cosmology - Why is void making CMBR lose energy as inflation speeds up?

The expansion of space is speeding up, so many voids are getting bigger. CMBR lose energy when moving through this void and then gain back the same energy as it leaves the void except in the case when the inflation is speeding up so that it doesn't have the same energy as it had before.

The void is a region of space that is totally empty meaning it is devoid of matter, the article explained that speed of light is constant so as it loses energy it's frequency becomes longer.

I can understand CMBR is being red shifted inside in the void and blue shifted when exiting the void but somehow this amount of blue shift is less than when it is red shifted, why?

Answer

This is the Sachs-Wolfe effect.

Suppose you're travelling through a region of the universe where the matter density is $\rho$. To enter a void takes energy because the matter outside the void is pulling you away from the void. The potential energy change will be some function of the density difference between the universe and the void, $\Delta\Phi = f(\Delta\rho)$. Without worrying about the exact form of this function it should be obvious that the bigger the density difference $\Delta\rho$ the bigger the PE change $\Delta\Phi$.

So as we enter the void we increase our potential energy by some value:

$$ \Delta\Phi_\text{in} = f(\Delta\rho_\text{in}) $$

And likewise when we exit the void we decease our potential energy by some value:

$$ \Delta\Phi_\text{out} = f(\Delta\rho_\text{out}) $$

So our net change in potential energy is:

$$ \Delta\Phi_\text{net} = \Delta\Phi_\text{out} - \Delta\Phi_\text{in} = f(\Delta\rho_\text{out}) - f(\Delta\rho_\text{in}) $$

But the universe has expanded a bit during the time we spent in the void, so the average density of matter in the universe decreased during this time. That means $\Delta\rho_\text{out}<\Delta\rho_\text{in}$ and therefore $\Delta\Phi_\text{out} < \Delta\Phi_\text{in}$ and therefore:

$$\Delta\Phi_\text{net} \ne 0$$

Our energy after leaving the void is less then when we entered it. For a massive object that means the velocity is reduced, and for a photon that means the photon energy has been reduced i.e. the photon is red shifted.

But this isn't the whole story. Remember that when we talk about the Sachs-Wolfe effect we are comparing the red shift of light passing through the void to the red shift of light that didn't go though the void. So it isn't enough for our light to be red shifted - it has to be red shifted by a different amount to light that bypassed the void and just got red shifted by the overall expansion of the universe.

And this is where dark energy comes in. In effect the accelerated expansion due to dark energy shrinks the void while we are passing through it, and the overall change in PE when passing through the void becomes different to the overall change when bypassing the void. This is the late time integrated Sachs-Wolfe effect.