Cosmic Calculator

This cosmic calculator is written in javascript and based on an Energy-Density Model, see link for details. However, if new to the ideas being presented below, see Model Results for some background of the data. In essence, the calculator results are displayed in the 3 tables below, where the first table corresponds to the present era, hence the scale-factor value [a=1]. The second table shows the calculated values for the redshift [z] value entered via the inset right.  The third table presents a view of the change in energy per comoving volume, which is explained below.

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 word.

  • z=1089: This is the default value calculated and displayed in the second table, which corresponds to the present-day value of the Cosmic Microwave Background (CMB) radiation, which has been used as a reference example throughout this entire section on Cosmology.

  • 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.