Spectral Index Of Curvature Perturbations Research Articles

Defying eternal inflation in warm inflation with a negative running

It was pointed out previously [1] that a sufficiently negative running of the spectral index of curvature perturbations from (ordinary i.e. cold) inflation is able to prevent eternal inflation from ever occurring. Here, we reevaluate those original results, but in the context of warm inflation, in which a substantial radiation component (produced by the inflaton) exists throughout the inflationary period. We demonstrate that the same general requirements found in the context of ordinary (cold) inflation also hold true in warm inflation; indeed an even tinier amount of negative running is sufficient to prevent eternal inflation. This is particularly pertinent, as models featuring negative running are more generic in warm inflation scenarios. Finally, the condition for the existence of eternal inflation in cold inflation — that the curvature perturbation amplitude exceed unity on superhorizon scales — becomes more restrictive in the case of warm inflation. The curvature perturbations must be even larger, i.e. even farther out on the potential, away from the part of the potential where observables, e.g. in the Cosmic Microwave Background, are produced.

Refined swampland conjecture in deformed Starobinsky gravity

In order to validate or invalidate a large class of low energy effective theories, the swampland conjecture has attracted significant attention recently. It can be stated as inequalities on the potential of a scalar field which is conjectured to satisfy certain constraints. In this work, we discuss the theoretical viability of deformed Starobinsky gravity in light of the refined swampland conjectures. We consider the deformation of the form [Formula: see text] with [Formula: see text] being a constant. We then constrain [Formula: see text] using the spectral index of curvature perturbation [Formula: see text] and the tensor-to-scalar ratio [Formula: see text]. We demonstrate that the model under consideration is in strong tension with the refined swampland conjecture. However, regarding our analysis with proper choices of parameters [Formula: see text] and [Formula: see text], we discover that the model can always satisfy this new refined swampland conjecture. Therefore, the model might be in “landscape” since the “further refining de Sitter swampland conjecture” is satisfied.

Why Must Primordial Non-Gaussianity Be Very Small?

One-loop correction to the power spectrum in generic single-field inflation is calculated by using standard perturbation theory. Because of the enhancement inversely proportional to the observed red tilt of the spectral index of curvature perturbation, the correction turns out to be much larger than previously anticipated. As a result, the primordial non-Gaussianity must be much smaller than the current observational bound in order to warrant the validity of cosmological perturbation theory.

Inflation from f(R) theories in gravity\u2019s rainbow

In this work, we study the f(R) models of inflation in the context of gravity’s rainbow theory. We choose three types of f(R) models: f(R)=R+alpha (R/M)^{n},,f(R)=R+alpha R^{2}+beta R^{2}log (R/M^{2}) and the Einstein–Hu–Sawicki model with n,,alpha ,,beta being arbitrary real constants. Here R and M are the Ricci scalar and mass scale, respectively. For all models, the rainbow function is written in the power-law form of the Hubble parameter. We present a detailed derivation of the spectral index of curvature perturbation and the tensor-to-scalar ratio and compare the predictions of our results with the latest Planck 2018 data. With the sizeable number of e-foldings and proper choices of parameters, we discover that the predictions of all f(R) models present in this work are in excellent agreement with the Planck analysis.

Deformed Starobinsky model in gravity\u2019s rainbow

In the context of gravity’s rainbow, we study the deformed Starobinsky model in which the deformations take the form f(R)sim R^{2(1-alpha )}, with R and alpha being the Ricci scalar and a positive parameter, respectively. We show that the spectral index of curvature perturbation and the tensor-to-scalar ratio can be written in terms of N,,lambda and alpha , with N being the number of e-foldings, lambda a rainbow parameter. We compare the predictions of our models with Planck data. With the sizeable number of e-foldings and proper choices of parameters, we discover that the predictions of the model are in excellent agreement with the Planck analysis. Interestingly, we obtain the upper limit and the lower limit of a rainbow parameter lambda and a positive constant alpha , respectively.

Inflationary scenario from higher curvature warped spacetime

We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + alpha R^2 in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of “inflationary scenario” by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n_s) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016).

Planck2015 results

We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be $n_\mathrm{s} = 0.968 \pm 0.006$ and tightly constrain its scale dependence to $d n_s/d \ln k =-0.003 \pm 0.007$ when combined with the Planck lensing likelihood. When the high-$\ell$ polarization data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is $r_{0.002} < 0.11$ (95% CL), consistent with the B-mode polarization constraint $r< 0.12$ (95% CL) obtained from a joint BICEP2/Keck Array and Planck analysis. These results imply that $V(\phi) \propto \phi^2$ and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as $R^2$ inflation. Three independent methods reconstructing the primordial power spectrum are investigated. The Planck data are consistent with adiabatic primordial perturbations. We investigate inflationary models producing an anisotropic modulation of the primordial curvature power spectrum as well as generalized models of inflation not governed by a scalar field with a canonical kinetic term. The 2015 results are consistent with the 2013 analysis based on the nominal mission data.

Composite Inflation in the light of 2015 Planck data

In this work, we examine cosmological constraints on models of composite inflation based on the slow-roll approximation by using the recent Planck measurement. We compare the spectral index of curvature perturbation (and its running) and the tensor-to-scalar ratio predicted by such models with Planck 2015 data. We find that the predictions of technicolor inflation are nicely consistent with the Planck analysis. Moreover, the predictions from the second model, glueball inflation, are in good agreement with the Planck data at 2σC.L. However, the final two models, super glueball inflation and orientifold inflation, favor only the rather large value of the tensor-to-scalar ratio of which the predictions are in tension with the Planck analysis.

Perfect fluid and F ( T ) $F(T)$ gravity descriptions of inflationary universe and comparison with observational data

We describe in this paper the observables of inflationary models, in particular the spectrum index of torsion scalar perturbations, the tensor-to-scalar ratio, and the running of the spectral index, in the framework of perfect fluid models and F(T) gravity theories through the reconstruction methods. Then, our results on the perfect fluid and F(T) gravity theories of inflation are compared with recent cosmological observations such as the Planck satellite and BICEP2 experiment. Ours studies prove that the perfect fluid and F(T) gravity models can reproduce the inflationary universe consistent above all with the Planck data. We have reconstructed several models and considered others which give the best fit values compatible with the spectral index of curvature perturbations, the tensor-to-scalar ratio, and the running of the spectral index within the allowed ranges suggested by the Planck and BICEP2 results.

Starobinsky model in rainbow gravity

In this paper, we study the Starobinsky model of inflation in the context of gravity's rainbow theory. We propose that gravity rainbow functions can be written in the power-law form of the Hubble parameter. We present a detailed derivation of the spectral index of curvature perturbation and the tensor-to-scalar ratio and compare the predictions of our models with Planck 2015 data. We discover that in order to be consistent with Planck data up to $2\sigma$ C.L., the viable values of $N_{k}$ $e$-folds would satisfy $42\lesssim N_{k}\lesssim 87$ and the rainbow parameter $\lambda$ is nicely constrained to be $\lambda \lesssim6.0$.

Generalized galilean genesis

The galilean genesis scenario is an alternative to inflation in which the universe starts expanding from Minkowski in the asymptotic past by violating the null energy condition stably. Several concrete models of galilean genesis have been constructed so far within the context of galileon-type scalar-field theories. We give a generic, unified description of the galilean genesis scenario in terms of the Horndeski theory, i.e., the most general scalar-tensor theory with second-order field equations. In doing so we generalize the previous models to have a new parameter (denoted by α) which results in controlling the evolution of the Hubble rate. The background dynamics is investigated to show that the generalized galilean genesis solution is an attractor, similarly to the original model. We also study the nature of primordial perturbations in the generalized galilean genesis scenario. In all the models described by our generalized genesis Lagrangian, amplification of tensor perturbations does not occur as opposed to what happens in quasi-de Sitter inflation. We show that the spectral index of curvature perturbations is determined solely from the parameter α and does not depend on the other details of the model. In contrast to the original model, a nearly scale-invariant spectrum of curvature perturbations is obtained for a specific choice of α.

Negative running can prevent eternal inflation

Current data from the Planck satellite and the BICEP2 telescope favor, at around the 2 σ level, negative running of the spectral index of curvature perturbations from inflation. We show that for negative running α < 0, the curvature perturbation amplitude has a maximum on scales larger than our current horizon size. A condition for the absence of eternal inflation is that the curvature perturbation amplitude always remain below unity on superhorizon scales. For current bounds on nS from Planck, this corresponds to an upper bound of the running α < −9 × 10−5, so that even tiny running of the scalar spectral index is sufficient to prevent eternal inflation from occurring, as long as the running remains negative on scales outside the horizon. In single-field inflation models, negative running is associated with a finite duration of inflation: we show that eternal inflation may not occur even in cases where inflation lasts as long as 104 e-folds.

Inflationary universe from perfect fluid andF(R)gravity and its comparison with observational data

We investigate the descriptions for the observables of inflationary models, in particular, the spectral index of curvature perturbations, the tensor-to-scalar ratio, and the running of the spectral index, in the framework of perfect fluid models and $F(R)$ gravity theories through the reconstruction methods. Furthermore, the perfect fluid and $F(R)$ gravity descriptions of inflation are compared with the recent cosmological observations such as the Planck satellite and BICEP2 experiment. It is demonstrated with explicit examples that perfect fluid may lead to the inflationary universe consistent with the Planck data. It is also shown that several $F(R)$ gravity models, especially, a power-law model gives the best fit values compatible with the spectral index and tensor-to-scalar ratio within the allowed ranges suggested by the Planck and BICEP2 results.

HIGGS INFLATION IN f(Φ, R) THEORY

We generalize the scalar-curvature coupling model ξΦ2R of Higgs inflation to ξΦaRb to study inflation. We compute the amplitude and spectral index of curvature perturbations generated during inflation and fix the parameters of the model by comparing these with the Planck + WP data. We find that if the scalar self-coupling λ is in the range 10-5–0.1, parameter a in the range 2.3–3.6 and b in the range 0.77–0.22 at the Planck scale, one can have a viable inflation model even for ξ ≃ 1. The tensor to scalar ratio r in this model is small and our model with scalar-curvature couplings is not ruled out by observational limits on r unlike the pure [Formula: see text] theory. By requiring the curvature coupling parameter to be of order unity, we have evaded the problem of unitarity violation in scalar-graviton scatterings which plague the ξΦ2R Higgs inflation models. We conclude that the Higgs field may still be a good candidate for being the inflaton in the early universe if one considers higher-dimensional curvature coupling.

Observational consequences of the standard model Higgs inflation variants

We consider the possibility to observationally differentiate the Standard Model (SM) Higgs driven inflation with non-minimal coupling to gravity from other variants of SM Higgs inflation based on the scalar field theories with non-canonical kinetic term such as Galileon-like kinetic term and kinetic term with non-minimal derivative coupling to the Einstein tensor.In order to ensure consistent results, we study the SM Higgs inflation variants by using the same method, computing the full dynamics of the background and perturbations of the Higgs field during inflation at quantum level.Assuming that all the SM Higgs inflation variants are consistent theories, we use the MCMC technique to derive constraints on the inflationary parameters and the Higgs boson mass from their fit to WMAP7+SN+BAO data set. We conclude that a combination of the SM Higgs mass measurement by the LHC and accurate determination by the PLANCK satellite of the spectral index of curvature perturbations and tensor-to-scalar ratio will enable to distinguish among these models. We also show that the consistency relations of the SM Higgs inflation variants are distinct enough to differentiate among them.

“Finite” non-Gaussianities and tensor–scalar ratio in large volume Swiss-cheese compactifications

Developing on the ideas of (Section 4 of) [A. Misra, P. Shukla, Moduli stabilization, large-volume dS minimum without anti- D3-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi–Yau's, Nucl. Phys. B 799 (2008) 165–198, arXiv: 0707.0105] and [A. Misra, P. Shukla, Large volume axionic Swiss-cheese inflation, Nucl. Phys. B 800 (2008) 384–400, arXiv: 0712.1260 [hep-th]] and using the formalisms of [S. Yokoyama, T. Suyama, T. Tanaka, Primordial non-Gaussianity in multi-scalar slow-roll inflation, arXiv: 0705.3178 [astro-ph]; S. Yokoyama, T. Suyama, T. Tanaka, Primordial non-Gaussianity in multi-scalar inflation, Phys. Rev. D 77 (2008) 083511, arXiv: 0711.2920 [astro-ph]], after inclusion of perturbative and non-perturbative α ′ corrections to the Kähler potential and ( D1- and D3-)instanton generated superpotential, we show the possibility of getting finite values for the non-linear parameter f NL while looking for non-Gaussianities in type IIB compactifications on orientifolds of the Swiss cheese Calabi–Yau WCP 4 [ 1 , 1 , 1 , 6 , 9 ] in the L(arge) V(olume) S(cenarios) limit. We show the same in two contexts. First is multi-field slow-roll inflation with D3-instanton contribution coming from a large number of multiple wrappings of a single (Euclidean) D3-brane around the “small” divisor yielding f NL ∼ O ( 1 ) . The second is when the slow-roll conditions are violated and for the number of the aforementioned D3-instanton wrappings being of O ( 1 ) but more than one, yielding f NL ∼ O ( 1 ) . Based on general arguments not specific to our (string-theory) set-up, we argue that requiring curvature perturbations not to grow at horizon crossing and at super-horizon scales, automatically picks out hybrid inflationary scenarios which in our set up can yield f NL ∼ O ( 1 ) and tensor–scalar ratio of O ( 10 −2 ) . For all our calculations, the world-sheet instanton contributions to the Kähler potential coming from the non-perturbative α ′ corrections, are restricted to appropriate choices of the degrees of genus-zero rational curves that correspond to very large values of Gopakumar–Vafa invariants for the chosen compact projective variety. To our knowledge, such values of non-Gaussianities and tensor–scalar ratio in slow-roll inflationary and/or slow-roll violating scenarios, have been obtained for the first time from string theory. We also make some observations pertaining to the possibility of the axionic inflaton also being a cold dark matter candidate as well as a quintessence field used for explaining dark energy. Our calculations predict, however, loss of scale invariance of the spectral index of curvature perturbations beyond the existing experimental bounds if one requires “freeze-out” of curvature perturbations at horizon crossing and super-horizon scales. The violation of scale invariance is within experimental bounds if the freeze-out is required only at super-horizon scales—in such scenarios, one can get f NL ∼ O ( 1 ) and r ∼ 10 −2 .

Is a dissipative regime during inflation in agreement with observations?

We study the spectral index of curvature perturbations for inflationary models where the driving scalar field is coupled to a relativistic fluid through a friction term $\ensuremath{\Gamma}$. In the regime in which $\ensuremath{\Gamma}$ can be at most as large as $H$, the Hubble parameter during inflation, we find that only $\ensuremath{\Gamma}\ensuremath{\ll}H$ is allowed by observations; otherwise curvature fluctuations are generated with a spectral index ${n}_{s}$ unacceptably red. These results are obtained starting from vacuum initial conditions and are generic with respect to the inflationary potential and known dependence of the friction term on the scalar field and the energy density of the relativistic fluid. We compare our findings with previous investigations.

Global fits for the spectral index of the cosmological curvature perturbation

Best-fit values of the spectral index of the curvature perturbation are presented, assuming the $\Lambda$CDM cosmology. Apart from the spectral index, the parameters are the Hubble parameter, the total matter density and the baryon density. The data points are intended to represent all measurements which are likely to significantly affect the result. The cosmic microwave anisotropy is represented by the COBE normalization, and heights of the first and second peaks given by the latest Boomerang and Maxima data. The slope of the galaxy correlation function and the matter density contrast on the $8h^{-1}\Mpc$ scale are each represented by a data point, as are the expected values of the Hubble parameter and matter density. The `low-deuterium' nucleosynthesis value of the baryon density provides a final data point, the fit giving a value about one standard deviation higher. The reionization epoch is calculated from the model by assuming that it corresponds to the collapse of a fraction $f\gsim 10^{-4}$ of matter. We consider the case of a scale-independent spectral index, and also the scale-dependent spectral index predicted by running mass models of inflation. In the former case, the result is compared with the prediction of models of inflation based on effective field theory, in which the field value is small on the Planck scale. Detailed comparison is made with other fits, and other approaches to the comparison with theory.