Today, the energy density of radiation is negligible in comparison to the other forms of energy density. However, this was not always the case and, before decoupling around +370,000 years, radiation was the dominant form of energy density within the ΛCDM model. In the post-inflation phase, a process called `baryogensis` is thought to have fuelled the universe after which the balance between matter and anti-matter is estimated to account for some 2 billion photons for every matter particle.


The apparent discrepancy between the number density and the energy density is based on the assumption that a photon is subject to an additional expansion factor based on Planck’s equation E=hf=hc/λ. While possibly being a slightly inappropriate analogy, the expansion of space may be thought to have stretched the wavelength [λ] associated with the photon and thereby reducing its frequency [f] and associated energy [E]. So, as the expansion continued with time, the photon-radiation energy density per unit volume decreased, even though there was no net change in the number of photons in the co-moving volume. This point is also said to explain why there is no pressure associated with radiation, i.e. there is no net flow of photons into or out of a given volume of the universe under expansion, at least, on the very large scale.

Cosmic Microwave Background (CMB)

Almost as a footnote to the discussion of radiation as a form of energy, CMB is the electromagnetic radiation associated with an event in the early history of the universe, i.e. decoupling at +370,000 years along a total timeline of 13.7 billion years. However, when first detected in 1965, it was originally thought to be noise in the microwave antenna being used. After this possibility was eliminated and it was realised that the signal was coming from all directions in space, the idea of CMB started to be taken seriously.


As the earlier universe cooled under expansion to approximately 3000K, the photons within the primordial plasma ceased to have enough energy to ionise atoms. The significance of this event marked a phase transition from a universe that was opaque to light to one that was essentially transparent.  In a model that assumes the universe to be both homogeneous and isotropic, any observer looking out into the universe is ‘seeing’ events in both space and time. Objects, such as distant galaxies, are seen in terms of photons arriving having travelled through space, which has taken a finite amount of time as defined by the speed of light, i.e. [ct]. So, within the definition of this photon-spacetime model, any observer is surrounded by a conceptual spherical surface that corresponds to the phase transition between a radiation and matter dominated universe. However, CMB is best described in terms of the physics of blackbody radiation within an expanding universe, which is assumed to explain why the CMB temperature has cooled to from 3000K to 2.7K.

Note: As space expands, the associated CMB wavelength is often described as also expanding by the same factor, which implies that the peak wavelength of the CMB spectrum is inversely proportional to the temperature of the CMB.  Therefore, a drop in temperature from 3000K to 2.7K corresponds to an expansion of the universe and the increase in the CMB wavelength by a factor of 1090 from the moment of decoupling until now.

However, the uniformity of the CMB temperature, measured in all directions, highlights an issue that has become known as the  'horizon problem` and relates to how regions of space that are not now causally connected, i.e. greater than [ct], can have the same CMB temperature. In part, the inflationary model is a proposed solution to this problem by suggesting that inflation causally connected the entire universe, within the first second of existence, which allowed the properties of the universe, such as CMB temperature to also become causally connected from the outset.

Note: In some ways, the temperature effect of CMB can also be used to answer Olbers’ paradox, which asks why the night sky isn’t lit up by the almost infinite number of stars and galaxies. Like CMB, the light from these billions and billions of stars is still arriving on Earth, but the wavelength of the radiation has also been stretched to near zero energy on-route.

CMB reflects the fact that much of what we infer about the large-scale universe is based on how we interpret the properties of the photons arriving from its furthest reaches. Therefore, in the most basic terms, it could be suggested that any model of the large-scale universe has to be built on 2 key properties of a photon, i.e. its velocity and frequency, if we overlook the property of polarisation. Of course, the velocity of a photon implies not only its speed [c], but also its direction, while frequency [f] also infers a wavelength [λ] and energy [E] via the following equations:

[1]      1

However, given the assumed constancy of [c] throughout time, we can calculate the distance travelled in time [t] given the basic equation [d=ct] and so, by a knock-on process, scientists have come to some conclusions about the distance and luminosity of a given source, e.g. stars and galaxies, and the underlying physics that power them, e.g. fusion and gravity. However, the constancy of [c] and [t] used to determine distance possibly needs some qualification:

  • While we might assume that a photon from a distant galaxy has always travelled at velocity [c], the position of the source will have subsequently receded in an expanding universe with some recession velocity [v], which is also a function of distance. So, when the photon set out, the original distance would have been less than [ct], but when it arrives, the source will have receded even further than [ct].

Note: If we assume that a photon exists within some very small region of space, we might question how its localised wavelength was affected by the large-scale expansion of the universe, i.e. if we assume that galaxies have not expanded, so why have photons?

  • There is also the potential issue of time dilation due to the position of the source within some large gravitation potential, which may depend on our assumed model of the universe. For example, if the source was positioned within a homogeneous density with a centre of gravity, the original frequency of the photon might have been subject to a different rate of time than its final destination, such that it appears to have been subject to an additional gravitational redshift.

Anyway, it is assumed that the basic description of CMB is a process that can be extrapolated backwards from the observation of present-day microwave radiation having an energy corresponding to 2.7K, which is being received from all directions in space. Of course, over time the on-going expansion of the universe is generally described as having ‘s-t-r-e-t-c-h-e-d’ the wavelengths of on-route photons to lower energy-temperature, when observed at some future time. However, as indicated, the original starting temperature of 3000K is associated with the energy level at which the photon radiation would have ceased to ionise hydrogen atoms, which then allowed photons to become ‘decoupled’ from matter. This temperature is related to the peak temperature of a blackbody spectrum distribution, which is then shifted to ever-longer wavelengths, as its associated temperature fell, due to the expansion of the universe, towards the present-day value of 2.7K. While it is convenient to talk of the photon temperature, this temperature is really a reflection of the photon energy [E=hf]. Therefore, the ratio of the start and end temperatures, i.e. 1090, also reflects the expansion of the photon wavelength and the expansion of the universe while the photon was in `transit`. Therefore, a CMB photon arriving on Earth today will have travelled for nearly the entire timeline of the universe, i.e. 13.7 billion years, which implies a distance of some 13.7 billion lightyears. However, at the start of this epic journey, the source would have been physically closer than 13.7 billion lightyears, as implied by [d=ct], but will now be much further away than implied by [ct].

So how are events on the timeline of the universe being estimated so accurately, i.e. decoupling at 370,000 years, without equal accuracy in correlating the pressure, density and temperature of the universe to a given volume-radius of the universe?

The actual figures will be discussed in a later results section associated with the energy density model. However, in principle, as we look out into the universe, the decoupling of matter and photons can be described as a spherical shell in our spacetime model of the universe, which exists in all directions in the sense that when looking out to ever greater distances, we are also looking back in time. Of course, lest we forget, we are not actually looking out at the universe, but rather it is just photons that come calling on us from the furthest reaches of spacetime to which we are still causally connected. Even so, scientists have continued to develop ever-more complex models on this basis, which they hope will shed even more `light’ on other aspects of the universe. For example:

Would an observer’s velocity with respect to the CMB frame of reference be detectable as a Doppler shift and would this imply the universe has an absolute frame of reference in violation of relativity?

To be honest, the answer to this question does seem to involve some careful semantics, which states NO, but then seems to imply YES. The negative answer is required to support the basic principle of relativity, which is normally interpreted to mean that there can be a ‘preferred frame’, but no absolute frame of reference. The clarification, which is said to resolve the situation, is based on the caveat that relativity does not apparently state that there are no special frames of reference, only that there are no special frames where the laws of physics are different. As such, it does appear that the CMB frame does allow a measure of velocity with respect to the universe. As it turns out, our Solar System is not quite co-moving, as we have a velocity of 370 km/sec relative to the observable Universe. However, the Local Group of galaxies, which includes the Milky Way, appears to be moving at 600 km/sec relative to the observable Universe. These velocities are called the ‘peculiar velocity’ of an object and are typically much, much less than [c], such that the relativistic effects can be normally ignored.