So the BICEP2 saga is definitely over, but the search for the primordial B-modes is not. The lesson we learned is that single frequency instruments like BICEP2 are not good in view of large galactic foregrounds. The road ahead is then clear: build more precise multi-frequency instruments, such that foregrounds can be subtracted. While we will not send a new CMB satellite observatory anytime soon, there are literally dozens of ground based and balloon CMB experiments already running or coming online in the near future. In particular, the BICEP program continues, with Keck Array running at other frequencies, and the more precise BICEP3 telescope to be completed this year. Furthermore, the SPIDER balloon experiment just completed the first Antarctica flight early this year, with a two-frequency instrument on board. Hence, better limits on

*r*are expected already this year. See the snapshots below, borrowed from these slides, for a compilation of upcoming experiments.

Impressive, isn't it? These experiments should be soon sensitive to

*r*~0.01, and in the long run to

*r*~0.001. Of course, there is no guarantee of a detection. If the energy scale of inflation is just a little below 10^16 GeV, then we will never observe the signal of gravitational waves. Thus, the success of this enterprise crucially depends on Nature being kind. However the high stakes make these searches worthwhile. A discovery, would surely count among the greatest scientific breakthrough of 21st century. Better limits, on the other hand, will exclude some simple models of inflation. For example, single-field inflation with a quadratic potential is already under pressure. Other interesting models, such as natural inflation, may go under the knife soon.

For quantitative estimates of future experiments' sensitivity to

*r,*see this paper.

## 20 comments:

In a piece on the BICEP-2 issue in Physics World, Neil Turok is quoted as saying: "For the past 35 years, theoretical physics has been an extravaganza of model-building" [adding that theories have] "sort of run amok".

In my opinion, if we insist on retaining the dubious and untested assumptions of absolute scale and strict reductionism, then theoretical physics will continue to offer only ad hoc and unnatural model-building.

Why is it impossible to detect gravitational waves if the scale of inflation is below 10^16 GeV?

Because r is then too small to be detectable. The tensor to scalar ratio is given by r = (E/3.3*10^16 GeV)^4 , where E is the energy scale of inflation (more precisely, E = V^1/4 where V is the value of the inflaton potential during inflation). So, for E = 2*10^16 GeV you get r~0.1, for E = 10^16 GeV you get r~0.01, and for E = 0.6*10^16 GeV you get r~0.001. If E is lower than that, we will not see gravitational waves anytime soon....

Is the GUT scale known any more accurately than "about 10^16 GeV"? Seems like it should be relevant here.

GUT scale, defined as the energy scale where the SM couplings meet, is model dependent. In a given model it is known very accurately, for example in the MSSM it is 2*10^16 GeV.

However, there's no theoretical reason why the energy scale of inflation should be equal to the GUT scale as defined above. Even if inflation has something to do with the breaking of the GUT symmetry, the value of the inflaton potential will depend on several other parameters of the mode.

Thanks Jester. How low does E have to be to be detected by direct searches for gravitons/inflatons or something like that?

Just for comparison: See the following presentation on Higgs & R2 Inflation.

http://www.phys.uconn.edu/~bezrukov/publ/R2-vs-HI-Ginsburg2012.pdf

Predictions

Higgs inflation: n = 0.967, r = 0.0032

R2 inflation: n = 0.965, r = 0.0036

These values of tensor-to-scalar ratio, r, will likely hard to nail down with 5 sigma certainty.

Planck 2013 results XXII paper constrain the inflation modes that still fit the experimental data.

Does anyone know if there is a book that fully explains this issue? (i.e., the inflation validation vs. tensor-to-scalar ratio of primordial fluctuations).

@Anonymous two above me: 3 sigma would be enough (and "in the long run [sensitive] to r~0.001" suggests that is possible), that gives funding to experiments that can reach 5 sigma.

Antonio, Mukhanov's textbook is good. Otherwise there are good reviews on the arxiv, e.g. 0907.5424 or 1001.5259

Anon-2, afaik there are no good prospects of seeing any signals from inflation elsewhere than in the CMB. If r were 0.2, as BICEP originally suggested, then maybe it would be possible to directly detect the gravitational waves in the next-to-next generation of interferometers. However, since r is smaller, that does not seem likely either.

But, who knows, maybe someone will come up with a new ingenious idea...

http://www.cosmos.esa.int/documents/387566/522789/Planck_2015_Results_XIII_Cosmological_Parameters.pdf/51ef1ba4-38d5-48f4-8448-57824fb864cf

This claims r is now < 0.09. Piecing together from comments above, the MSSM seems ruled out or close to ruled out?

No, why? The MSSM makes no prediction about r. It depends on the model of inflation the MSSM is embedded in.

Ah, sorry. MSSM makes the GUT scale 10^16 GeV, not the inflation scale. My mistake.

2*10^16...

Thanks Jester for the info. About the detectability of gravitational waves, the bound you have commented: > 10^16 GeV for the energy scale of inflation, is in those lectures always related to a V^(1/4) potential, so, may this energy depend on the inflation model?. That is, the bound could be right for inflationary models with power-law potentials, but may be not right for models that nowadays still meet the cosmological constrains r<0.12 and ns = 0.96 (see them in fig 1 in PL13-XXII paper), i.e., natural and Ricci-scalar-squared inflations.

I am not an expert Jester, so I might be mistaken.

Here's what should be done:

http://arxiv.org/abs/1502.00625

Antonio, by the energy scale of inflation E I meant exactly V^1/4. Of course, the predicted value of V^1/4 is model dependent, that's why some models (like phi^2 inflation) are almost excluded, while others (like phi^1 inflation, or R^2 inflation) are still allowed.

@Jester: The constraint's on inflation paper is now out. The plot you probably care about the most is figure 54 on page 55. This figure covers the constraints on r-n_s space using the full Planck data along with the BKP cross-correlation results.

Looks like we now have a sub-1% uncertainty on n_s and an 95% upper-limit on r at 0.08.

Yes, there is a separate post about that plot.

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