Gravitational lensing and Dark Energy

[astrolollo]

Hi everyone
I have been told that gravitational lensing affects CMB power spectra (TT, TE, EE) for high values of l (i.e. the least, low peaks on the right, say l>1000). But how? Isn't the effect of the varying gravitational potential along the line of sight the cause of Integrated Sachs-Wolfe effect which affects the spectrum, on the contrary, for low values of l (say, l< 30)? How can we know that the lensing is caused in an accelerating universe scenario? And how can gravitational lensing constrain DE, both in density and in equation of state?

 

[Chalnoth]

The primary impact of gravitational lensing is that it "mixes" the polarization signal, so that some of the E-mode power shows up in the B-modes (the primordial B-modes are much, much smaller than the E-modes, so there isn't much contamination in the other direction). Lensing shows up at higher $\ell$ values in the B-modes because the E-modes have more power at higher $\ell$ values (peaking at around $\ell=1000$ or so).

 

[astrolollo]

And how is it useful to determine the features of DE?

 

[Chalnoth]

What do you mean useful?

Many people think dark energy is interesting, and understanding dark energy would give us deeper insight into the most fundamental physical laws. But I don't know what you mean by, "useful."

 

[astrolollo]

No, I'm just asking how what you wrote in your answer could be used to determine the presence of dark energy

 

[Chalnoth]

No, I'm just asking how what you wrote in your answer could be used to determine the presence of dark energy

Ahhh, that makes more sense :)

Dark energy's effect on the CMB is pretty small. For the most part it impacts the low-$\ell$ modes through the ISW effect. The effect of lensing on the CMB has very little to do with dark energy.

What you get from gravitational lensing that is useful for dark energy are measurements of the distribution of large scale structure. Measurements of the distribution of large scale structure provide a measurement of how the universe has expanded over time, which is currently the primary method for detecting dark energy (dark energy changes the rate of expansion depending upon its amount and properties).

 

[astrolollo]

"The effect of lensing on the CMB has very little to do with dark energy." Are you sure? Planck alone can put some constraints on DE only with lensing..

 

[Chalnoth]

Not from lensing, I don't think. Or, at least, not directly. The main direct constraint comes from the ISW effect, which isn't a matter of lensing. As I mentioned, lensing can be used to measure large scale structure, and that can be used to measure dark energy through the rate of change of expansion.