Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data

Abstract

Abstract.The implications of the WMAP (Wilkinson Microwave Anisotropy Probe) third year data for inflation are investigated using both the slow-roll approximation and an exact numerical integration of the inflationary power spectra including a phenomenological modelling of the reheating era. At slow-roll leading order, the constraints ǫ 1 < 0.022 and −0.07 < ǫ 2 < 0.07 are obtained at 95% CL (Confidence Level) implying a tensor-to-scalar ratio r 10 < 0.21 and a Hubble parameter during inflation H/m Pl < 1.3 × 10 −5 . At next-to-leading order, a tendency for ǫ 3 > 0 is observed. With regards to the exact numerical integration, large field models, V (φ) ∝ φ p , with p > 3.1 are now excluded at 95% CL. Small field models, V (φ) ∝ 1 − (φ/µ) p , are still compatible with the data for all values of p. However, if µ/m Pl < 10 is assumed, then the case p = 2 is slightly disfavoured. In addition, mild constraints on the reheating temperature for an extreme equation of state w reh −1/3 are found, namely T reh > 2 TeV at 95% CL. Hybrid models are disfavoured by the data, the best fit model having ∆χ 2 ≃ +5 with two extra parameters in comparison with large field models. Running mass models remain compatible, but no prior independent constraints can be obtained. Finally, superimposed oscillations of trans-Planckian origin are studied. The vanilla slow-roll model is still the most probable one. However, the overall statistical weight in favour of superimposed oscillations has increased in comparison with the WMAP first year data, the amplitude of the oscillations satisfying 2|x|σ 0 < 0.76 at 95% CL. The best fit model leads to an improvement of ∆χ 2 ≃ −12 for 3 extra parameters. Moreover, compared to other oscillatory patterns, the logarithmic shape is favoured.

Information gain on reheating: The one bit milestone

“…[11,12] (see also subsequent works [13][14][15][16]), the epoch of reheating, the era during which the vacuum energy of the inflaton is converted into * Electronic address: jmartin@iap.fr † Electronic address: christophe.ringeval@uclouvain.be ‡ Electronic address: vincent.vennin@port.ac.uk radiation, impacts the predicted values of the scalar spectral index and tensor-to-scalar ratio for all inflationary models. As a result, reducing uncertainties on the measured values of these two parameters provides some nontrivial information on how reheating proceeds, even if inflation is as simple as a slow-roll single-field scenario [17].…”

“…Within a given model of inflation, predicting the scalar spectral index and tensor-to-scalar ratio requires us to specify a value for the so-called rescaled reheating parameter R reh [11]. More specifically, once R reh is given, one can uniquely determine the number of e-folds before the end of inflation at which an observable mode k * crosses the Hubble radius [18], a quantity which is required to get the actual values of the observed slowroll parameters [19,20].…”

Classical bounce: Constraints and consequences

“…We found however that in a large part of the parameter space in which a bounce is realized (see Section III), the spectrum of CMB multipoles (Fig. 9) is merely modified in a way reminiscent of superimposed oscillations, a possibility that has attracted some attention in recent years [33], and was found to be not inconsistent with the data. Any oscillations in the matter power spectrum or CMB multipoles are expected to be mostly smoothed out either by transfer functions or observational windowing functions.…”

“…This can however be handled by assuming the bounce-making negative energy component to be merely phenomenological, acting only for a short time, the bounce duration, in general assumed comparable with the Planck scale. In any case, there are no generic properties that can be derived in a model-independent way as in slow-roll inflation [33]. Very often, though, it is found that a reasonable model connects two almost de Sitter phases.…”

Constraining scalar-Gauss-Bonnet inflation by reheating, unitarity, and Planck data

“…However, recently there has been an interesting development [15,19,20] to distinguish various inflationary models by indirectly looking at the possible physically motivated reheating mechanism through the evaluation of a particular observable scale and the entropy density till to- , and equal number of e-folding parameters N re1 = N re2 .The light blue shaded region corresponds to the 1σ bounds on ns from Planck. The brown shaded region corresponds to the 1σ bounds of a further CMB experiment with sensitivity ±10 −3 [17,18], using the same central ns value as Planck.…”