WMAP Q&A: Information about Powerspectrum & Inflation

[gluon]

Hello,i have a question about wmap measurements.Can someone tell me what information we get from wmap powerspectum only?except from density parameters did we get information for inflation?if we don't from which measurement did we get information about inflation?and what other information we get ,except this from powerspectrum?

 

[Orodruin]

There is currently no experimental verification of inflation. Inflation is a mechanism proposed to explain why the universe is spatially flat (among other things). This information can be deduced from the CMB. The CMB on its own does not really constrain the density parameters, you need additional information from other measurements such as supernova data and baryon acoustic oscillations.

You can also look for remnants from inflation in the form of B-mode polarisation in the CMB caused by gravitational waves. This was reported by the BICEPII colaboration, but the signal was far larger than expected and was later attributed to foreground dust. The expected signal is currently to weak to be detected by our most sensitive instruments.

 

[Chalnoth]

The primary inflation parameters constrained by the CMB temperature power spectrum are the amplitude of the primordial fluctuations and the "tilt" of the spectrum. The amplitude sets the overall size of the power spectrum, while the tilt is due to the fact that inflation ends: if inflation were governed by a field that had constant energy density, then it would produce a perfectly scale-invariant power spectrum. However, as inflation has to end, the energy density of the inflaton changes over time. This creates a deviation from scale invariance called a "tilt".

Together these parameters constrain the possible inflation models that might fit the data.

The tensor-to-scalar ratio is also well-measured if the power spectrum of the primordial B modes can be accurately measured (so far we haven't yet definitively detected this signal). If we could measure this signal (it may be too small to ever measure, sadly), then we could dramatically improve our constraints on inflation models.

 

[Chalnoth]

The expected signal is currently to weak to be detected by our most sensitive instruments.

This statement is a bit strong. The signal is too weak to be detected by our current instruments. There's no solid theoretical expectation of any particular amplitude of the B-mode polarization just yet, and there's quite a bit that can be done to improve measurements. The current problem is that Planck, our current best instrument for measuring the CMB, was not designed with polarization in mind, and it has significant problems with systematic errors where polarization is concerned. Other ground-based and balloon-borne instruments do a much better job of dealing with instrument systematics, but at the same time they have to deal with the atmosphere.

Maybe we'll be able to detect B-modes in the future with better instruments, maybe not. Our best bet is to have a ground-based or balloon-borne instrument provide an initial detection to stimulate interest in another CMB satellite, one designed with polarization in mind from the start.

 

[gluon]

thanks for the answers.but can someone tell what info we get from power spectrum of wmap only? chalnoth what actually means the tilt of the spectrum,what info we get from this ?

 

[Chalnoth]

I don't know quite what you're asking for. The power spectrum is used to estimate parameters and their error bars. The parameters most relevant to inflation that WMAP measures are, from their 9-year data set (taken from here):
The amplitude of the fluctuations:
$10^9 \Delta_R^2 = 2.41 \pm 0.10$
The spectral tilt:
$n_s = 0.972 \pm 0.013$

Different inflation models have different predictions for these values.

The amplitude is given by how big the differences in temperature across the sky are. The tilt is a deviation from a perfectly scale-invariant spectrum (a scale-invariant spectrum would have $n_s = 1$). If you want to know what these parameters do to the power spectrum itself, see Tegmark's animations:
http://space.mit.edu/home/tegmark/movies.html
Click the parameters on the right to see how changing each parameter changes the power spectrum.
(He uses $A_s$ as the parameter for the amplitude. It's the same basic thing, just different units.)

 

[Chalnoth]

If you're trying to ask what these measurements say about inflation, the answer is not a whole lot. WMAP just doesn't have the accuracy to get a good handle on it. In principle, the main measurable thing that inflation has is its potential energy. The shape of the potential energy function determines the values of these parameters. For example, a potential energy function that results in a lower change in potential energy over time would produce less of a spectral tilt ($n_s$ closer to 1).

 

[Garth]

The current problem is that Planck, our current best instrument for measuring the CMB, was not designed with polarization in mind, and it has significant problems with systematic errors where polarization is concerned. Other ground-based and balloon-borne instruments do a much better job of dealing with instrument systematics, but at the same time they have to deal with the atmosphere.

Maybe we'll be able to detect B-modes in the future with better instruments, maybe not. Our best bet is to have a ground-based or balloon-borne instrument provide an initial detection to stimulate interest in another CMB satellite, one designed with polarization in mind from the start.

This paper on todays physics ArXiv may be pertinent: Forecasting sensitivity on tilt of power spectrum of primordial gravitational waves after Planck satellite.

Even though at present there are no evidence for the primordial gravitational waves, several future polarization experiments might reach the sensitivity to detect the primordial gravitational waves in the coming years. As a recent analysis, Ref. [25] forecasted that the primordial gravitational waves with theoretically motivated r ~ 2x10^-3 can be achievable by certain future experiments if the noise is reduced to ~1 \mu K -arcmin and the lensing B-modes reduced to 10%. Their forecasts are not changed signicantly with respect to previous estimates [26]. In this paper, we study the sensitivity on the tensor tilt n_t for several future ground-based (AdvACT, CLASS, Keck/BICEP3, Simons Array, SPT-3G),
balloon-borne (EBEX, Spider) and satellite (CMBPol, COrE, LiteBIRD) experiments.

Garth