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UniverseModelData
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UniverseModelData

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returns properties of the universe based on the default model at specification defined by the time after the Big Bang, the distance to the comoving object, or the redshift of such an object.

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UniverseModelData[spec,model]

returns properties of universe model at spec.

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UniverseModelData[spec,property]

returns the specified property at the time or distance spec.

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UniverseModelData[spec,property,model]

returns the specified property at the time or distance spec for the universe model.

Details

  • The specification spec can be a Quantity object with units of times and distances, or it can be an association with the key "Time" for the age of the universe, "TimeAgo" for the time in the past measured from the present time, "Distance" for the distance to an object, or "Redshift" for the redshift of a distant object. For the keys "Time", "TimeAgo", and "Distance", the values must be Quantity objects.
  • Results are limited to after the epoch of cosmic inflation.
  • UniverseModelData["Models"] returns the list of available models. Use UniverseModelData[model] to learn the values for specific models.
  • UniverseModelData["Properties"] gives the list of all properties available.
  • Properties are returned using Quantity where appropriate.
  • General universe properties include:
  • "UniverseCurvature"curvature of the universe
  • Properties referring to an object seen at a distance that corresponds to a time after the Big Bang include:
  • "AngularDiameterDistance"distance determined by angular diameter
    "ComovingDistance"distance measure not affected by the expansion or contraction of space
    "ComovingVolume"volume of space within the comoving distance
    "ConformalTime"time measure not affected by the expansion or contraction of space
    "DarkEnergyDensityRatio"ratio of dark energy density to the total energy density in the universe
    "Epoch"overall composition of the universe model
    "EventHorizon"maximum distance from which light emitted at a given time can reach the observer in the future
    "HubbleDistance"distance to objects receding from observer at light speed
    "HubbleParameter"rate of expansion of the universe model
    "LuminosityDistance"distance determined by luminosity
    "MatterEnergyDensityRatio"ratio of matter density to the total energy density in the universe
    "MaximumUniverseAge"maximum age the universe can ever reach
    "ParticleHorizon"maximum distance traveled by light from the Big Bang to a given time
    "RadiationEnergyDensityRatio"ratio of radiation density to the total energy density in the universe
    "RadiationTemperature"temperature of background radiation
    "Redshift"shift in wavelength due to expansion or contraction of space
    "ScaleFactor"change in distance due to expansion or contraction of space
    "TimeAgo"time in past measured from the present time
    "TotalObservableRadiusFraction"fraction of the universe seen out of total possible for all time
    "TransverseComovingDistance"comoving distance between two objects located at the same redshift
  • model can be specified by one of the available models, by supplying the parameters for the composition of the universe, or by supplying the model and the parameters that diverge from it.
  • The default universe model is "LambdaCDM".
  • Parameters include:
  • "HubbleH0"Hubble constant H
    "OmegaLambda"ratio of dark energy density to the critical density
    "OmegaMatter"ratio of matter density to the critical density
    "OmegaRadiation"ratio of radiation density to the critical density
    "OmegaK"ratio of curvature density to the critical density
  • All parameters refer to their values now.
  • "HubbleH0" should be a Quantity with dimension of inverse time. All other parameters should be dimensionless or percentage quantities.
  • Parameters should be supplied as an association.
  • Calculations use the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the Friedmann equations, and the equations of state for the matter, radiation, and dark energy components.

Examples

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Basic Examples  (3)Summary of the most common use cases

Calculate the scale factor of the universe 100 million years after the Big Bang:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-2ksq1d
Out[1]=1

Determine the redshift of a comoving object a billion light years away:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-fwkeo9
Out[1]=1

Explore properties of cosmological models of arbitrary composition:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-ekpnk7
Out[1]=1

Scope  (7)Survey of the scope of standard use cases

Obtain a list of properties:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-ibo62x
Out[1]=1

Find a list of supported models:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-bsojuu
Out[1]=1

Explore their default values:

In[2]:=2
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https://wolfram.com/xid/0b7gkcjc7ql108iq-ibftr9
Out[2]=2

Learn about the composition of the universe 100 million years after the Big Bang:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-fg3c7q
Out[1]=1

Explore the scale factor 10 billion years ago:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-bqemgp
Out[1]=1

Find all properties for a particular age of the universe:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-3d6vw7
Out[1]=1

Examine how the particle horizon differs for different models of the universe:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-qcpijj
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b7gkcjc7ql108iq-sg79cn
Out[2]=2

Modify aspects of the standard model:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-p86mt
Out[1]=1

Applications  (7)Sample problems that can be solved with this function

Examine the expansion of the observable radius of the universe over time:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-jxp3rj
Out[1]=1

Discover the properties of a matter-dominated universe:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-ci3a6f
Out[1]=1

Explore how the uncertainty in the Hubble constant () affects estimates of the background radiation temperature in the early universe:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-264c9v
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b7gkcjc7ql108iq-cmf9d4
Out[2]=2

Examine the effect of the Hubble constant value on the present-day particle horizon:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-qne34h
In[2]:=2
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https://wolfram.com/xid/0b7gkcjc7ql108iq-fx6856
Out[2]=2

Discover when the background radiation temperature would have been 300 K:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-oa3095
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b7gkcjc7ql108iq-gvg91g
Out[2]=2

Calculate the comoving distance to objects in the Virgo galaxy cluster:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-qwphgw
In[2]:=2
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https://wolfram.com/xid/0b7gkcjc7ql108iq-rnzt6s

Examine how they deviate with increasing distance:

In[3]:=3
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https://wolfram.com/xid/0b7gkcjc7ql108iq-crys4o
Out[3]=3

Examine the variation of temperature in the cosmic microwave background (CMB) over time:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-j48i38
Out[1]=1

Possible Issues  (5)Common pitfalls and unexpected behavior

Specifications for universe composition should be positive numbers or percentages:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-xdapfg
Out[1]=1

Components of the universe can sum to greater than unity:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-0jy52i
Out[1]=1

Results are limited to at least seconds after the Big Bang:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-qiqx0p
Out[1]=1

All cosmological components plus the curvature should add up to one:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-qa9gpd
Out[1]=1

Missing components will be derived when curvature is included:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-vgymbv
Out[1]=1

Use UniverseModelData[model] to help determine the best values to include:

In[2]:=2
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https://wolfram.com/xid/0b7gkcjc7ql108iq-dpeydc
Out[2]=2

Neat Examples  (1)Surprising or curious use cases

Explore how the composition of the universe changes over time:

In[1]:=1
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https://wolfram.com/xid/0b7gkcjc7ql108iq-88uspi
In[2]:=2
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https://wolfram.com/xid/0b7gkcjc7ql108iq-xwqz27
Out[2]=2
Wolfram Research (2016), UniverseModelData, Wolfram Language function, https://reference.wolfram.com/language/ref/UniverseModelData.html.
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Wolfram Research (2016), UniverseModelData, Wolfram Language function, https://reference.wolfram.com/language/ref/UniverseModelData.html.

Text

Wolfram Research (2016), UniverseModelData, Wolfram Language function, https://reference.wolfram.com/language/ref/UniverseModelData.html.

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Wolfram Research (2016), UniverseModelData, Wolfram Language function, https://reference.wolfram.com/language/ref/UniverseModelData.html.

CMS

Wolfram Language. 2016. "UniverseModelData." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/UniverseModelData.html.

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Wolfram Language. 2016. "UniverseModelData." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/UniverseModelData.html.

APA

Wolfram Language. (2016). UniverseModelData. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UniverseModelData.html

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Wolfram Language. (2016). UniverseModelData. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UniverseModelData.html

BibTeX

@misc{reference.wolfram_2025_universemodeldata, author="Wolfram Research", title="{UniverseModelData}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/UniverseModelData.html}", note=[Accessed: 28-April-2025 ]}

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@misc{reference.wolfram_2025_universemodeldata, author="Wolfram Research", title="{UniverseModelData}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/UniverseModelData.html}", note=[Accessed: 28-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_universemodeldata, organization={Wolfram Research}, title={UniverseModelData}, year={2016}, url={https://reference.wolfram.com/language/ref/UniverseModelData.html}, note=[Accessed: 28-April-2025 ]}

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@online{reference.wolfram_2025_universemodeldata, organization={Wolfram Research}, title={UniverseModelData}, year={2016}, url={https://reference.wolfram.com/language/ref/UniverseModelData.html}, note=[Accessed: 28-April-2025 ]}