History of Astronomy Example Exam Question Hints and Suggestions

Bondi and Gold base their argument explicitly on the argument that observed physics laws have only been tested against the background of the currently observed universe, and that changes in the parameters of the "background" universe, e.g. higher average density, might result in changes in physical constants or laws (e.g. a change in G. Therefore, they argue that the only logically consistent theory of cosmology is one in which the reference universe does not change, i.e. a "Steady State" universe, and they set out to investigate whether such a model is tenable.

[Their exact words are "We do not claim that this principle must be true, but we say that if it does not hold, one's choice of the variability of physical laws becomes so wide that cosmology is no longer a science."]

Hoyle, on the other hand, has a rather more concrete motivation: he points out that, with the then accepted value of H, the universe should be only 1.3 Gyr old, or at least should have been in an ultra-dense state 1.3 Gyr ago, whereas astrophysical arguments suggest that this has not been the case for at least 5 Gyr, and the Earth itself is at least 2 Gyr old. This is an absolutely valid Popperian/Kuhnian motivation for proposing an alternative model: the existing model is falsified by this observation (Popper), or at least is suffering from a serious anomaly (Kuhn).

Therefore, we see that Bondi and Gold do not have any practical objections to the existing Friedmann-Lemaître models - the problem is that they do not believe that we can justify applying the physical laws we observe in our present universe to a universe with very different physical conditions. Hoyle, on the other hand, does raise a practical objection: he notes, correctly, that the then accepted value of the Hubble constant produces too young a universe in the Friedmann-Lemaître models, and he provides reasoned arguments against the use of a cosmological constant to solve the problem. (He does not consider the correct resolution, namely the radical revision of H, but nobody else at the time did either, so that isn't his fault!)

[Hoyle does also refer to "aesthetic objections to the creation of the universe in the remote past". Although he emphasises the practical aspects much more in his paper, it would seem that this more "philosophical" or emotional objection better reflects his real feelings, since if he were motivated purely by pragmatic considerations, he would not have clung to the Steady State model long after unbiased observers felt that it had been conclusively disproved. This is why the question specifies the stated motivations!]

The basic feature of the Steady State model is that it is a Steady State model: its properties should not change with time. Note that this does not mean that it is static - just that the density, rate of expansion, radius of curvature, stellar populations, etc., should not change with time. Given the finite speed of light, this is equivalent to saying that the properties of the universe should not change with redshift - i.e., that the high redshift universe should look essentially identical, on a large enough scale, to the local universe.

Therefore, the testable predictions of the Steady State model are:

1. The value of H should not vary with time/redshift. This is in principle testable (and has now been disproved using Type Ia supernovae), but it could not be either verified or disproved with 1960s data.
2. The space density of any population of objects (e.g. spiral galaxies, radio sources, etc.) should remain constant with time/redshift.
3. The average age of any population of objects should likewise remain constant (e.g. galaxies observed at high redshift should not appear systematically younger than local galaxies).
4. There should be no evidence for any change in ambient conditions (temperature, density, etc.) with time.

The 1960s observational evidence contradicting these predictions was:

Radio source counts

Since flux goes down like 1/r², and volume goes up like r³, the number of radio sources brighter than flux ƒ₀ should be proportional to ƒ₀^-3/2. In fact, observed source could do not decrease this quickly, i.e. there is an excess of faint sources.

This was initially less conclusive than might be thought, because (1) the poor resolution of radio telescopes tends to create a spurious excess of sources close to the limit of the telescope's sensitivity (source confusion, caused by two faint sources lying in the same "pixel" of the telescope's resolution, and therefore being combined to form a single, non-existent, stronger source), and (2) the lack of optical counterparts meant that it was possible to argue that the "extra" faint sources were due to a second population of faint radio emitters in our own Galaxy. However, by the 1960s better catalogues (particularly 3C) and more source identifications were making these explanations progressively harder to sustain.

Quasars

These objects, discovered in 1963, appeared to exist only at rather high redshift (no local examples). This is contrary to the prediction of constant space density for any given class of objects. The suggestion that the redshifts reflected local motion (objects expelled from our own Galaxy) was very difficult to accept because (1) there were no blushifted objects shot out from other galaxies and (2) none of the quasars had any detectable proper motion (i.e. they're moving radially away from us, not from the Galactic centre). The idea that the redshifts were gravitational required unphysically large masses, and invoking yet more new physics is not good practice. If we assume that the quasar phenomenon is seen only in young galaxies, we need the age distribution to change with redshift, which is also counter to Steady State principles.

The cosmic microwave background

By 1968 there was rather good evidence that this was at least approximately a blackbody (ƒ ∝ ν², the Rayleigh-Jeans law for the long-wavelength tail of the Planck function). A universal blackbody relic radiation is most naturally explained by assuming that the universe was hot, dense and opaque (i.e. radiation in thermal equilibrium with matter, generating a blackbody spectrum) at some well-defined time in the past (because a superposition of blackbody spectra with different redshifts is not itself a blackbody). This is completely counter to the Steady State principle of no changes in ambient conditions. The argument that we are seeing only locally generated radiation, because intergalactic space strongly absorbs microwaves, is very difficult to make credible.

It may be seen that objections can be raised to any one piece of contrary evidence (some of the objections being less credible than others). However, the combination of evidence is devastating: you are comparing natural expectations on the one hand (in the Big Bang model evolution of populations is to be expected, so more radio sources and quasars at high redshift is perfectly reasonable though not a prediction, while the existence of a relic blackbody background at a few kelvin is a prediction) with not one but three ad hoc after-the-fact rationalisations on the other. At this point there is no contest!

• Evidence for:
  • cosmic microwave background - as discussed above, this is a natural consequence of the universe's having evolved from an initial hot, dense state, and the temperature of ~2.7 K is consistent with the observed parameters of the universe (H, Ω).
  • abundance of light elements - the relative abundances of deuterium (first measured in 1973), helium-4 and lithium-7 are broadly consistent with the predictions of Big Bang nucleosynthesis (in fact, in 1980 they were rather more consistent than they are now, because the error bars were bigger!)
  • evolution of cosmic populations such as quasars and radio galaxies - this is less decisive, because it favours any universe of finite age, but it at least disfavours Steady State models
  • approximate self-consistency (the value of H is about what you would expect given the measured ages of cosmic objects; the value of Ω that you deduce from the light element abundances is not unphysical - for example, it's not 0.0001 or 10)
• Evidence against:
  • the horizon problem: the CMB is extremely isotropic even though regions more than a degree or so apart on the sky should not have had time to exchange photons (this requires fine-tuning of initial conditions)
  • the flatness problem: the universe is within a factor of 10 or so of Ω = 1, even though it should evolve rapidly away from this state (this again requires fine-tuning of initial conditions)
  • lack of self-consistency when examined in detail: the age implied by 2/(3H) is starting to look alarmingly young, especially for the higher suggested values of H (recall that at this time the uncertainty in H was a factor of 2); the value of Ω required by BBN seems too small compared with dynamical measurements using galaxy rotation and galaxy clusters

The first two points against constitute Guth's motivation for inflation. Introducing a brief period of exponential expansion in the very early universe (long before BBN, let alone the CMB emission) can ensure that our entire visible universe originates inside a single causally connected domain (thus solving the horizon problem), and the expansion dilutes away any initial curvature (thus solving the flatness problem). [Inflation does not address the last problem, which is solved by the introduction of dark energy - which increases the age of the universe - and dark matter - which provides an additional contribution to Ω which does not contribute to nucleosynthesis.]