I'm trying to calculate the conformal Hubble parameter $H_\eta$ using Astropy, but I'm unsure about the correct approach. I know that the standard Hubble parameter $H(t)$ is related to the scale factor $a(t)$ by

$$ H(t) = \frac{\dot{a}(t)}{a(t)}, $$

but the conformal Hubble parameter $\mathcal H$ depends on the conformal time $\eta$ and can be expressed as

$$ \mathcal H = \frac{a'(\eta)}{a(\eta)}, $$

where $a'(\eta)$ is the derivative of the scale factor with respect to the conformal time. Does Astropy provide a function to directly calculate $\mathcal H$, or is there a method to numerically derive it from the standard Hubble parameter $H(t)$ using the cosmological models defined in Astropy?

Specifically, I'd like to know how to compute $\mathcal H$ from the cosmological model, such as the LambdaCDM model, for a given redshift $z$. Any help or guidance would be greatly appreciated!

I'm trying to calculate the conformal Hubble parameter $\mathcal H$ using Astropy, but I'm unsure about the correct approach. I know that the standard Hubble parameter $H(t)$ is related to the scale factor $a(t)$ by

$$ H(t) = \frac{\dot{a}(t)}{a(t)}, $$

but the conformal Hubble parameter $\mathcal H$ depends on the conformal time $\eta$ and can be expressed as

$$ \mathcal H = \frac{a'(\eta)}{a(\eta)}, $$

where $a'(\eta)$ is the derivative of the scale factor with respect to the conformal time. Does Astropy provide a function to directly calculate $\mathcal H$, or is there a method to numerically derive it from the standard Hubble parameter $H(t)$ using the cosmological models defined in Astropy?

Specifically, I'd like to know how to compute $\mathcal H$ from the cosmological model, such as the LambdaCDM model, for a given redshift $z$. Any help or guidance would be greatly appreciated!