Christophe Ringeval

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

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 epsilon1 0 is observed. With regard to the exact numerical integration, large field models, V(\phi)\propto \phi^p , with p > 3.1 are now excluded at the 95% CL. Small field models, V(\phi)\propto 1-(\phi /\mu)^p , are still compatible with the data for all values of p. However, if μ/mPl 2 TeV at the 95% CL. Hybrid models are disfavoured by the data, the best fit model having \Delta \chi ^2\simeq+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|σ0 < 0.76 at the 95% CL. The best fit model leads to an improvement of \Delta \chi^2\simeq-12 for three extra parameters. Moreover, compared to other oscillatory patterns, the logarithmic shape is favoured.

The best inflationary models after Planck

We compute the Bayesian evidence and complexity of 193 slow-roll single-field models of inflation using the Planck 2013 Cosmic Microwave Background data, with the aim of establishing which models are favoured from a Bayesian perspective. Our calculations employ a new numerical pipeline interfacing an inflationary effective likelihood with the slow-roll library ASPIC and the nested sampling algorithm MultiNest. The models considered represent a complete and systematic scan of the entire landscape of inflationary scenarios proposed so far. Our analysis singles out the most probable models (from an Occams razor point of view) that are compatible with Planck data, while ruling out with very strong evidence 34% of the models considered. We identify 26% of the models that are favoured by the Bayesian evidence, corresponding to 15 different potential shapes. If the Bayesian complexity is included in the analysis, only 9% of the models are preferred, corresponding to only 9 different potential shapes. These shapes are all of the plateau type.

Cosmological evolution of cosmic string loops

The existence of a scaling evolution for cosmic string loops in an expanding universe is demonstrated for the first time by means of numerical simulations. In contrast with what is usually assumed, this result does not rely on any gravitational back reaction effect and has been observed for loops as small as a few thousandths the size of the horizon. We give the energy and number densities of expected cosmic string loops in both the radiation and matter eras. Moreover, we quantify previous claims on the influence of the network initial conditions and the formation of numerically unresolved loops by showing that they only concern a transient relaxation regime. Some cosmological consequences are discussed.

First CMB Constraints on the Inflationary Reheating Temperature

We present the first Bayesian constraints on the single field inflationary reheating era obtained from cosmic microwave background (CMB) data. After demonstrating that this epoch can be fully characterized by the so-called reheating parameter, we show that it is constrained by the seven years Wilkinson microwave anisotropies probe (WMAP7) data for all large and small field models. An interesting feature of our approach is that it yields lower bounds on the reheating temperature which can be combined with the upper bounds associated with gravitinos production. For large field models, we find the energy scale of reheating to be higher than those probed at the Large Hadron Collider, rho(1/4)(reh) > 17.3 TeV at 95% of the confidence limit. For small field models, we obtain the two-sigma lower limits rho(1/4)(reh) > 890 TeV for a mean equation of state during reheating (w) over bar (reh) = -0.3 and rho(1/4)(reh) > 390 GeV for (w) over bar (reh) = -0.2. The physical origin of these constraints is pedagogically explained by means of the slow-roll approximation. Finally, when marginalizing over all possible reheating history, the WMAP7 data push massive inflation under pressure (p < 2.2 at 95% of the confidence limit where p is the power index of the large field potentials) while they slightly favor super-Planckian field expectation values in the small field models.

Exploring the superimposed oscillations parameter space

The space of parameters characterizing an inflationary primordial power spectrum with small superimposed oscillations is explored using Monte Carlo methods. The most interesting region corresponding to high frequency oscillations is included in the analysis. The oscillations originate from some new physics taking place at the beginning of the inflationary phase and characterized by the new energy scale Mc. It is found that the standard slow roll model remains the most probable one given the first-year WMAP data. At the same time, the oscillatory models fit the data better on average, which is consistent with previous works on the subject. This is typical of a situation where volume effects in the parameter space play a significant role. Then, we find the amplitude of the oscillations to be less than 22% of the mean amplitude and the new scale Mc to be such that H/Mc<6.6 × 10−4 at 1σ level, where H is the scale of inflation.

Observing inflationary reheating.

Reheating is the epoch which connects inflation to the subsequent hot big-bang phase. Conceptually very important, this era is, however, observationally poorly known. We show that the current Planck satellite measurements of the cosmic microwave background (CMB) anisotropies constrain the kinematic properties of the reheating era for most of the inflationary models. This result is obtained by deriving the marginalized posterior distributions of the reheating parameter for about 200 models of slow-roll inflation. Weighted by the statistical evidence of each model to explain the data, we show that the Planck 2013 measurements induce an average reduction of the posterior-to-prior volume by 40%. Making some additional assumptions on reheating, such as specifying a mean equation of state parameter, or focusing the analysis on peculiar scenarios, can enhance or reduce this constraint. Our study also indicates that the Bayesian evidence of a model can substantially be affected by the reheating properties. The precision of the current CMB data is therefore such that estimating the observational performance of a model now requires incorporating information about its reheating history.

Addendum to ‘‘Superimposed oscillations in the WMAP data?’’

We elaborate further on the possibility that the inflationary primordial power spectrum contains superimposed oscillations. We study various effects which could influence the calculation of the multipole moments in this case. We also present the theoretical predictions for two other cosmological observables, the matter power spectrum and the EE polarization channel.

Hunting Down the Best Model of Inflation with Bayesian Evidence

We present the first calculation of the Bayesian evidence for different prototypical single field inflationary scenarios, including representative classes of small field and large field models. This approach allows us to compare inflationary models in a well-defined statistical way and to determine the current “best model of inflation.” The calculation is performed numerically by interfacing the inflationary code FieldInf with MultiNest. We find that small field models are currently preferred, while large field models having a self-interacting potential of power p>4 are strongly disfavored. The class of small field models as a whole has posterior odds of approximately 3∶1 when compared with the large field class. The methodology and results presented in this article are an additional step toward the construction of a full numerical pipeline to constrain the physics of the early Universe with astrophysical observations. More accurate data (such as the Planck data) and the techniques introduced here should allow us to identify conclusively the best inflationary model.

CMB temperature bispectrum induced by cosmic strings

The Cosmic Microwave Background (CMB) bispectrum of the temperature anisotropies induced by a network of cosmic strings is derived for small angular scales, under the assumption that the principal cause of temperature fluctuations is the Gott-Kaiser-Stebbins (GKS) effect. We provide analytical expressions for all isosceles triangle configurations in Fourier space. Their overall amplitude is amplified as the inverse cube of the angle and diverges for flat triangles. The isosceles configurations generically lead to a negative bispectrum with a power law decay l^(-6) for large multipole l. However, collapsed triangles are found to be associated with a positive bispectrum whereas the squeezed triangles still exhibit negative values. We then compare our analytical estimates to a direct computation of the bispectrum from a set of 300 statistically independent temperature maps obtained from Nambu-Goto cosmic string simulations in a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. We find good agreement for the overall amplitude, the power law behaviour and angle dependency of the various triangle configurations. At l~500 the cosmic string GKS effect contributes approximately the same equilateral CMB bispectrum amplitude as an inflationary model with |fNL|~10^3, if the strings contribute about 10% of the temperature power spectrum at l=10. Current bounds on fNL are not derived using cosmic string bispectrum templates, and so our fNL estimate cannot be used to derive bounds on strings. However it does suggest that string bispectrum templates should be included in the search of CMB non-Gaussianities. Comment: 15 pages, 12 figures, uses RevTex. References and physical discussion added. Matches published version

Cosmic strings and their induced non-Gaussianities in the cosmic microwave background

Motivated by the fact that cosmological perturbations of inflationary quantum origin were born Gaussian, the search for non-Gaussianities in the cosmic microwave background (CMB) anisotropies is considered as the privileged probe of nonlinear physics in the early universe. Cosmic strings are active sources of gravitational perturbations and incessantly produce non-Gaussian distortions in the CMB. Even if, on the currently observed angular scales, they can only contribute a small fraction of the CMB angular power spectrum, cosmic strings could actually be the main source of its non-Gaussianities. In this paper, after having reviewed the basic cosmological properties of a string network, we present the signatures Nambu-Goto cosmic strings would induce in various observables ranging from the one-point function of the temperature anisotropies to the bispectrum and trispectrum. It is shown that string imprints are significantly different than those expected from the primordial type of non-Gaussianity and could therefore be easily distinguished.