The derivative of the Hubble parameter can be written in terms of the deceleration parameter:

The Hubble parameter, , in terms of the scale factor is:

In order to differentiate between these scenarios, precise measurements of the Hubble parameter as a function of redshift are needed.

Many inflationary models are approximately de Sitter space and can be modelled by giving the Hubble parameter a mild time dependence.

If the system can be matched with an optical counterpart, then this provides an completely independent way of determining the Hubble parameter at cosmic distances.

Apart from notations for the Hubble parameter, the matter density parameter and the vacuum energy parameter, there is no explanation.

In this case the temperature is proportional to the Hubble parameter , i.e. .

Where is the Hubble parameter and is the gravitational constant.

Here is the Hubble parameter, a measure of the rate at which the universe is expanding.

In this case, the above expression for the scale factor is not valid and , where the constant H is the Hubble parameter.