Planck2013 results. XXII. Constraints on inflation

Abstract

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be n s = 0.9603 ± 0.0073, ruling out exact scale invariance at over 5σ. Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n ≥ 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dn s /dln k = −0.0134 ± 0.0090. We verify these conclusions through a numerical analysis, which makes no slowroll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by ∆χ 2 eff ≈ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on f NL. Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the χ 2 eff by approximately 4 as a result of slightly lowering the theoretical prediction for the < ∼ 40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.

Inflationary Cosmology in Modified Gravity Theories

“…Indeed, the WMAP and Planck data [2][3][4][5][6][7][8] support a kind of the trace-anomaly driven inflation with the R 2 term. Such a theory can be regarded as modified gravity because the R 2 term or its higher derivative term of the trace-anomaly term R, which leads to the long enough inflation and graceful exit from it [21], is the effective action of gravity, where is the covariant d'Alembertian for a scalar quantity.…”

“…Inflation in the early universe has recently been studied much more extensively because of the BICEP2 experiment [1] in terms of the primordial gravitational waves, in addition to the Wilkinson Microwave anisotropy probe (WMAP) [2][3][4][5][6] and the Planck satellite [7,8] on the unisotropy of the cosmic microwave background (CMB) radiation. For a standard inflationary scenario like chaotic inflation [9], the existence of the inflaton field is assumed, whose potential contributes to inflation.…”

Inflation in no-scale supergravity

“…In the point of view of conformal symmetry, expected to hold at the high curvature regime where masses are negligible, an additional motivation to consider the Starobinsky model is supplied by the fact that the quadratic curvature term is bound to be generated by the conformal anomaly at the quantum level. Actually, the Starobinsky model is among the few possibilities realizing slow-roll inflation that is in perfect agreement with the PLANCK experiment data [6], although its predictions were challenged by BICEP2 results [7], claiming the discovery of primordial gravitational waves resulting to a ratio r ¼ 0.16 þ0.06 −0.05 . In the meantime, the Planck Collaboration released new data of increased precision [8], reconfirming its previous analyses, according to which r < 0.11.…”

Polyinstanton axion inflation

“…The e-folding number is required to be larger than 50 in order to solve the problems of the standard cosmology. Furthermore, the Planck results constrain the power spectrum of curvature perturbation P ξ , its spectral index n s , and the tensor-toscalar ratio r [30,31], These can be written by use of the slow-roll parameters as…”