Hubble scale and energy density during inflation

[spaghetti3451]

Is the energy density $\rho$ in the early universe and the Hubble scale $H$ during inflation related by the formula

$$H^{4} = \frac{9}{64\pi^{2}} \frac{\rho^{2}}{M_{P}^{4}}?$$

Here, $M_{P}$ is the Planck mass.

Can you suggest any resources where this is explained?

 

[spaghetti3451]

Let me rephrase my question.

The energy density for a spatially flat universe (without a cosmological constant) is $\rho = 3 M_{\text{Pl}}^{2}H^{2}.$

How is this formula modified during inflation?