Spectral Index Of Scalar Perturbations Research Articles

Reheating Constraints and the H0 Tension in Quintessential Inflation

In this work, we focus on two important aspects of modern cosmology: reheating and Hubble constant tension within the framework of a unified cosmic theory, namely the quintessential inflation connecting the early inflationary era and late-time cosmic acceleration. In the context of reheating, we use instant preheating and gravitational reheating, two viable reheating mechanisms when the evolution of the universe is not affected by an oscillating regime. After obtaining the reheating temperature, we analyze the number of e-folds and establish its relationship with the reheating temperature. This allows us to connect, for different quintessential inflation models (in particular for models coming from super-symmetric theories such as α-attractors), the reheating temperature with the spectral index of scalar perturbations, thereby enabling us to constrain its values. In the second part of this article, we explore various alternatives to address the H0 tension. From our perspective, this tension suggests that the simple Λ-Cold Dark Matter model, used as the baseline by the Planck team, needs to be refined in order to reconcile its results with the late-time measurements of the Hubble constant. Initially, we establish that quintessential inflation alone cannot mitigate the Hubble tension by solely deviating from the concordance model at low redshifts. The introduction of a phantom fluid, capable of increasing the Hubble rate at the present time, becomes a crucial element in alleviating the Hubble tension, resulting in a deviation from the Λ-Cold Dark Matter model only at low redshifts. On a different note, by utilizing quintessential inflation as a source of early dark energy, thereby diminishing the physical size of the sound horizon close to the baryon–photon decoupling redshift, we observe a reduction in the Hubble tension. This alternative avenue, which has the same effect of a cosmological constant changing its scale close to the recombination, sheds light on the nuanced interplay between the quintessential inflation and the Hubble tension, offering a distinct perspective on addressing this cosmological challenge.

Canonical Hubble-Tension-Resolving Early Dark Energy Cosmologies Are Inconsistent with the Lyman-α Forest.

Current cosmological data exhibit discordance between indirect and some direct inferences of the present-day expansion rate H_{0}. Early dark energy (EDE), which briefly increases the cosmic expansion rate prior to recombination, is a leading scenario for resolving this "Hubble tension" while preserving a good fit to cosmic microwave background (CMB) data. However, this comes at the cost of changes in parameters that affect structure formation in the late-time universe, including the spectral index of scalar perturbations n_{s}. Here, we present the first constraints on axionlike EDE using data from the Lyman-α forest, i.e., absorption lines imprinted in background quasar spectra by neutral hydrogen gas along the line of sight. We consider two independent measurements of the one-dimensional Lyα forest flux power spectrum from the Sloan Digital Sky Survey (SDSS eBOSS) and from the MIKE/HIRES and X-Shooter spectrographs. We combine these with a baseline dataset comprised of Planck CMB data and baryon acoustic oscillation (BAO) measurements. Combining the eBOSS Lyα data with the CMB and BAO dataset reduces the 95% confidence level (C.L.) upper bound on the maximum fractional contribution of EDE to the cosmic energy budget f_{EDE} from 0.07 to 0.03 and constrains H_{0}=67.9_{-0.4}^{+0.4} km/s/Mpc (68% C.L.), with maximum aposteriori value H_{0}=67.9 km/s/Mpc. Similar results are obtained for the MIKE/HIRES and X-Shooter Lyα data. Our Lyα-based EDE constraints yield H_{0} values that are in >4σ tension with the SH0ES distance-ladder measurement and are driven by the preference of the Lyα forest data for n_{s} values lower than those required by EDE cosmologies that fit Planck CMB data. Taken at face value, the Lyα forest severely constrains canonical EDE models that could resolve the Hubble tension.

Reheating constraints in instant preheating

We use Instant Preheating as a mechanism to reheat the universe when its evolution is modeled by a non-oscillating background. Once we obtain the reheating temperature, we calculate the number of e-folds using two different methods, which allows us to establish a relationship between the reheating temperature and the spectral index of scalar perturbations. We explore this connection to constrain the spectral index for different Quintessential Inflation models.

Logarithmic inflation?

We consider a scalar–tensor action model, both simple and peculiar at the same time, with a boundary term added that it is form-invariant both under the conformal transformation of the metric as well as under the reparametrization of the scalar field. Under this assumption, the boundary term proposed matches (except factors) with the Gibbons–Hawking–York term proposed in such a way it cancels the term(s) involving [Formula: see text]. A matter term is added to the action also. In the Jordan frame, the pure gravitational action becomes the Einstein–Hilbert action with a cosmological constant when the scalar field takes the constant value of their vev, [Formula: see text], which is no otherwise but the only stable minimum of the classical potential chosen which is logarithmic type. This potential presents a large plateau in which it is almost fully flat and the decay of the field from its initial value (assumed to be close to [Formula: see text]) to vacuum draws a Low Field (or New Inflation) scenario. The model fits very well with the current paradigm of the universe and, under some assumptions, gives a good account of the value of the Higgs mass, the current value of the cosmological constant, e-folding, the Hubble parameter, the spectral index of scalar perturbations, etc. The model is not studied in Einstein’s frame. In this, only the expressions of the field and the potential, for a simple case, are achieved. As a result, we get that the nature of the decay of the initial value to its ground state for the scalar field, in this frame, should be by quantum tunneling and not by slow rolling.

Cosmic Inflation and Genetic Algorithms

AbstractLarge classes of standard single‐field slow‐roll inflationary models consistent with the required number of e‐folds, the current bounds on the spectral index of scalar perturbations, the tensor‐to‐scalar ratio, and the scale of inflation can be efficiently constructed using genetic algorithms. The setup is modular and can be easily adapted to include further phenomenological constraints. A semi‐comprehensive search for sextic polynomial potentials results in viable models for inflation. The analysis of this dataset reveals a preference for models with a tensor‐to‐scalar ratio in the range . We also consider potentials that involve cosine and exponential terms. In the last part we explore more complex methods of search relying on reinforcement learning and genetic programming. While reinforcement learning proves more difficult to use in this context, the genetic programming approach has the potential to uncover a multitude of viable inflationary models with new functional forms.

Quasi-matter Bounce Cosmology in Light of Planck

Abstract We study quasi-matter bounce cosmology in light of Planck cosmic microwave background angular anisotropy measurements along with the BICEP2/Keck Array data. We propose a new primordial scalar power spectrum by considering a linear approximation of the equation of state w ≅ w 0 + κ(η − η 0) for quasi-matter field in the contracting phase of the universe. Using this new primordial scalar power spectrum, we constrain the zeroth-order approximation of the equation of state w 0 = −0.00340 ± 0.00044 and first-order correction 10 4 ζ = − 1.67 − 0.83 + 1.50 at the 1σ confidence level by Planck temperature and polarization in combination with the BICEP2/Keck Array data in which ζ = 12κ/k * with pivot scale k *. The spectral index of scalar perturbations is determined to be n Bs = 0.9623 ± 0.0055, which lies 7σ away from the scale-invariant primordial spectrum. We find scale dependency for n s at the 1σ confidence level and a tighter constraint on the running of the spectral index compared to ΛCDM+α s cosmology. The running of the spectral index in quasi-matter bounce cosmology is α Bs = π ζ/2c s = −0.0021 ± 0.0016, which is nonzero at the 1.3σ level, whereas in ΛCDM+α s it is nonzero at the 0.8σ level for Planck temperature and polarization data. The sound speed of density fluctuations of the quasi-matter field at the crossing time is c s = 0.097 − 0.023 + 0.037 , which is not a very small value in the contracting phase.

Cosmological consequences of a scalar field with oscillating equation of state. III. Unifying inflation with dark energy and small tensor-to-scalar ratio

We investigate the inflationary consequences of the oscillating dark energy model proposed by Ti\'an [\href{https://doi.org/10.1103/PhysRevD.101.063531}{Phys. Rev. D {\bf 101}, 063531 (2020)}], which aims to solve the cosmological coincidence problem with multi-accelerating Universe (MAU). We point out that the inflationary dynamics belong to slow-roll inflation. The spectral index of scalar perturbations and the tensor-to-scalar ratio $r$ are shown to be consistent with current \textit{Planck} measurements. Especially, this model predicts $r\sim10^{-7}$, which is far below the observation limits. This result motivates us to explore the smallness of $r$ in the general MAU. We propose a quintessential generalization of the original model and prove $r<0.01$ in general. The null detection to date of primordial gravitational waves provides a circumstantial evidence for the MAU. After the end of inflation, the scalar field rolls toward infinity instead of a local minimum, and meanwhile its equation of state is oscillating with an average value larger than $1/3$. In this framework, we show that gravitational particle creation at the end of inflation is capable of reheating the Universe.

Resilience of long modes in cosmological observables

By a careful implementation of gauge transformations involving long-wavelength modes, we show that a variety of effects involving squeezed bispectrum configurations, for which one Fourier mode is much shorter than the other two, cannot be gauged away, except for the unphysical exactly infinite-wavelength (k=0) limit. Our result applies, in particular, to the Maldacena consistency relation for single-field inflation, yielding a local non-Gaussianity strength fNLlocal = − (5/12)(nS−1) (with nS the primordial spectral index of scalar perturbations), and to the fNLGR = −5/3 term, appearing in the dark matter bispectrum and in the halo bias, as a consequence of the general relativistic non-linear evolution of matter perturbations. Such effects are therefore physical and observable in principle by future high-sensitivity experiments.

Planck2018 results

We report on the implications for cosmic inflation of the 2018 release of thePlanckcosmic microwave background (CMB) anisotropy measurements. The results are fully consistent with those reported using the data from the two previousPlanckcosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles.Plancktemperature, polarization, and lensing data determine the spectral index of scalar perturbations to bens = 0.9649 ± 0.0042 at 68% CL. We find no evidence for a scale dependence ofns, either as a running or as a running of the running. The Universe is found to be consistent with spatial flatness with a precision of 0.4% at 95% CL by combiningPlanckwith a compilation of baryon acoustic oscillation data. ThePlanck95% CL upper limit on the tensor-to-scalar ratio,r0.002 &lt; 0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtainr0.002 &lt; 0.056. In the framework of standard single-field inflationary models with Einstein gravity, these results imply that: (a) the predictions of slow-roll models with a concave potential,V″(ϕ) &lt; 0, are increasingly favoured by the data; and (b) based on two different methods for reconstructing the inflaton potential, we find no evidence for dynamics beyond slow roll. Three different methods for the non-parametric reconstruction of the primordial power spectrum consistently confirm a pure power law in the range of comoving scales 0.005 Mpc−1 ≲ k ≲ 0.2 Mpc−1. A complementary analysis also finds no evidence for theoretically motivated parameterized features in thePlanckpower spectra. For the case of oscillatory features that are logarithmic or linear ink, this result is further strengthened by a new combined analysis including thePlanckbispectrum data. The newPlanckpolarization data provide a stringent test of the adiabaticity of the initial conditions for the cosmological fluctuations. In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3%, 1.7%, and 1.7% at 95% CL for cold dark matter, neutrino density, and neutrino velocity, respectively.Planckpower spectra plus lensing set constraints on the amplitude of compensated cold dark matter-baryon isocurvature perturbations that are consistent with current complementary measurements. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadupolar modulation of the primordial fluctuations. However, the polarization data do not support physical models for a scale-dependent dipolar modulation. All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.

Generalization of cosmological attractor approach to Einstein\u2013Gauss\u2013Bonnet gravity

We construct models with the Gauss–Bonnet term multiplied by a function of the scalar field leading to an inflationary scenario. The consideration is related to the slow-roll approximation. The cosmological attractor approach gives the spectral index of scalar perturbations which is in a good agreement with modern observation and allows for variability of the tensor-to-scalar ratio. We reconstruct models with variability of parameters, which allows one to reproduce cosmological attractor predictions for inflationary parameters in an approximation of the leading order of 1/N in Einstein–Gauss–Bonnet gravity.

Can power spectrum observations rule out slow-roll inflation?

The spectral index of scalar perturbations is an important observable that allows us to learn about inflationary physics. In particular, a detection of a significant deviation from a constant spectral index could enable us to rule out the simplest class of inflation models. We investigate whether future observations could rule out canonical single-field slow-roll inflation given the parameters allowed by current observational constraints. We find that future measurements of a constant running (or running of the running) of the spectral index over currently available scales are unlikely to achieve this. However, there remains a large region of parameter space (especially when considering the running of the running) for falsifying the assumed class of slow-roll models if future observations accurately constrain a much wider range of scales.

Inflation from cosmological constant and nonminimally coupled scalar

We consider inflation in a universe with a positive cosmological constant and a nonminimally coupled scalar field, in which the field couples both quadratically and quartically to the Ricci scalar. When considered in the Einstein frame and when the nonminimal couplings are negative, the field starts in slow roll and inflation ends with an asymptotic value of the principal slow roll parameter, $\epsilon_E=4/3$. Graceful exit can be achieved by suitably (tightly) coupling the scalar field to matter, such that at late time the total energy density reaches the scaling of matter, $\epsilon_E=\epsilon_m$. Quite generically the model produces a red spectrum of scalar cosmological perturbations and a small amount of gravitational radiation. With a suitable choice of the nonminimal couplings, the spectral slope can be as large as $n_s\simeq 0.955$, which is about one standard deviation away from the central value measured by the Planck satellite. The model can be ruled out by future measurements if any of the following is observed: (a) the spectral index of scalar perturbations is $n_s>0.960$; (b) the amplitude of tensor perturbations is above about $r\sim 10^{-2}$; (c) the running of the spectral index of scalar perturbations is positive.

Bmodes and the sound speed of primordial fluctuations

It was recently shown that a large value of the tensor to scalar ratio $r$ implies a constraint on the minimum value of the sound speed $c_s$ of primordial curvature perturbations during inflation that is stronger than current bounds coming from non-Gaussianity measurements. Here we consider additional aspects related to the measurement of B-modes that may provide additional leverage to constrain the sound speed parametrizing non-canonical models of inflation. We find that a confirmation of the consistency relation $r = -8 n_t$ between the tensor to scalar ratio $r$ and the tensor spectral index $n_t$ is not enough to rule out non-canonical models of inflation with a sound speed $c_s$ different from unity. To determine whether inflation was canonical or not, one requires knowledge of additional parameters, such as the running of the spectral index of scalar perturbations $\alpha$. We also study how other parameters related to the ultra violet completion of inflation modify the dependence of $r$ on $c_s$. For instance, we find that heavy degrees of freedom interacting with curvature fluctuations generically tend to make the constraint on the sound speed stronger. Our results, combined with future observations of primordial B-modes, may help to constrain the background evolution of non-canonical models of inflation.

Relic gravity waves and 7 keV dark matter from a GeV scale inflaton

We study the mechanism of generation of 7 keV sterile neutrino Dark Matter (DM) in the model with light inflaton χ, which serves as a messenger of scale invariance breaking. In this model the inflaton, in addition to providing reheating to the Standard Model (SM) particles, decays directly into sterile neutrinos. The latter are responsible for the active neutrino oscillations via seesaw type I mechanism. While the two sterile neutrinos may also produce the lepton asymmetry in the primordial plasma and hence explain the baryon asymmetry of the Universe, the third one being the lightest may be of 7 keV and serve as DM. For this mechanism to work, the mass of the inflaton is bound to be light (0.1–1 GeV) and uniquely determines its properties, which allows to test the model. For particle physics experiments these are: inflaton lifetime (10−5–10−12 s), branching ratio of B-meson to kaon and inflaton (10−6–10−4) and inflaton branching ratios into light SM particles like it would be for the SM Higgs boson of the same mass. For cosmological experiments these are: spectral index of scalar perturbations (ns≃0.957–0.967), and amount of tensor perturbations produced at inflation (tensor-to-scalar ratio r≃0.15–0.005).

THE EFFECT OF ASYMMETRIC BEAMS IN THEWILKINSON MICROWAVE ANISOTROPY PROBEEXPERIMENT

We generate simulations of the CMB temperature field as observed by the WMAP satellite, taking into account the detailed shape of the asymmetric beams and scanning strategy of the experiment, and use these to re-estimate the WMAP beam transfer functions. This method avoids the need of artificially symmetrizing the beams, as done in the baseline WMAP approach, and instead measures the total convolution effect by direct simulation. We find only small differences with respect to the nominal transfer functions, typically less than 1% everywhere, and less than 0.5% at l<400. The net effect on the CMB power spectrum is less than 0.6%. The effect on all considered cosmological parameters are negligible. For instance, we find that the spectral index of scalar perturbations after taking into account the beam asymmetries is n_s = 0.964 +- 0.014, corresponding to a negative shift of -0.1 sigma compared to the previously released WMAP results. Our CMB sky simulations are made publicly available, and can be used for general studies of asymmetric beam effects in the WMAP data.

COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION BY A GAUSSIANIZED BLACKWELL-RAO ESTIMATOR

We introduce a new CMB temperature likelihood approximation called the Gaussianized Blackwell-Rao (GBR) estimator. This estimator is derived by transforming the observed marginal power spectrum distributions obtained by the CMB Gibbs sampler into standard univariate Gaussians, and then approximate their joint transformed distribution by a multivariate Gaussian. The method is exact for full-sky coverage and uniform noise, and an excellent approximation for sky cuts and scanning patterns relevant for modern satellite experiments such as WMAP and Planck. A single evaluation of this estimator between l=2 and 200 takes ~0.2 CPU milliseconds, while for comparison, a single pixel space likelihood evaluation between l=2 and 30 for a map with ~2500 pixels requires ~20 seconds. We apply this tool to the 5-year WMAP temperature data, and re-estimate the angular temperature power spectrum, $C_{\ell}$, and likelihood, L(C_l), for l<=200, and derive new cosmological parameters for the standard six-parameter LambdaCDM model. Our spectrum is in excellent agreement with the official WMAP spectrum, but we find slight differences in the derived cosmological parameters. Most importantly, the spectral index of scalar perturbations is n_s=0.973 +/- 0.014, 1.9 sigma away from unity and 0.6 sigma higher than the official WMAP result, n_s = 0.965 +/- 0.014. This suggests that an exact likelihood treatment is required to higher l's than previously believed, reinforcing and extending our conclusions from the 3-year WMAP analysis. In that case, we found that the sub-optimal likelihood approximation adopted between l=12 and 30 by the WMAP team biased n_s low by 0.4 sigma, while here we find that the same approximation between l=30 and 200 introduces a bias of 0.6 sigma in n_s.

Latest inflation model constraints from cosmic microwave background measurements: Addendum

In this addendum to Phys. Rev. D 74, 023502 (2006), we present an update of cosmological constraints on single-field inflation in light of the Wilkinson Microwave Ansiotropy Probe satellite mission five-year results (WMAP5). We find that the cosmic microwave background data are quite consistent with a Harrison-Zel'dovich primordial spectrum with no running and zero tensor amplitude. We find that the three main conclusions of our analysis of the WMAP three-year data (WMAP3) are consistent with the WMAP5 data: (1) the Harrison-Zel'dovich model is within the 95% confidence level contours; (2) there is no evidence for running of the spectral index of scalar perturbations; (3) from the WMAP 5 data alone, potentials of the form V{proportional_to}{phi}{sup p} are consistent with the data for p=2 and are ruled out for p=4. Furthermore, consistent with our WMAP3 analysis, we find no evidence for primordial tensor perturbations, this time with a 95% confidence upper limit of r<0.4 for the WMAP5 data alone, and r<0.35 for the WMAP5 data taken in combination with the Arcminute Cosmology Bolometer Array (ACBAR)

Bayesian Analysis of the Low-Resolution Polarized 3 Year WMAP Sky Maps

We apply a previously developed Gibbs sampling framework to the foreground corrected 3-yr WMAP polarization data and compute the power spectrum and residual foreground template amplitude posterior distributions. We first analyze the co-added Q- and V-band data, and compare our results to the likelihood code published by the WMAP team. We find good agreement, and thus verify the numerics and data processing steps of both approaches. However, we also analyze the Q- and V-bands separately, allowing for non-zero EB cross-correlations and including two individual foreground template amplitudes tracing synchrotron and dust emission. In these analyses, we find tentative evidence of systematics: The foreground tracers correlate with each of the Q- and V-band sky maps individually, although not with the co-added QV map; there is a noticeable negative EB cross-correlation at l <~ 16 in the V-band map; and finally, when relaxing the constraints on EB and BB, noticeable differences are observed between the marginalized band powers in the Q- and V-bands. Further studies of these features are imperative, given the importance of the low-l EE spectrum on the optical depth of reionization tau and the spectral index of scalar perturbations n_s.

The Lyth Bound and the end of inflation

We derive an extended version of the well-known Lyth Bound on the total variation of theinflaton field, incorporating higher-order corrections in slow roll. We connect the field variationΔϕ to both the spectral index of scalar perturbations and the amplitude of tensor modes. We theninvestigate the implications of this bound for ‘small field’ potentials, where the field rolls off alocal maximum of the potential. The total field variation during inflation is generically of ordermPl, even for potentials with a suppressed tensor/scalar ratio. Much of the total field excursionarises in the last e-fold of inflation and in single field models this problem can only beavoided via fine-tuning or the imposition of a symmetry. Finally, we discuss theimplications of this result for inflationary model building in string theory and supergravity.

Inflation model constraints from the Wilkinson Microwave Anisotropy Probe three-year data

We extract parameters relevant for distinguishing among single-field inflation models from the Wilkinson Microwave Anisotropy Probe (WMAP) three-year data set, and also from WMAP in combination with the Sloan Digital Sky Survey (SDSS) galaxy power spectrum. Our analysis leads to the following conclusions: (1) the Harrison---Zel'dovich model is consistent with both data sets at a 95% confidence level; (2) there is no strong evidence for running of the spectral index of scalar perturbations; (3) potentials of the form $V\ensuremath{\propto}{\ensuremath{\phi}}^{p}$ are consistent with the data for $p=2$, and are marginally consistent with the WMAP data considered alone for $p=4$, but ruled out by WMAP combined with SDSS. We perform a ``Monte Carlo reconstruction'' of the inflationary potential, and find that: (1) there is no evidence to support an observational lower bound on the amplitude of gravitational waves produced during inflation; (2) models such as simple hybrid potentials which evolve toward an inflationary late-time attractor in the space of flow parameters are strongly disfavored by the data, (3) models selected with even a weak slow-roll prior strongly cluster in the region favoring a red power spectrum and no running of the spectral index, consistent with simple single-field inflation models.