The calculator is primarily driven by the value of the redshift [z] entered through the input panel on the right, where [z] has a normal range between [0 to 9999] corresponding to source events in the past. However, negative values of [z] are permissible in the range [0 to -0.99], which when transposed into a corresponding scale-factor [a=1/1+z] might be interpreted as a reflection of future expansion. All the tables presented above are discussed in more detail under the link 'Graphical Interpretation' so the following is only by way of a quick introduction. While the Hubble [H] parameter and the relative energy-density of each component of the model can be changed, the defaults are generally reflective of the accepted values. Therefore, it might be more useful to focus on the limits of the redshift [z] ranges outlined below.
- z=0: In this case, the result in the second table will simply
mirror those displayed in the first table. However, it might be
worth clarifying that the real role of [z] is primarily to specify
a point in spacetime from which light is being received in the present
era from which the original (proper) distance and the current
(comoving) distance can be calculated.
- z=1.46: This value is highlighted because the recessional velocity
of the source is approaching and will subsequently exceed the speed
of light [c]. Again, the implication of an apparent superluminal
velocity is discussed several sections, which can be found by doing
a 'search' on this key
- z=1089: This is the default value calculated and displayed in
the second table, which corresponds to the present-day value of
Cosmic Microwave Background (CMB) radiation, which has
been used as a reference example throughout this entire section
- z=9999: It should be noted that z=1089 defines the limits of
the observable universe due to the opaque nature of the universe
to light prior to 'decoupling'.
Therefore, the usefulness of values displayed are primarily in that
they show how radiation was initially the dominant component in
the early universe.
- z=-0.5: This value is possibly best interpreted in terms of
its corresponding scale-factor [a=2]. Due to the accelerated expansion
caused by the equation of state
of dark energy, our universe will double its present-day size after
24 billion years along a timeline, which conceptually started with
the 'Big Bang'.
- z=-0.99: The upper limit of [z=-1] would correspond to an infinite expansion. The current value being discussed corresponds to a scale-factor [a=100], which would be reached after 86 billion years. However, the reality of our future observable universe will ultimately be defined by its 'cosmological horizons' at that time.
The third table is a speculative interpretation of the total energy-density shown in tables 1 and 2, which respectively correspond to the present era and some point along the expanding timeline defined by the input redshift [z]. By multiplying the energy-density figure by the comoving volume [a3], we obtain a relative value of the energy contained within an expanding volume. The calculations are finally presented as a '% change' in the energy and suggests that the total energy is increasing due to the equation of state of dark energy, because its energy-density does not change under expansion - see 'Graphical Interpretation' for more details.