General Single-field Inflation Model Research Articles

Planck2018 results

We analyse thePlanckfull-mission cosmic microwave background (CMB) temperature andE-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results:fNLlocal= −0.9 ± 5.1;fNLequil= −26 ± 47; andfNLortho= −38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5σ. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of thePlanckCMB bispectrum. Our final constraint on the local primordial trispectrum shape isgNLlocal= (−5.8 ± 6.5) × 104(68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

Planck2013 results. XXIV. Constraints on primordial non-Gaussianity

The Planck nominal mission cosmic microwave background (CMB) maps yield unprecedented constraints on primordial non-Gaussianity (NG). Using three optimal bispectrum estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result fNL^local= 2.7+/-5.8, fNL^equil= -42+/-75, and fNL^ortho= -25+\-39 (68% CL statistical). NG is detected in the data; using skew-C_l statistics we find a nonzero bispectrum from residual point sources, and the ISW-lensing bispectrum at a level expected in the LambdaCDM scenario. The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are confirmed by skew-C_l, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, 3-dimensional reconstructions of the Planck CMB bispectrum and thus derive constraints on early-Universe scenarios that generate primordial NG, including general single-field models of inflation, excited initial states (non-Bunch-Davies vacua), and directionally-dependent vector models. We provide an initial survey of scale-dependent feature and resonance models. These results bound both general single-field and multi-field model parameter ranges, such as the speed of sound, c_s \geq 0.02 (95% CL), in an effective field theory parametrization, and the curvaton decay fraction r_D \geq 0.15 (95% CL). The Planck data significantly limit the viable parameter space of the ekpyrotic/cyclic scenarios. The amplitude of the 4-point function in the local model tauNL < 2800 (95% CL). These constraints represent the highest precision tests to date of physical mechanisms for the origin of cosmic structure.

Strong restriction on inflationary vacua from the local gauge invariance III: Infrared regularity of graviton loops

It has been claimed that the super-Hubble modes of the graviton generated during inflation can make loop corrections diverge. Even if we introduce an infrared (IR) cutoff at a comoving scale as an ad hoc but practical method of regularization, we encounter secular growth, which may lead to the breakdown of perturbative expansion for a sufficiently long-lasting inflation. In this paper, we show that the IR pathology concerning the graviton can be attributed to the presence of residual gauge degrees of freedom in the local observable universe, as in the case of the adiabatic curvature perturbation. We will show that choosing the Euclidean vacuum as the initial state ensures invariance under the above-mentioned residual gauge transformations. We will also show that, as long as we consider a gauge invariant quantity in the local universe, we encounter neither IR divergence nor secular growth. The argument in this paper applies to general single-field models of inflation up to a sufficiently high order in perturbation.

Full bispectra from primordial scalar and tensor perturbations in the most general single-field inflation model

We compute the full bispectra, namely both auto- and cross- bispectra, of primordial curvature and tensor perturbations in the most general single-field inflation model whose scalar and gravitational equations of motion are of second order. The formulae in the limits of k-inflation and potential-driven inflation are also given. These expressions are useful for estimating the full bispectra of temperature and polarization anisotropies of the cosmic microwave background radiation.

Constraints on primordial gravitational waves with variable sound speed from current CMB data

We make a comprehensive investigation of the observational effect of the inflation consistency relation. We focus on the general single-field inflation model with the consistency relation $r=-8c_s n_t$, and investigate the observational constraints of sound speed $c_s$ by using the Seven-Year WMAP data, the BICEP tensor power spectrum data, and the constraints on $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ from the Five-Year WMAP observations. We find that the constraints on the tensor-to-scalar ratio $r$ is much tighter if $c_s$ is small, since a large tilt $n_t$ is strongly constrained by the observations. We obtain $r<0.37, 0.27$ and 0.09 ($dn_s/d\ln k=0$) for $c_s$=1, 0.1 and 0.01 models at 95.4% confidence level. When taking smaller values of $c_s$, the positive correlation between $r$ and $n_s$ also leads to slightly tighter constraint on the upper bound of $n_s$, while the running of scalar spectral index $dn_s/d\ln k$ is generally unaffected. For the sound speed $c_s$, it is not well constrained if only the CMB power spectrum data is used, while the constraints are obtainable by taking $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ priors into account. With the constraining data of $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$, we find that, $c_s\lesssim 0.01$ region is excluded at 99.7% CL, and the $c_s=1$ case (the single-field slow-roll inflation) is slightly disfavored at 68.3% CL. In addition, the inclusion of $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ into the analysis can improve the constraints on $r$ and $n_s$. We further discuss the implications of our constraints on the test of inflation models.

Generalized Higgs inflation

We study Higgs inflation in the context of generalized $G$-inflation, i.e., the most general single-field inflation model with second-order field equations. The four variants of Higgs inflation proposed so far in the literature can be accommodated at one time in our framework. We also propose yet another class of Higgs inflation, the running Einstein inflation model, that can naturally arise from the generalized $G$-inflation framework. As a result, five Higgs inflation models in all should be discussed on an equal footing. Concise formulas for primordial fluctuations in these generalized Higgs inflation models are provided, which will be helpful to determine which model is favored from the future experiments and observations such as the Large Hadron Collider and the Planck satellite.

A field range bound for general single-field inflation

We explore the consequences of a detection of primordial tensor fluctuations for general single-field models of inflation. Using the effective theory of inflation, we propose a generalization of the Lyth bound that applies to models of inflation coupled to Einstein gravity.Our strongest bound applies to all single-field models with two-derivative kinetic terms for the scalar fluctuations and is always stronger than the corresponding bound for slow-roll models.This shows that non-trivial dynamics of the inflaton can't evade the Lyth bound. We also present a weaker, but more universal bound that holds when the Null Energy Condition (NEC) is satisfied at horizon crossing.

G-INFLATION: INFLATION WITH THE MOST GENERAL SECOND-ORDER FIELD EQUATIONS

In this talk, we have discussed generalized Galileons as a framework to develop the most general single-field inflation models ever, (Generalized) G-inflation, containing previous examples such as k-inflation, extended inflation, and new Higgs inflation as special cases. We have also investigated the background and perturbation evolution in this model, calculating the most general quadratic actions for tensor and scalar cosmological perturbations to give the stability criteria and the power spectra of primordial fluctuations.

Primordial Non-Gaussianities of Gravitational Waves in the Most General Single-Field Inflation Model with Second-Order Field Equations

We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in the most general single-field inflation model with second-order field equations. It is shown that the most general cubic action for the tensor perturbation h(ij) is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each h(ij). The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct detection experiments.

Generalized G-Inflation: --Inflation with the Most General Second-Order Field Equations--

We study generalized Galileons as a framework to develop the most general single-field inflation models ever, Generalized G-inflation, containing yet further generalization of G-inflation, as well as previous examples such as k-inflation, extended inflation, and new Higgs inflation as special cases. We investigate the background and perturbation evolution in this model, calculating the most general quadratic actions for tensor and scalar cosmological perturbations to give the stability criteria and the power spectra of primordial fluctuations. It is pointed out in the Appendix that the Horndeski theory and the generalized Galileons are equivalent. In particular, even the non-minimal coupling to the Gauss-Bonnet term is included in the generalized Galileons in a non-trivial manner.

Non-Gaussianity of quantum fields during inflation

In this paper, we discuss how non-Gaussianity of cosmological perturbations arises from inflation. After introducing the in–in formalism to calculate the n-point correlation function of quantum fields, we present the computation of the bispectrum of the curvature perturbation generated in general single-field inflation models. The shapes of the bispectrum are compared with the local-type non-Gaussianity that arises from nonlinear dynamics on super-horizon scales.

Large primordial trispectra in general single field inflation

We compute the large scalar four-point correlation functionsin general single field inflation models, where the inflatonLagrangian is anarbitrary function of the inflaton and its first derivative.We find that theleading order trispectra have four different shapes determined bythree parameters. We study features in these shapes that can be used todistinguish among themselves, and between them and the trispectra of the local form. For thepurpose of data analyses, we give two simple representative formsfor these ``equilateral trispectra''. Wealso study the effects on the trispectra if the initial state of inflationdeviates from the standard Bunch-Daviesvacuum.

Enhancement of superhorizon scale inflationary curvature perturbations

We show that there exists a simple mechanism which can enhance the amplitude of curvature perturbations on superhorizon scales, relative to their amplitude at horizon crossing, even in some single-field inflation models. We give a criterion for this enhancement in general single-field inflation models; the condition for a significant effect is that the quantity $a\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\varphi}}/H$ become sufficiently small, as compared to its value at horizon crossing, for some time interval during inflation.