first minutes, protons and neutrons formed and fused into light nuclei such as hydrogen, helium and traces of lithium (Big Bang nucleosynthesis). After roughly 380 000 years the universe cooled enough for electrons and nuclei to combine into neutral atoms, so radiation could travel freely; this radiation is now the cosmic microwave background (CMB), cooled to about 2.7 K. Gravity then pulled matter into stars and galaxies, and later expansion accelerated. Evidence for this sequence includes the CMB, the observed abundances of light elements, and the redshifting of distant galaxies.

Current cosmological models describe the universe as dominated by components that cannot be seen directly. Ordinary (baryonic) matter, the atoms of stars, planets and gas, makes up only a small percentage of the total content, roughly 5%. Dark matter, roughly 27%, does not emit or absorb light but exerts gravity; evidence includes galaxy rotation curves and gravitational lensing. Dark energy, roughly 68%, is associated with the accelerating expansion of the universe. These proportions come from combining observations such as the CMB, supernova distances and galaxy surveys, and they remain an active area of research.