Running Of Spectral Index Research Articles

Predictions of single field inflation for the tensor/scalar ratio and the running spectral index

We study the single field slow-roll inflation models that better agree with the available CMB and LSS data including the three years WMAP data: new inflation and hybrid inflation. We study these models as effective field theories in the Ginsburg-Landau context: a trinomial potential turns out to be a simple and well motivated model. The spectral index n{sub s} of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations and the running index dn{sub s}/dlnk are studied in detail. We derive explicit formulas for n{sub s}, r and dn{sub s}/dlnk and provide relevant plots. In new inflation, and for the chosen central value n{sub s}=0.95, we predict 0.03 1 behavior. Hybrid inflation for {mu}{sub 0}{sup 2}>{lambda}{sub 0}M{sub Pl}{sup 2}/192 fulfills all the present CMB+LSS data for a large enough initial inflaton amplitude. Even if chaotic inflation predicts n{sub s} values compatible with the data, chaotic inflation is disfavored since it predicts a too high value r{approx_equal}0.27 for the ratio of tensor to scalar fluctuations. The model which best agrees with the current data and which best prepares the way to the expected data r(less-or-similar sign)0.1, is the trinomial potential with negative mass term: new inflation.« less

Early structure formation in quintessence models and its implications for cosmic reionization from first stars

We present the first hydrodynamic N-body simulations of primordial gas clouds responsible for the reionization process in dark energy cosmologies. We compare the cosmological constant scenario with a SUGRA quintessence model with marked dynamics in order to highlight effects due to the different acceleration histories imposed by the dark energy. We show that both the number density of gas clouds and their clumpiness keep a record of the expansion rate during evolution, similar to the non-linear dark matter profile at virialization, as was recently demonstrated by Dolag et al. Varying the shape of the primordial power spectrum, we show how this effect is mitigated by a running spectral index decreasing the power at small scales. Our results demonstrate that, in order to constrain the dark energy from large-scale structures, one must track its effects down to the distribution of luminous matter.

Noncommutative Kachru-Kallosh-Linde-Maldacena-McAllister-Trivedi model

In the noncommutative spacetime the fine tuning in KKLMMT model can be significantly released and a nice running of spectral index fitting the WMAP 3 yr data can be achieved. The fitting results show that the noncommutative mass scale is roughly $5\ifmmode\times\else\texttimes\fi{}{10}^{14}\text{ }\text{ }\mathrm{Gev}$. The string mass scale is higher than the noncommutative scale unless the string coupling is smaller than ${10}^{\ensuremath{-}10}$.

Running spectral index in noncommutative inflation and WMAP three year results

A model independent analysis shows that the running of the spectral index of the three year WMAP results can be nicely realized in noncommutative inflation. We also re-examine some concrete noncommutative inflation models. We find that a large tensor–scalar ratio is required, corresponding to a low number of e-folds before the end of inflation in some simple models.

Implications of a running spectral index for slow roll inflation

We analyse the weak (2σ) evidence for a running spectral index seen in the three year WMAP data set and itsimplications for single field, slow roll inflation. We assume that the running is comparableto the central value found from the WMAP data analysis, and use the Hubble slow rollformalism to follow the evolution of the slow roll parameters. For all parameter choicesconsistent with a large, negative running, single field, slow roll inflation lasts less than 30e-folds after CMB scales leave the horizon. Thus, a definitive observation of a large negativerunning would imply that any inflationary phase requires multiple fields or thebreakdown of slow roll. Alternatively, if single field, slow roll inflation sourcesthe primordial fluctuations, we can expect the observed running to move muchcloser to zero as the CMB is measured more accurately at small angular scales.

Power spectrum of the density perturbations from smooth hybrid new inflation model

We numerically investigate density perturbations generated in the smooth hybrid new inflation model, a kind of double inflation model that is designed to reproduce the running spectral index suggested by the WMAP results. We confirm that this model provides the running spectral index within $1\ensuremath{\sigma}$ range of the 3 yr WMAP result. In addition, we find a sharp and strong peak on the spectrum of primordial curvature perturbation at small scales. This originates from amplification of fluctuation in the first inflaton fields due to parametric resonance, which takes place in the oscillatory phase between two inflationary regime. Formation probability of primordial black holes (PBHs) is discussed as a consequence of such peak.

Noncommutative chaotic inflation and WMAP three year results

Abstract Noncommutative inflation is based upon the consideration of some effects of the space–time uncertainty principle motivated by ideas from string/M theory. The CMB anisotropies may carry a signature of this very early Universe correction from the space–time uncertainty principle and can be used to place constraints on the parameters of the noncommutative inflation model. In this Letter we analyze the noncommutative chaotic inflation model by means of the WMAP three year results. We show that the noncommutative chaotic inflation model can produce a large negative running of spectral index within a reasonable range of e-folding number N, provided that the value of p in the potential V ( ϕ ) ∝ ϕ p is enhanced roughly to p ∼ 12 – 18 . Applying a likelihood analysis to the WMAP results, we find the best-fit values of parameters for the noncommutative chaotic inflation model. In addition, this model predicts a rather big gravitational wave which may be tested by the upcoming experiments.

The neutrino mass bound from WMAP 3 year data, the baryon acoustic peak, the SNLS supernovae and theLyman-α forest

We have studied bounds on the neutrino mass using new data from theWMAP 3 year data, the Sloan Digital Sky Survey measurement of thebaryon acoustic (BAO) peak, the Type Ia supernovae from SNLS, and theLyman-α forest. We find that even in the most general models with a running spectral index wherethe number of neutrinos and the dark energy equation of state are allowed to vary, the 95%confidence limit (C.L.) bound on the sum of neutrino masses is eV (95% C.L.), a bound which we believe to be robust. In the more often used constrained analysiswith Nν = 3, w = −1,and αs = 0, we find a bound of 0.48 eV without using theLyman-α data.If the Lyman-α data are used, the bound shrinks to eV (95% C.L.), depending strongly on theLyman-α analysis used. Finally, we have also calculated how the effectiveA-parameter used in the SDSS BAO analyses changes under the influence of a non-zero neutrino mass. Wefind that A = 0.469(n/0.98)−0.35(1+0.94Ων/Ωm) ± 0.017.

The epoch of reionization

We have modelled the process of reionization of the intergalactic medium (IGM) by photoionization by galaxies, in order to learn what galaxy formation in the framework of the cold dark matter (CDM) model predicts for the epoch of reionization. We use a sophisticated semi-analytic model of galaxy formation to track the formation of these galaxies, their influence on the IGM and the back reaction of the state of the IGM on further galaxy formation. Our study represents a much more complete and physically consistent modelling of reionization than has been conducted in the past. In particular, compared to previous work by ourselves and others, our new calculations contain significant improvements in the modelling of the effects of reionization of the IGM on the collapse of baryons into dark matter haloes (this is now computed self-consistently from the properties of model galaxies), and in the model for the cooling and condensation of gas within haloes (our new model includes photoheating from a self-consistently computed ionizing background and also includes cooling due to molecular hydrogen). We find that reionization can be achieved by z∼ 10–20 in a ΛCDM cosmological model with σ8≈ 0.9. However, a cosmological model with a running spectral index is only able to achieve reionization before z≈ 9, and thus be consistent with an optical depth of 0.1, if very extreme assumptions are made about the physics of feedback at high redshifts. We also consider the specific galaxy formation model recently discussed by Baugh et al., which includes a top-heavy initial mass function (IMF) in starbursts, and find that it is able to reionize the Universe by z≈ 12. The previous results assume that all of the ionizing photons produced by stars in galaxies are able to escape and ionize the IGM. If this is not the case, then the redshift of reionization could be substantially reduced. We find that extended periods of partial reionization and double reionizations can occur in models in which the first stars formed via cooling by H2 molecules, are very massive, and in which the escape fraction of ionizing photons ∼10–30 per cent. Such models do not fully reionize until z≈ 6–7, but predict an electron scattering optical depth as large as 0.15. The recent Wilkinson Microwave Anisotropy Probe (WMAP) three-year data suggest lower values of σ8= 0.7–0.8. Models with lower σ8 have reduced redshifts of reionization, consistent with the lower optical depth also suggested by the WMAP three-year data.

Approximate consistency condition from a running spectral index in slow-roll inflationary models

Density perturbations generated from inflation almost always have a spectral index ${n}_{s}$ which runs (varies with the wavelength). We explore a running spectral index scenario in which the scalar spectral index runs from blue (${n}_{s}g1$) on large length scales to red (${n}_{s}l1$) on short length scales. Specifically, we look for a correlation between the length scale at which ${n}_{s}\ensuremath{-}1=0$ and the length scale at which tensor to scalar ratio $\mathcal{T}/\mathcal{S}$ reaches a minimum for single field slow-roll inflationary models. By computing the distribution of length scale ratios, we conclude that there indeed is a new approximate consistency condition that is characteristic of running spectral index scenarios that run from blue to red. Specifically, with strong running, we expect 96% of the slow-roll models to have the two length scales to be within a factor of 2, with the length scale at which the tensor to scalar ratio reaching a minimum longer than the wavelength at which ${n}_{s}\ensuremath{-}1=0$.

The running spectral index as a probe of physics at high scales

The WMAP results on the scalar spectral indexn and its running with scale, though preliminary, open a very interesting window to physicsat very high energies. We address the problem of finding inflaton potentials well motivatedby particle physics which can accommodate WMAP data. We make a model independentanalysis of a large class of models: those with flat tree-level potentials lifted byradiative corrections, which cause the slow rolling of the inflaton and the running ofn. Thisincludes typical hybrid inflation models. In the small coupling regime the predictions for the size andrunning of n are remarkably neat, e.g. , and n doesnot cross n = 1, contrary to WMAP indications. On the other hand,n can run significantly if the couplings are stronger, but at the price of having a small number of e-folds,Ne. We also examine the effect of mass thresholds crossed during inflation. Finally, we showthat the presence of non-renormalizable operators for the inflaton, suppressed by a massscale above the inflationary range, is able to give both and Ne∼50.

Multibrane inflation and dynamical flattening of the inflaton potential

We investigate the problem of fine tuning of the potential in the KKLMMT warped flux compactification scenario for brane-antibrane inflation in Type IIB string theory. We argue for the importance of an additional parameter psi_0 (approximated as zero by KKLMMT), namely the position of the antibrane, relative to the equilibrium position of the brane in the absence of the antibrane. We show that for a range of values of a particular combination of the Kahler modulus, warp factor, and psi_0, the inflaton potential can be sufficiently flat. We point out a novel mechanism for dynamically achieving flatness within this part of parameter space: the presence of multiple mobile branes can lead to a potential which initially has a metastable local minimum, but gradually becomes flat as some of the branes tunnel out. Eventually the local minimum disappears and the remaining branes slowly roll together, with assisted inflation further enhancing the effective flatness of the potential. With the addition of Kahler and superpotential corrections, this mechanism can completely remove the fine tuning problem of brane inflation, within large regions of parameter space. The model can be falsified if future cosmic microwave background observations confirm the hint of a large running spectral index.

Smoothing spline primordial power spectrum reconstruction

We reconstruct the shape of the primordial power spectrum (PPS) using a smoothing spline. Our adapted smoothing spline technique provides a complementary method to existing efforts to search for smooth features in the PPS, such as a running spectral index. With this technique we find no significant indication with Wilkinson Microwave Anisotropy Probe first-year data that the PPS deviates from a Harrison-Zeldovich spectrum and no evidence for loss of power on large scales. We also examine the effect on the cosmological parameters of the additional PPS freedom. Smooth variations in the PPS are not significantly degenerate with other cosmological parameters, but the spline reconstruction greatly increases the errors on the optical depth and baryon fraction.

TEST OF PATCH COSMOLOGY WITH WMAP

We calculate the power spectrum, spectral index, and running spectral index for inflationary patch cosmology arisen from Gauss–Bonnet braneworld scenario using the Mukhanov equation. This patch cosmology consists of Gauss–Bonnet (GB), Randall–Sundrum (RS-II), and four-dimensional (4D) cosmological models. There exist several modifications in higher order calculations. However, taking the power-law inflation by choosing different potentials depending on the model, there exist minor changes up to second order corrections. Since second order corrections are rather small in the slow-roll limit, we could not choose a desired power-law model which explains the WMAP data. Finally we discuss the reliability of high order calculations based on the Mukhanov equation by comparing the perturbed equation including 5D metric perturbations. It turns out that first order corrections are reliable, while second order corrections are not proved to be reliable.

THE MASS FUNCTION OF DARK MATTER HALOES IN A COSMOLOGICAL MODEL WITH A RUNNING PRIMORDIAL POWER SPECTRUM

We present the first study on the mass functions of Jenkins et al. (J01) and an estimate of their corresponding largest virialized dark halos in the Universe for a variety of dark-energy cosmological models with a running spectral index. Compared with the PL–CDM model, the RSI–CDM model can raise the mass abundance of dark halos for small mass halos at lower redshifts, but it is not apparent on scales of massive mass halos. Particularly, this discrepancy increases largely with the decrease of redshift, and the RSI–CDM model can suppress the mass abundance on any scale of halo masses at higher redshift. As for the largest mass of virialized halos, the spatially flat ΛCDM models give more massive mass of virialized objects than other models for both of PL–CDM and RSI–CDM power spectral indexs, and the RSI–CDM model can enhance the mass of largest virialized halos for all of models considered in this paper. So we probably distinguish the PL–CDM and RSI–CDM models by the largest virialized halos in the future survey of cluster of galaxies.

Joint modelling of the probability distribution function and power spectrum of the Ly forest: comparison with observations at z= 3

We present results of joint modelling of the probability distribution function (PDF) and the one-dimensional power spectrum (PS) of the Lya forest flux decrement. The sensitivity of these statistical measures to the shape and amplitude of the linear matter power spectrum is investigated using N-body simulations of two variants of the ACDM cosmology. In the first model, the linear power spectrum has a scale-invariant spectral index n s = 1, whereas in the second, it has a negative running spectral index (RSI), dn/d lnk < 0. We generate mock catalogues of quasi-stellar object (QSO) spectra, and compare their statistical properties to those of the observations at z = 3. We perform a joint fit of the PS and the PDF. A scale-invariant model with σ 8 = 0.9 matches the data well if the mean temperature of the intergalactic medium is T ≤ 1.5 x 10 4 K. For higher temperature, it tends to overestimate the flux PS over scales k ≤ 0.01 s km -1 . The discrepancy is less severe when the PS alone is fitted. However, models matching the PS alone do not yield a good fit to the PDF. A joint analysis of the flux PS and PDF tightens the constraints on the model parameters and reduces systematic biases. The RSI model is consistent with the observed PDF and PS only if the temperature is T ≥ 2 x 10 4 K. The best-fitting models reproduce the slope and normalization of the column density distribution, irrespective of the shape and amplitude of the linear power spectrum. They are also consistent with the observed linewidth distribution, given the large uncertainties. Our joint analysis suggests that σ 8 is likely to be in the range 0.7-0.9 for a temperature 1 x 10 4 ≤ T ≤ 2 x 10 4 K and a reasonable reionization history.

Sneutrino hybrid inflation in supergravity

We propose a hybrid inflation scenario in which the singlet sneutrino, the superpartner of the right-handed neutrino, plays the role of the inflaton. We study a minimal model of sneutrino hybrid inflation in supergravity, where we find a spectral index ${n}_{\mathrm{s}}\ensuremath{\approx}1+2\ensuremath{\gamma}$ with $|\ensuremath{\gamma}|\ensuremath{\lesssim}0.02$, and predict a running spectral index $|\mathrm{d}{n}_{\mathrm{s}}/\mathrm{d}\mathrm{ln}k|\ensuremath{\ll}|\ensuremath{\gamma}|$ and a tensor-to-scalar ratio $r\ensuremath{\ll}{\ensuremath{\gamma}}^{2}$ for field values well below the Planck scale. In our scenario, the baryon asymmetry of our universe can be explained via nonthermal leptogenesis and a low reheat temperature ${T}_{\mathrm{RH}}\ensuremath{\approx}{10}^{6}$ GeV can be realized.

STRONG LENSING PROBABILITIES IN A COSMOLOGICAL MODEL WITH A RUNNING PRIMORDIAL POWER SPECTRUM

The combination of the first-year Wilkinson Microwave Anisotropy Probe (WMAP) data with other finer scale cosmic microwave background (CMB) experiments (CBI and ACBAR) and two structure formation measurements (2dFGRS and Lyman α forest) suggest a ΛCDM cosmological model with a running spectral power index of primordial density fluctuations. Motivated by this new result on the index of primordial power spectrum, we present the first study on the predicted lensing probabilities of image separation in a spatially flat ΛCDM model with a running spectral index (RSI-ΛCDM model). It is shown that the RSI-ΛCDM model suppresses the predicted lensing probabilities on small splitting angles of less than about 4″ compared with that of standard power-law ΛCDM (PL-ΛCDM) model.

Testing for double inflation with WMAP

With the WMAP data we can now begin to test realistic models of inflation involving multiple scalar fields. These naturally lead to correlated adiabatic and isocurvature (entropy) perturbations with a running spectral index. We present the first full ($9$ parameter) likelihood analysis of double inflation with WMAP data and find that despite the extra freedom, supersymmetric hybrid potentials are strongly constrained with less than $7%$ correlated isocurvature component allowed when standard priors are imposed on the cosomological parameters. As a result we also find that Akaike and Bayesian model selection criteria rather strongly prefer single-field inflation, just as equivalent analysis prefers a cosmological constant over dynamical dark energy in the late universe. It appears that simplicity is the best guide to our universe.

Pre-inflation physics and scalar perturbations

The effect of pre-inflation physics on the power spectrum of scalar perturbations is investigated. Considering various pre-inflation models with radiation-dominated or matter-dominated periods before inflation, the power spectra of curvature perturbations for large scales are calculated, and the spectral index and running spectral index are derived. It is shown that pre-inflation models in which the length of inflation is near 60 e-folds may reproduce some key properties implied by the Wilkinson microwave anisotropy probe data.