Running Of Scalar Spectral Index Research Articles

Effectiveness of rastall gravity in modified chaplygin gas inspired viscous-flation

This paper is a contribution to study the effectiveness of Rastall gravity (RG) by another mechanism of warm viscous inflation inspired by modified Chaplygin gas (MCG). The matter contents of our cosmos are taken to be standard scalar field (ϕ) and radiation within flat FRW geometry. We establish the current model using intermediate form of scale factor and calculate the analytic solution of inflaton, effective potential V(ϕ) necessary to inflate the Universe and entropy density S under slow-roll limit. The further work in this paper is restricted to high dissipative regime, taking constant and variable dissipative (Γ) and viscous coefficients (ξ). The evaluated exact solutions are the main source in developing the inflationary observable like scalar/tensor power spectra, scalar/tensor spectral indices, tensor to scalar ratio and running of scalar spectral index for our model. The model parameters as well as additional theory parameter λ are constrained to check the compatibility of RG with Planck 2018 data via and α s − n s trajectories. We conclude that RG along with modification of CG model can lead to significant changes in the early universe.

An exact solution approach to warm inflation using Tsallis and Barrow holographic dark energy entropy within Rastall gravity.

This paper studies the phenomena of warm inflation in a modified cosmological scenario within Rastall gravity. In this context, we modify the standard Friedmann equations using recently proposed Tsallis and Barrow holographic dark energy entropies, alternatively. For both entropies, the exact solutions including the inflaton field, potential required to produce inflation and the scale factor are obtained under slow-roll approximation for low- and high-dissipative regimes. We obtain exponentially growing scale factors for both dark energy models. To confront the theoretical predictions of these models with recent observational data, we calculate the slow-roll parameters, number of e-folds, scalar spectral index, running of scalar spectral index and the tensor-to-scalar ratio for both extremes of dissipation. The Planck bounds on inflationary trajectories are being used to constraint the free parameters. The results are interesting and physically viable up to 2sigma level.

Attractor and slow roll parameterized inflation in extended teleparallel gravity

The study of inflation through different prospects is being done for specific model of scalar f(T) gravity in two phases such as attractor (ns(N)−1∝N−1) and slow roll parameterizations. In the presence of these ingredients, we evaluate all inflationary parameters such as scalar spectral index, tensor to scalar ratio r and running of scalar spectral index and local non Gaussianity parameter. We also develop the inflationary planes ns−N, r−N, dnsdlnκ−N, dnsdlnκ−ns and fNL−ns. These planes show the viability of our outcomes with Planck data 2018.

Inflation model selection revisited

We update the constraints on the power spectra of primordial curvature perturbation and tensor perturbation including Planck data 2015 (P15) and recently released BICEP2/Keck data (BK15), Baryon Acoustic Oscillation data and the Type Ia supernovae data. We find that the upper limits of tensor-to-scalar ratio are $0.061$, $0.064$ and $0.072$ at $95\%$ confidence level (CL) in the $\Lambda$CDM+$r$, $\Lambda$CDM+$r$+$\alpha_s$ and $\Lambda$CDM+$r$+$\alpha_s$+$\beta_s$ models respectively, where $\alpha_s$ and $\beta_s$ are the running of scalar spectral index and running of running. The inflation model with a concave potential is favored at more than $95\%$ CL. In addition, parametrizing the slow-roll parameter $\epsilon\sim 1/N^p$, where $N$ is the e-folding number before the end of inflation and taken in the range of $[50,60]$ and $[14,75]$ respectively, we conclude that the inflation model with a monomial potential $V(\phi)\sim \phi^n$ is disfavored at more than $95\%$ CL, and both the Starobinsky inflation model and brane inflation model are still consistent with the data.

Measuring the spectral running from cosmic microwave background and primordial black holes

We constrain the spectral running by combining cosmic microwave background (CMB) data, baryon acoustic oscillation (BAO) data and the constraint from primordial black holes (PBHs). We find that the constraint from PBHs has a significant impact on the running of running of scalar spectral index, and a power-law scalar power spectrum without running is consistent with observational data once the constraint from PBHs is taken into account. In addition, from the constraints on the slow-roll parameters, the derived tensor spectral index in the single-field slow-roll inflation model is quite small, namely |n_t|lesssim 9.3times 10^{-3} which will be very difficult to be measured by CMB data only in the future, and the absolute value of derived running of tensor spectral index is not larger than 2.1times 10^{-4} at 95% confidence level.

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.

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.

Dynamics of bulk viscous pressure effected inflation in braneworld scenario

The main goal of the present work is to examine the possible realization of warm chaotic inflation and logamediate inflation within the framework of a modified Chaplygin gas brane-world model. In this respect, the slow-roll parameters, number of e-folds, scalar-tensor power spectra, spectral indices, tensor–scalar ratio and running of scalar spectral index is being evaluated. These parameters are being analyzed for variable as well as constant dissipation and bulk viscous coefficients. Further, the trajectories among the inflationary parameters such as ns−ϕ,ns−r,αs−ϕ and ns−αs are also developed to examine their behavior as well as physical cosmology. Some of results of inflationary parameters in all cases are: r < 0.11, ns=0.96±0.025 and αs=−0.019±0.025. It is interesting to mention here that the results of inflationary parameters are consistent with BICEP2, WMAP (7+9) and Planck data.

Running of scalar spectral index in multi-field inflation

We compute the running of the scalar spectral index in general multi-field slow-roll inflation. By incorporating explicit momentum dependence at the moment of horizon crossing, we can find the running straightforwardly. At the same time, we can distinguish the contributions from the quasi de Sitter background and the super-horizon evolution of the field fluctuations.

Modified Lyth bound and implications of BICEP2 results

To reconcile the BICEP2 measurement on the tensor-to-scalar ratio $r$ with Planck constraint, a large negative running of scalar spectral index $n_s$ is needed. So the inflationary observable such as $n_s$ should be expanded at least to the second-order slow-roll parameters for single-field inflationary models. The large value of $r$ and the Lyth bound indicate that it is impossible to obtain the sub-Planckian excursion for the inflaton. However, we derive an absolutely minimal bound $\Delta\phi/M_{\rm Pl}>\sqrt{r/2}$ on the inflaton excursion for single-field inflationary models, which can be applied to non-slow-roll inflationary models as well. This bound excludes the possibility of the small-field inflation with $\Delta\phi<0.1 M_{\rm Pl}$ if the BICEP2 result on $r$ stands and it opens the window of sub-Planckian excursion with $\Delta\phi<M_{\rm Pl}$ even if $r$ is as large as $0.1$. To get the sub-Planckian excursion with $\Delta\phi<0.1 M_{\rm Pl}$, our modified bound requires $r<0.02$. Using a fifth-order polynomial potential as an explicit example, we show that it not only agrees with the observational results, but also violates the Lyth bound.

Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes r < 0.083 at 95% confidence level in the base ΛCDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to r < 0.116 at 95% confidence level. Our resultsimply that the inflation model with a single monomial potential is marginally disfavored at around 95% confidence level. Especially, the m2ϕ2/2 inflation model is disfavored at more than 2σ level. However, the Starobinsky inflation model gives a nice fit.

What can we learn from the tension between PLANCK and BICEP2 data?

Recently BICEP2 collaboration has announced the detection of the primordial gravitational waves at high confidence level. In light of the results of B-modes power spectrum from BICEP2 and using the based ΛCDM, a constraint on the tensor-to-scalar ratio r = 0.20−0.05+0.07 (68% C.L.) can be obtained, however, this result is in apparent tension with the limit on standard inflation models from the recent PLANCK measurement, r < 0.11 (95% C.L.). Herein we review the recent progress on the cosmological studies after BICEP2 and discuss on different ways of reconciling the tension between PLANCK and BICEP2 data. We will discuss possible modifications on the standard cosmological model, such as including the running of scalar spectral index or other cosmological parameters correlated with inflationary cosmological parameters, or tilting the primordial power spectrum at large scales by introducing a cut off which can be predicted by bouncing cosmology. We will also comment on another possibility of generating extra B-modes of CMB polarization, namely by a non-zero polarization rotation angle during its transferring from the last scattering surface.

Ruling out the power-law form of the scalar primordial spectrum

Combining Planck CMB temperature [1] and BICEP2 B-mode polarization data [2,3] we show qualitatively that, assuming inflationary consistency relation, the power-law form of the scalar primordial spectrum is ruled out at more than 3σ CL. This is an important finding, since the power-law form of the scalar primordial spectrum is one of the main assumptions of concordance model of cosmology and also a direct prediction of many inflationary scenarios. We show that a break or step in the form of the primordial scalar perturbation spectrum, similar to what we studied recently analyzing Planck data [4], can address both Planck and BICEP2 results simultaneously. Our findings also indicate that the data may require more flexibilities than what running of scalar spectral index can provide. Finally we show that an inflaton potential, originally appeared in [5], can generate both the step and the break model of scalar primordial spectrum in two different limits. The discussed potential is found to be favored by Planck data but marginally disfavored by BICEP2 resultsas it produces slightly lower amplitude of tensor primordial spectrum. Hence, if the tensor-to-scalar ratio (r) quoted by BICEP2 persists, it is of importance that we generate inflationarymodels with large r and at the same time provide suppression in scalar primordial spectrum at large scales.

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.