Undergrad Testing Inflation: A Definitive Test & Laymen Explanation

[windy miller]

A new paper has recently popped up claiming it is possible to make a more definitive test of inflation versus certain alternatives like the matter bounce or ekpyrotic universe. https://arxiv.org/pdf/1809.02603.pdf
I was wondering what people thought of it. Any good laymen explanation of what is going on here?

 

[kimbyd]

From my skimming of the paper, the meat of it seems to be that the main difference between inflation and most alternative scenarios is that the energy scale of inflation is nearly constant, while the alternatives tend to have an energy scale which increases with time, and that increasing energy scale produces a particular signature on the CMB. They don't actually process any data to look for this signature, but it would be interesting to see.

In principle it's conceivable that this process could rule out a whole group of alternatives to inflation. But it all depends upon the details: it's possible this signal is just too small to measure for reasonable parameter choices for the inflation alternative.

Anyway, I don't see this paper as being all that interesting for non-cosmologists (yet). It could be interesting for model builders to see if their models produce this kind of signal, and for data analysts to compare these predicted signals against the CMB data. Until those tasks are performed, it's just a proposal for future work.

 

[bapowell]

Energy scales that increase in time would also generate a blue tensor spectrum. A red tensor spectrum is a "smoking gun" signature of inflation that, though very difficult to detect, would be a strong discriminator between inflation, bounces models, and string gases.

 

[kimbyd]

Energy scales that increase in time would also generate a blue tensor spectrum. A red tensor spectrum is a "smoking gun" signature of inflation that, though very difficult to detect, would be a strong discriminator between inflation, bounces models, and string gases.

Which would be nice, though it's unfortunately all too possible that the tensor amplitude will be too faint to detect.

An explanation of this for non-experts:
Inflation predicts that there will both a scalar and a tensor source of density fluctuations. The tensor perturbations do have an impact on the power spectrum, are mostly distinguished because they are the only source for primordial "B-mode" polarization: polarization can be divided into two components, with polarization pointing outwards from a source being "E-mode" (named because it's similar to the electric field by having a charge with field lines emanating outward) and "B-mode" (named because it's similar to the magnetic field, traditionally denoted with a B, where field lines form closed loops rather than pointing outward).

At small angular scales, you can get B-mode polarization signal in the sky from gravitational lensing of large scale structure, which tends to mix polarization between E and B modes (this has been detected definitively), but at large angular scales, the only source for the B-mode signal is if it existed when the CMB was emitted, which can only come if the density perturbations laid them down.

Most alternatives to inflation don't predict any measurable B-mode signal at all, and many inflation models sadly have a pretty large parameter space where the B-mode signal is also too small to be detected. So we may never be able to use this signal to determine which models are (or aren't) correct.

That said, tensor amplitudes don't only impact the B-mode polarization. They also have an effect on all other parts of the CMB signal. So it is conceivable that detailed measurements of the temperature and E-mode spectrum might be enough to detect tensor perturbations anyway. The problem is that the signal is very faint and hard to separate from other systematic effects.

 

[bapowell]

Most alternatives to inflation don't predict any measurable B-mode signal at all, and many inflation models sadly have a pretty large parameter space where the B-mode signal is also too small to be detected. So we may never be able to use this signal to determine which models are (or aren't) correct.

Each of the alternatives I listed can generate tensors. Now, whether they do, as with inflation, is totally unknown and depends on things like the energy scale of the epoch.

That said, tensor amplitudes don't only impact the B-mode polarization. They also have an effect on all other parts of the CMB signal. So it is conceivable that detailed measurements of the temperature and E-mode spectrum might be enough to detect tensor perturbations anyway. The problem is that the signal is very faint and hard to separate from other systematic effects.

I doubt this. I'll bet that for a given T/E spectrum from an inflation model w/ tensors, I can give you at least one statistically indistinguishable T/E spectrum from a model without tensors.

 

[kimbyd]

I doubt this. I'll bet that for a given T/E spectrum from an inflation model w/ tensors, I can give you at least one statistically indistinguishable T/E spectrum from a model without tensors.

It depends upon what you mean by distinguishable. I forget the details, but the tensor spectrum definitely has an impact, and it is measurable. It's just likely to be too faint. See, for example, the 2018 Planck release:
https://arxiv.org/pdf/1807.06209.pdf

Fig. 28 on page 39 shows the error contours on the tensor-scalar ratio and scalar spectral index, using only temperature and E-mode polarization data. Current measurements are consistent with zero, but with a best fit slightly higher than zero. If the tensor-scalar ratio is, say, close to 0.05, it's not inconceivable that a more accurate mission might be able to resolve it. The main thing you'd need is a satellite which is constructed to measure polarization from the start*, and to cover a wider range of frequencies to better subtract foreground signals. A satellite is required because the atmosphere drastically limits the measurable frequencies (the atmosphere is pretty opaque across most of the CMB band, with only a few windows where the signal is relatively clear).

The problem is that if the ratio is closer to 0.01, then it's probably never going to be detectable in this way

* Planck's polarization measurement design is sub-optimal in part because it was originally designed to measure temperature only, and in part because space agencies are very skittish about flying new technology. Today, the best polarization measurement designs for the CMB are used in balloons like EBEX, where they used a half wave plate rotating on a superconducting magnetic bearing. The rotating plate makes systematic removal very easy because the predictable period of rotation creates a strong signal that can be easily subtracted from the data. This is in contrast to Planck which has fixed polarimeters which may not be pointing in the precise direction the design calls for, and which have slightly different beam shapes which must be measured.

 

[bapowell]

Yes, if you fit a LCDM+tensors model to the CMB T/E spectra, you might eventually get an r > 0 at some level of confidence. But that's not what it means to detect tensors, since I can always fit a plain old LCDM model to the same data and get a good fit as well. You ultimately need to do some sort of model comparison to see if the T/E data alone warrant the inclusion of tensors: I'm just saying I'm skeptical of this.