Scalar Spectral Index Research Articles

Tachyon inflation with steep potentials

Within the framework of tachyon inflation, we consider different steep potentials and check their viability in light of the Planck 2015 data. We see that in this scenario, the inverse power-law potential $V(\phi)=V_{0}(\phi/\phi_{0})^{-n}$ with $n=2$ leads to the power-law inflation with the scale factor $a(t)\propto t^{q}$ where $q>1$, while with $n<2$, it gives rise to the intermediate inflation with the scale factor $a(t)\propto\exp\left(At^{f}\right)$ where $A>0$ and $0<f<1$. We find that, although the inverse power-law potential with $n\leq 2$ is completely ruled out by the Planck 2015 data, the result of this potential for $n>2$ can be compatible with the 95\% CL region of Planck 2015 TT, TE, EE+lowP data. We further conclude that the exponential potential $V(\phi)=V_{0}e^{-\phi/\phi_{0}}$, the inverse $\cosh$ potential $V(\phi)=V_{0}/\cosh(\phi/\phi_{0})$, and the mutated exponential potential $V(\phi)=V_{0}\left[1+(n-1)^{-(n-1)}(\phi/\phi_{0})^{n}\right]e^{-\phi/\phi_{0}}$ with $n=4$, can be consistent with the 95\% CL region of Planck 2015 TT, TE, EE+lowP data. Moreover, using the $r-n_s$ constraints on the model parameters, we also estimate the running of the scalar spectral index $dn_{s}/d\ln k$ and the local non-Gaussianity parameter $f_{{\rm NL}}^{{\rm local}}$. We find that the lower and upper bounds evaluated for these observables are compatible with the Planck 2015 results.

Thermal inflation with a thermal waterfall scalar field coupled to a light spectator scalar field

A new model of thermal inflation is introduced, in which the mass of the thermal waterfall field is dependent on a light spectator scalar field. Using the $\delta N$ formalism, the "end of inflation" scenario is investigated in order to ascertain whether this model is able to produce the dominant contribution to the primordial curvature perturbation. A multitude of constrains are considered so as to explore the parameter space, with particular emphasis to key observational signatures. For natural values of the parameters, the model is found to yield a sharp prediction for the scalar spectral index and its running, well within the current observational bounds.

Chaotic initial conditions for nonminimally coupled inflation via a conformal factor with a zero

Nonminimally coupled inflation models based on a nonminimal coupling $\xi \phi^{2} R$ and a $\phi^{4}$ potential are in excellent agreement with the scalar spectral index observed by Planck. Here we consider the modification of these models by a conformal factor with a zero. This enables a nonminimally coupled model to have a Planck-scale potential energy density at large values of the inflaton field, which can account for the smooth, potential-dominated volume that is necessary for inflation to start. We show that models with a conformal factor zero generally predict a correlated increase of the spectral index $n_{s}$ and tensor-to-scalar ratio $r$. For values of $n_{s}$ that are within the present $2-\sigma$ bounds from Planck, modification by $\Delta r$ as large as 0.0013 is possible, which is large enough to be measured by next generation cosmic microwave background polarization satellites.

K-essence for warm inflation on the brane

In this paper, [Formula: see text]-inflation is analyzed in warm braneworld scenario. A general class of [Formula: see text]-essence models with power-law kinetic term is investigated and weak and strong dissipation regimes are studied. Scalar perturbations and spectral index are derived. The results are discussed and applied to specific examples.

Shaft potential inspired warm inflation

We discuss the warm inflation in the presence of shaft potential [Formula: see text], tachyon scalar field and the generalized form of dissipative coefficient [Formula: see text]. In this respect, we investigate the inflationary parameters (slow-roll parameters, number of e-folds, scalar-tensor power spectra, spectral indices, tensor-to-scalar ratio and running of scalar spectral index) in both strong and weak dissipative regimes. It is interesting to mention that our inflationary parametric results (tensor-scalar ratio, spectral index and running of spectral) are consistent with the recent observational data such as BICEP[Formula: see text], WMAP[Formula: see text] and latest Planck data.

Dynamics of warm power-law plateau inflation with a generalized inflaton decay rate: predictions and constraints after Planck 2015

In the present work, we study the consequences of considering a new family of single-field inflation models, called power-law plateau inflation, in the warm inflation framework. We consider the inflationary expansion is driven by a standard scalar field with a decay ratio Gamma having a generic power-law dependence with the scalar field phi and the temperature of the thermal bath T given by Gamma (phi ,T)=C_{phi }frac{T^a}{phi ^{a-1}}. Assuming that our model evolves according to the strong dissipative regime, we study the background and perturbative dynamics, obtaining the most relevant inflationary observable as the scalar power spectrum, the scalar spectral index and its running and the tensor-to-scalar ratio. The free parameters characterizing our model are constrained by considering the essential condition for warm inflation, the conditions for the model evolves according to the strong dissipative regime and the 2015 Planck results through the n_mathrm{s}–r plane. For completeness, we study the predictions in the n_mathrm{s}–mathrm{d}n_mathrm{s}/mathrm{d}ln k plane. The model is consistent with a strong dissipative dynamics and predicts values for the tensor-to-scalar ratio and for the running of the scalar spectral index consistent with current bounds imposed by Planck and we conclude that the model is viable.

KiDS-450: testing extensions to the standard cosmological model

We test extensions to the standard cosmological model with weak gravitational lensing tomography using 450 deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). In these extended cosmologies, which include massive neutrinos, nonzero curvature, evolving dark energy, modified gravity, and running of the scalar spectral index, we also examine the discordance between KiDS and cosmic microwave background measurements from Planck. The discordance between the two datasets is largely unaffected by a more conservative treatment of the lensing systematics and the removal of angular scales most sensitive to nonlinear physics. The only extended cosmology that simultaneously alleviates the discordance with Planck and is at least moderately favored by the data includes evolving dark energy with a time-dependent equation of state (in the form of the $w_0-w_a$ parameterization). In this model, the respective $S_8 = \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$ constraints agree at the $1\sigma$ level, and there is `substantial concordance' between the KiDS and Planck datasets when accounting for the full parameter space. Moreover, the Planck constraint on the Hubble constant is wider than in LCDM and in agreement with the Riess et al. (2016) direct measurement of $H_0$. The dark energy model is moderately favored as compared to LCDM when combining the KiDS and Planck measurements, and remains moderately favored after including an informative prior on the Hubble constant. In both of these scenarios, marginalized constraints in the $w_0-w_a$ plane are discrepant with a cosmological constant at the $3\sigma$ level. Moreover, KiDS constrains the sum of neutrino masses to 4.0 eV (95% CL), finds no preference for time or scale dependent modifications to the metric potentials, and is consistent with flatness and no running of the spectral index. The analysis code is public at https://github.com/sjoudaki/kids450

Inflection point in running kinetic term inflation

In this work, we calculate the general form of the scalar potential with polynomial superpotential in the framework of running kinetic term inflation, then focus on a polynomial superpotential with two terms and obtain the inflection point inflationary model. We study the inflationary dynamics and show that the predicted value of the scalar spectral index and tensor-to-scalar ratio can lie within the [Formula: see text] confidence region allowed by the result of Planck 2015.

Minimal Higgs inflation

In this paper we propose minimal Higgs inflation scenarios by non-polynomial modification of the Higgs potential. The modification is done in such a way that it creates a flat plateau for a huge range of field values at the inflationary energy scale μ≃(λ)1/4α. Assuming the perturbative Higgs quartic coupling, λ≃O(1), our model prediction for all the cosmologically relevant quantities, (ns,r,dnsk), fit extremely well with observations made by PLANCK. For both the models the inflation energy scale turned out to be μ≃(1014,1015) GeV. Considering observed central value of the scalar spectral index, ns=0.968, models predict efolding number, N=(52,47). Within a wide range of viable parameter space, we found that the prediction of tensor to scalar ratio r(≤10−5) is far below the current experimental limit. The prediction for the running of scalar spectral index, dnsk, remains very small. We also computed the background field dependent unitarity scale Λ(h), which turned out to be much larger than the aforementioned inflationary energy scale.

Bounce and cyclic cosmology in weakly broken Galileon theories

We investigate the bounce and cyclicity realization in the framework of weakly broken Galileon theories. We study bouncing and cyclic solutions at the background level, reconstructing the potential and the Galileon functions that can give rise to a given scale factor and presenting analytical expressions for the bounce requirements. We proceed to a detailed investigation of the perturbations, which after crossing the bouncing point give rise to various observables, such as the scalar and tensor spectral indices and the tensor-to-scalar ratio. Although the scenario at hand shares the disadvantage of all bouncing models, namely that it provides a large tensor-to-scalar ratio, introducing an additional light scalar significantly reduces it through the kinetic amplification of the isocurvature fluctuations.

Axion, μ term, and supersymmetric hybrid inflation

We show how successful supersymmetric hybrid inflation is realized in realistic models where the resolution of the minimal supersymmetric standard model mu problem is intimately linked with axion physics. The scalar fields that accompany the axion, such as the saxion, are closely monitored during and after inflation to ensure that the axion isocurvature perturbations lie below the observational limits. The scalar spectral index n_s is about 0.96 - 0.97, while the tensor-to-scalar ratio r, a canonical measure of gravity waves, lies well below the observable range in our example. The axion domain walls are inflated away, and depending on the axion decay constant f_a and the magnitude of the mu parameter, the axions and/or the lightest supersymmetric particle compose the dark matter in the universe. Non-thermal leptogenesis is naturally implemented in this class of models.

No-scale mu -term hybrid inflation

To solve the fine-tuning problem in mu -term hybrid inflation, we will realize the supersymmetry scenario with the TeV-scale supersymmetric particles and intermediate-scale gravitino from anomaly mediation, which can be consistent with the WMAP and Planck experiments. Moreover, we for the first time propose the mu -term hybrid inflation in no-scale supergravity. With four scenarios for the SU(3)_Ctimes SU(2)_Ltimes SU(2)_Rtimes U(1)_{B-L} model, we show that the correct scalar spectral index n_s can be obtained, while the tensor-to-scalar ratio r is predicted to be tiny, about 10^{-10}–10^{-8}. Also, the SU(2)_Rtimes U(1)_{B-L} symmetry breaking scale is around 10^{14} GeV, and all the supersymmetric particles except gravitino are around the TeV scale, while the gravitino mass is around 10^{9}–10^{10} GeV. Considering the complete potential terms linear in S, we for the first time show that the tadpole term, which is the key for such kind of inflationary models to be consistent with the observed scalar spectral index, vanishes after inflation. Thus, to obtain the mu term, we need to generate the supersymmetry breaking soft term A^{S Phi Phi '}_{kappa } kappa S Phi Phi ' due to A^{S Phi Phi '}_{kappa }=0 in no-scale supergravity, where Phi and Phi ' are vector-like Higgs fields at high energy. We show that the proper A^{S Phi Phi '}_{kappa } kappa S Phi Phi ' term can be obtained in the M-theory inspired no-scale supergravity. We also point out that A^{S Phi Phi '}_{kappa } around 700 GeV can be generated via the renormalization group equation running from string scale. We briefly comment on the supersymmetry phenomenological consequences as well.

Hamilton\u2013Jacobi approach for quasi-exponential inflation: predictions and constraints after Planck 2015 results

In the present work we study the consequences of considering an inflationary universe model in which the Hubble rate has a quasi-exponential dependence in the inflaton field, given by H(phi )=H_{mathrm{inf}}exp [frac{frac{phi }{m_mathrm{p}}}{pleft( 1+frac{phi }{m_mathrm{p}}right) }]. We analyze the inflation dynamics under the Hamilton–Jacobi approach, which allows us to consider H(phi ), rather than V(phi ), as the fundamental quantity to be specified. By comparing the theoretical predictions of the model together with the allowed contour plots in the n_mathrm{s}-r plane and the amplitude of primordial scalar perturbations from the latest Planck data, the parameters charactering this model are constrained. The model predicts values for the tensor-to-scalar ratio r and for the running of the scalar spectral index mathrm{d}n_mathrm{s}/ mathrm{d}ln k consistent with the current bounds imposed by Planck, and we conclude that the model is viable.

Generalized Brans–Dicke inflation with a quartic potential

Within the framework of Brans–Dicke gravity, we investigate inflation with the quartic potential, λφ4/4, in the presence of generalized Brans–Dicke parameter ωGBD(φ). We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of general form of the potential U(φ) and ωGBD(φ). For the quartic potential, our results show that the predictions of the model are in well agreement with the Planck 2015 data for the generalized Brans–Dicke parameters ωGBD(φ)=ω0φn and ω0ebφ. This is in contrast with both the Einstein and standard Brans–Dicke gravity, in which the result of quartic potential is disfavored by the Planck data.

Dynamics of modified Chaplygin gas inflation on the Brane with bulk viscous pressure

We investigate the role of bulk viscous pressure on the warm inflationary modified Chaplygin gas (MCG) in braneworld framework in the presence of standard scalar field. We assume the intermediate inflationary scenario in strong dissipative regime and constructed the inflaton, potential, entropy density, slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor-to-scalar ratio. We develop various trajectories such as [Formula: see text], [Formula: see text] and [Formula: see text] (where [Formula: see text] is the spectral index, [Formula: see text] is the running of spectral index, [Formula: see text] is the number of e-folds and [Formula: see text] is tensor-to-scalar ratio) for variable as well as constant dissipation and bulk viscous coefficients at high dissipative regime. It is interesting to remark here that our results of these parameters are compatible with recent observational data such as WMAP [Formula: see text], BICEP[Formula: see text] and Planck data.

Inflationary dynamics in f(𝒢) gravity

This paper investigates inflationary dynamics for isotropic and homogeneous universe model in the background of [Formula: see text] gravity. We construct Hubble-flow functions, slow-roll parameters, amplitude of scalar power spectrum, spectral index and tensor–scalar ratio for a particular form of equation of state which describes quasi-de Sitter expansion. The dynamics of inflationary epoch is analyzed for scalar field as well as fluid cosmology with viable power-law [Formula: see text] model. We obtain different potential functions that correspond to chaotic inflation and Starobinsky type models. The graphical behavior of these parameters shows compatible results with observational Planck 2015 data in this gravity.

Unifying Inflation with the Axion, Dark Matter, Baryogenesis, and the Seesaw Mechanism.

A minimal extension of the standard model (SM) with a single new mass scale and providing a complete and consistent picture of particle physics and cosmology up to the Planck scale is presented. We add to the SM three right-handed SM-singlet neutrinos, a new vectorlike color triplet fermion, and a complex SM-singlet scalar σ that stabilizes the Higgs potential and whose vacuum expectation value at ∼10^{11} GeV breaks lepton number and a Peccei-Quinn symmetry simultaneously. Primordial inflation is produced by a combination of σ (nonminimally coupled to the scalar curvature) and the SM Higgs boson. Baryogenesis proceeds via thermal leptogenesis. At low energies, the model reduces to the SM, augmented by seesaw-generated neutrino masses, plus the axion, which solves the strong CP problem and accounts for the dark matter in the Universe. The model predicts a minimum value of the tensor-to-scalar ratio r≃0.004, running of the scalar spectral index α≃-7×10^{-4}, the axion mass m_{A}∼100 μeV, and cosmic axion background radiation corresponding to an increase of the effective number of relativistic neutrinos of ∼0.03. It can be probed decisively by the next generation of cosmic microwave background and axion dark matter experiments.

Hamilton-Jacobi formalism to warm inflationary scenario

Hamilton-Jacobi formalism as a powerful method is being utilized to reconsider warm inflationary scenario, where the scalar field as the main component deriving inflation interacts with other field. Separating the context to strong and weak dissipative regimes, the goal is followed for two popular function of dissipation coefficient. Applying slow-rolling approximations, the required perturbation parameters are extracted and by comparison to the latest Planck data, the free parameters are restricted. Possibility of producing an acceptable inflation is studied where the result shows that for all cases the model could successfully suggests amplitude of scalar perturbation, scalar spectral index , its running, and the tensor-to-scalar ratio.

How Gaussian can our Universe be?

Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of kℓ2/ks2, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × (ns−1).

The double-soft limit in cosmological correlation functions and graviton exchange effects

The graviton exchange effect on cosmological correlation functions is examined by employing the double-soft limit technique. A new relation among correlation functions that contain the effects due to graviton exchange diagrams in addition to those due to scalar-exchange and scalar-contact-interaction, is derived by using the background field method and independently by the method of Ward identities associated with dilatation symmetry. We compare these three terms, putting small values for the slow-roll parameters and (1−ns) ≈ 0.042, where ns is the scalar spectral index. It is argued that the graviton exchange effects are more dominant than the other two and could be observed in the trispectrum in the double-soft limit. Our observation strengthens the previous work by Seery, Sloth and Vernizzi, in which it has been argued that the graviton exchange dominates in the counter-collinear limit for single field slow-roll inflation.