Compatibility of Planck and BICEP2 results in light of inflation

Abstract

We investigate the implications for inflation of the detection of B-modes polarization in the Cosmic Microwave Background (CMB) by BICEP2. We show that the hypothesis of primordial origin of the measurement is favored only by the first four bandpowers, while the others would prefer unreasonably large values of the tensor-to-scalar ratio. Using only those four bandpowers, we carry out a complete analysis in the cosmological and inflationary slow-roll parameter space using the BICEP2 polarization measurements alone and extract the Bayesian evidences and complexities for all the Encyclopaedia Inflationaris models. This allows us to determine the most probable and simplest BICEP2 inflationary scenarios. Although this list contains the simplest monomial potentials, it also includes many other scenarios, suggesting that focusing model building efforts on large field models only is unjustified at this stage. We demonstrate that the sets of inflationary models preferred by Planck alone and BICEP2 alone are almost disjoint, indicating a clear tension between the two data sets. We address this tension with a Bayesian measure of compatibility between BICEP2 and Planck. We find that for models favored by Planck the two data sets tend to be incompatible, whereas there is a moderate evidence of compatibility for the BICEP2 preferred models. As a result, it would be premature to draw any conclusion on the best Planck models, such as Starobinsky and/or Kähler moduli inflation. For the subset of scenarios not exhibiting data sets incompatibility, we update the evidences and complexities using both data sets together.

Tensors, BICEP2 results, prior dependence, and dust

“…There were various attempts at addressing the discrepancy by invoking a cosmological origin. These branched mainly into investigating modifications of the scalar sector of the perturbations as well as parameters which are degenerate with it [8][9][10][11][12][13][14], and into analyses considering a positive value for the tilt of the tensor perturbations n T [11,[15][16][17][18][19][20][21] which would be in contradiction to normal models of inflation. However, these analyses make prior assumptions in the modeling of the tensor perturbations which we shall show may be inappropriate.…”

Analysis of the Planck data

“…A similar analysis has been performed for Planck plus BICEP2 [10], assuming that the Bmodes detected by BICEP2 are of primordial origin, and using only the first four band powers (the others prefering a large value of the tensor-to-scalar ratio already strongly disfavored by Planck and WMAP).…”

“…This section is mostly based on the recent work by J. Martin, C. Ringeval, R. Trotta and V. Vennin [5,10], to which we invite the interested reader to refer for further details.…”

“…One can rewrite them in e-fold time N 10) and one sees that the scalar field evolves independently of the Hubble rate dynamics.…”

“…This equation is easily integrated when w is constant. One has 10) where Ω K0 is the curvature today. Since it is constrained by observations (|Ω − 1| 0.01 [17]) one has roughly at radiation-matter equality 11) and at the Planck time,…”