# 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?

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.

• I think I get it already it is because matter density is always decreasing as the universe expands like the slope of the hill becoming less steep and therefore CMBR is like a ball rolling down the hill which is less steep now. – user6760 Nov 10 '17 at 9:01
• @user6760: yes, but bear in mind my last two paragraphs. Light reaching us from distant parts of the universe is always redshifted. The late time SW effect means light reaching us from distant parts of the universe through a void is redshifted even more. This effect is dependent on an accelerated expansion shrinking the voids - it wouldn't happen if dark energy didn't exist. – John Rennie Nov 10 '17 at 9:11
• do you mean the void is getting bigger so that it is analogous to the slope of a hill becoming less steep(shrinking)? – user6760 Nov 10 '17 at 9:17