Abstract
A large inflationary tensor-to-scalar ratio r0.002=0.20−0.05+0.07 is reported by the BICEP2 team based on their B-mode polarization detection, which is outside of the 95% confidence level of the Planck best fit model. We explore several possible ways to reduce the tension between the two by considering a model in which αs, nt, ns and the neutrino parameters Neff and Σmν are set as free parameters. Using the Markov Chain Monte Carlo (MCMC) technique to survey the complete parameter space with and without the BICEP2 data, we find that the resulting constraints on r0.002 are consistent with each other and the apparent tension seems to be relaxed. Further detailed investigations on those fittings suggest that Neff probably plays the most important role in reducing the tension. We also find that the results obtained from fitting without adopting the consistency relation do not deviate much from the consistency relation. With available Planck, WMAP, BICEP2 and BAO data sets altogether, we obtain r0.002=0.14−0.11+0.05, nt=0.35−0.47+0.28, ns=0.98−0.02+0.02, and αs=−0.0086−0.0189+0.0148; if the consistency relation is adopted, we get r0.002=0.22−0.06+0.05.
Highlights
The BICEP2 experiment[1, 2], a dedicated cosmic microwave background (CMB) polarization experiment, has announced recently the detection of the B-mode polarization in CMB, based on an observation of about 380 square degrees low-foreground area of sky during 2010 to 2012 in the South Pole
The BICEP2 team [1] pointed out that a simple way to relax this tension is to take the running of spectrum index into account, but large |αs| leads to an unacceptably small value of e-folds number for slow roll inflation[27]
We find that with the inclusion of the neutrino parameters, there is no significant conflict between the result of including and excluding the BICEP2 data set, the allowed parameter range or region overlap with each other in these two cases
Summary
The BICEP2 experiment[1, 2], a dedicated cosmic microwave background (CMB) polarization experiment, has announced recently the detection of the B-mode polarization in CMB, based on an observation of about 380 square degrees low-foreground area of sky during 2010 to 2012 in the South Pole. The BICEP2 team reported their measured value of tensorto-scalar ratio, at scale k = 0.002 Mpc−1, as r0.002 = 0.20+−00..0075, based on the lensed-ΛCDM+tensor model. Some mechanisms have been proposed to alleviate this tension [26], by (a) adjusting the running of the scalar power spectrum tilt; (b) considering the blue tilt tensor power spectrum; and (c) including the effect of the neutrinos. The BICEP2 team [1] pointed out that a simple way to relax this tension is to take the running of spectrum index into account, but large |αs| leads to an unacceptably small value of e-folds number for slow roll inflation[27]. We derive constraints using the publicly available code COSMOMC [46], which implements a MetropolisHastings algorithm to perform a MCMC simulation in order to fit the cosmological parameters This method provides reliable error estimates on the measured variables.
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