A certain kind of gravitational waves evident in the cosmic background radiation are predicted by all but a handful of the hundreds of versions of cosmological inflation theory. A reanalysis of observations designed to see evidence of these waves now concludes that they are either absent or only negligible in magnitude.

A joint analysis of data collected by the Planck and BICEP2+Keck teams has previously givenr=0.09+0.06−0.04 for BICEP2 andr=0.02+0.04−0.02 for Keck. Analyzing BICEP2 using its published noise estimate, we had earlier (Colley & Gott 2015) foundr=0.09±0.04 , agreeing with the final joint results for BICEP2. With the Keck data now available, we have done something the joint analysis did not: a correlation study of the BICEP2 vs. Keck B-mode maps. Knowing the correlation coefficient between the two and their amplitudes allows us to determine the noise in each map (which we check using the E-modes). We find the noise power in the BICEP2 map to be twice the original BICEP2 published estimate, explaining the anomalously highr value obtained by BICEP2. We now findr=0.004±0.04 for BICEP2 andr=−0.01±0.04 for Keck. Sincer≥0 by definition, this implies a maximum likelihood value ofr=0 , or no evidence for gravitational waves. Starobinsky Inflation (r=0.0036 ) is not ruled out, however. Krauss & Wilzcek (2014) have already argued that "measurement of polarization of the CMB due to a long-wavelength stochastic background of gravitational waves from Inflation in the early Universe would firmly establish the quantization of gravity," and, therefore, the existence of gravitons. We argue it would also constitute a detection of gravitational Hawking radiation (explicitly from the causal horizons due to Inflation).

J. Richard Gott III and Wesley N. Colley, "Reanalysis of the BICEP2, Keck and Planck Data: No Evidence for Gravitational Radiation" (July 21, 2017).

This implies a 95% upper bound on r=0.05 as opposed to the current upper bound of r=0.11.

Starobinsky Inflation (which implies f(R) gravity) is also supported by another recent study:

We obtain a differential equation which allows to reconstruct af(R) theory from the α -Attractors class of inflationary models and solve it in the limit of high energies, showing an analogy between a f(R)=R+aRn−1+bR2 theory, with a , b and n free parameters, and the α -Attractors. We then calculate the predictions of the model f(R)=R+aRn−1+bR2 on the scalar spectral index ns and the tensor-to-scalar ratio r and show that the power law correction Rn−1 allows for a production of gravitational waves enhanced with respect to the one in the Starobinsky model, while maintaining a viable prediction on ns . We also investigate the case of a single power law f(R)=γR2−δ theory, with γ and δ free parameters. We calculate analytically the predictions of this model on the scalar spectral index ns and the tensor-to-scalar ratio r and the values of δ which are allowed from the current observational results. We find that −0.015<δ<0.016 , confirming once again the excellent agreement between the Starobinsky model and observation.

T. Miranda, J. C. Fabris, O. F. Piattella, "Reconstructing a f(R) theory from the α-Attractors" (July 19, 2017)

This implies a 95% upper bound on r=0.05 as opposed to the current upper bound of r=0.11.

Starobinsky Inflation (which implies f(R) gravity) is also supported by another recent study:

We obtain a differential equation which allows to reconstruct a

T. Miranda, J. C. Fabris, O. F. Piattella, "Reconstructing a f(R) theory from the α-Attractors" (July 19, 2017)

## 5 comments:

This sounds like a dodgy paper, several times over. Wait a while and I'm sure you'll see it debunked.

Not sure why you would doubt the paper. (The first one anyway). Looks legit to me.

By the way, if you combine the BICEP and Keck revised estimates, you get a best fit of r= -0.006 (a simple average since the margins of error are the same), which is equivalent to r=0 since r>=0, and you get a 95% exclusion of values in excess of r=0.05 (the mean plus two sigma of the combined error of +/- 0.028). The error bars are sufficiently big that the exclusion isn't all that dramatic, although it is still much more tightly constrained than the old results.

It's precisely this set of claims... that by definition r>=0, but our best fit is r<0, "therefore" r=0 and we can rule out theories with a positive but unobservably small r. That makes no sense at all.

Physicists use Gaussian error distributions that include unphysical amounts all of the time. In a case like this one, if the best fit value is impossible, they use the boundary value as the prediction (i.e. r=0) and then the positive range is the part of the Gaussian distribution which is in the physically possible range (i.e. r<= 0.05).

The old values were r=0.04, r=0.09 ad r<=0.11, so honestly, while it is an important refinement, it isn't even a huge one.

The theories that are ruled out are those with r>0.05 (which is observable). The theories that are not ruled out have a value of r<=0.05 (in which some would have an observable r and some would not), which makes lots of sense in a scenario where the observed value of r is consistent with and a best fit to zero.

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