Single Field Inflationary Models Research Articles

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.

Reconciling low multipole anomalies and reheating in single field inflationary models

Reheating phase of inflationary Universe can be modeled by parameters Treh, w̄reh and Nreh, which can be constrained by the scalar spectral amplitude As and the scalar spectral index ns. On the other hand the low multipole anomalies in the CMB can be modeled by suitable features in the inflaton potential. We show that the parameters of these features in the inflaton potential provide additional constraints on the reheating parameters. For several single field models we find that the reheating parameters are substantially more constrained by the requirement of compatibility with the proposed explanation for low multipole anomalies.

Measuring the duration of inflation with the curvaton

Simple models of single-field inflation in the very early universe can generate the observed amplitude and scale dependence of the primordial density perturbation, but models with multiple fields can provide an equally good fit to current data. We show how future observations will be able to distinguish between currently favoured models. If a curvaton field generates the primordial perturbations after inflation, we show how the total duration of inflation can be measured.

Magnetogenesis in Natural Inflation Model

We study the process of inflationary magnetogenesis in the natural single-field inflation model, whose parameters are chosen in accordance with the recent observations by the Planck collaboration [1]. The conformal invariance of the Maxwell action is broken by a kinetic coupling with the inflaton field by means of the coupling function as a power of the scale factor, I(ф) ∝ aa, and a < 0 is used in order to avoid the strong coupling problem. For such a, the electric component of the energy density dominates over the magnetic one and, for a <- −2.2, it causes a strong back-reaction, which can spoil inflation and terminate the enhancement of the magnetic field. It is found that the magnetic fields generated without back-reaction problem cannot exceed ∼10−20G at the present epoch, and their spectrum has a blue tilt.

Imprints of Oscillatory Bispectra on Galaxy Clustering

Long-short mode coupling during inflation, encoded in the squeezed bispectrum of curvature perturbations, induces a dependence of the local, small-scale power spectrum on long-wavelength perturbations, leading to a scale-dependent halo bias. While this scale dependence is absent in the large-scale limit for single-field inflation models that satisfy the consistency relation, certain models such as resonant non-Gaussianity show a peculiar behavior on intermediate scales. We reconsider the predictions for the halo bias in this model by working in Conformal Fermi Coordinates, which isolate the physical effects of long-wavelength perturbations on short-scale physics. We find that the bias oscillates with scale with an envelope similar to that of equilateral non-Gaussianity. Moreover, the bias shows a peculiar modulation with the halo mass. Unfortunately, we find that upcoming surveys will be unable to detect the signal because of its very small amplitude. We also discuss non-Gaussianity due to interactions between the inflaton and massive fields: our results for the bias agree with those in the literature.

A Note on Inflation and the Swampland

AbstractWe provide some comments about the constraints on the inflationary models inferred from the two Swampland criteria which have been recently proposed. In particular we argue that, in the absence of any knowledge about the origin of the adiabatic curvature perturbations, within the slow‐roll single field models of inflation there is no tension between the swampland criteria and the current lower bound on the tensor‐to‐scalar ratio.

Quantum diffusion beyond slow-roll: implications for primordial black-hole production

Primordial black-holes (PBH) can be produced in single-field models of inflation with a quasi-inflection point in the potential. In these models, a large production of PBHs requires a deviation from the slow-roll (SR) trajectory. In turn, this SR violation can produce an exponential growth of quantum fluctuations. We study the back-reaction of these quantum modes on the inflationary dynamics using stochastic inflation in the Hamilton-Jacobi formalism. We develop a methodology to solve quantum diffusion beyond SR in terms of the statistical moments of the probability distribution. We apply these techniques to a toy model potential with a quasi-inflection point. We find that there is an enhancement of the power spectrum due to the dominance of the stochastic noise in the phase beyond SR. Moreover, non-Gaussian corrections become as well relevant with a large positive kurtosis. Altogether, this produces a significant boost of PBH production. We discuss how our results extend to other single-field models with similar dynamics. We conclude that the abundance of PBHs in this class of models should be revisited including quantum diffusion.

Inflationary study of non-Gaussianity using two-dimensional geometrical measures of CMB temperature maps

In this work we effectively calculated the two-dimensional Minkowski functionals for cosmic microwave background (CMB) temperature maps generated by single field models of inflation with a standard kinetic term. We started with calculation of the bispectrum of initial perturbations and then calculated the two-dimensional configuration space cubic moments for temperature fluctuations. These cubic moments give rise to first order non-Gaussian correction terms to the Minkowski functionals. Thus, we developed a robust mechanism to predict the amount of non-Gaussianity generated by inflation in the CMB temperature maps using Minkowski functionals.

Mechanisms for primordial black hole production in string theory

We consider mechanisms for producing a significant population of primordial black holes (PBHs) within string inspired single field models of inflation. The production of PBHs requires a large amplification in the power spectrum of curvature perturbations between scales associated with CMB and PBH formation. In principle, this can be achieved by temporarily breaking the slow-roll conditions during inflation. In this work, we identify two string setups that can realise this process. In string axion models of inflation, subleading non-perturbative effects can superimpose steep cliffs and gentle plateaus onto the leading axion potential. The cliffs can momentarily violate the slow-roll conditions, and the plateaus can lead to phases of ultra slow-roll inflation. We thus achieve a string motivated model which both matches the Planck observations at CMB scales and produces a population of light PBHs, which can account for an order one fraction of dark matter. In DBI models of inflation, a sharp increase in the speed of sound sourced by a steep downward step in the warp factor can drive the amplification. In this scenario, discovery of PBHs could indicate non-trivial dynamics in the bulk, such as flux-antibrane annihilation at the tip of a warped throat.

Small field models with gravitational wave signature supported by CMB data.

We study scale dependence of the cosmic microwave background (CMB) power spectrum in a class of small, single-field models of inflation which lead to a high value of the tensor to scalar ratio. The inflaton potentials that we consider are degree 5 polynomials, for which we precisely calculate the power spectrum, and extract the cosmological parameters: the scalar index ns, the running of the scalar index nrun and the tensor to scalar ratio r. We find that for non-vanishing nrun and for r as small as r = 0.001, the precisely calculated values of ns and nrun deviate significantly from what the standard analytic treatment predicts. We study in detail, and discuss the probable reasons for such deviations. As such, all previously considered models (of this kind) are based upon inaccurate assumptions. We scan the possible values of potential parameters for which the cosmological parameters are within the allowed range by observations. The 5 parameter class is able to reproduce all of the allowed values of ns and nrun for values of r that are as high as 0.001. Subsequently this study at once refutes previous such models built using the analytical Stewart-Lyth term, and revives the small field brand, by building models that do yield an appreciable r while conforming to known CMB observables.

Degeneracy in the spectrum and bispectrum among featured inflaton potentials

We study the degeneracy of the primordial spectrum and bispectrum of the curvature perturbation in single field inflationary models with a class of features in the inflaton potential. The feature we consider is a discontinuous change in the shape of the potential and is controlled by a couple of parameters that describe the strength of the discontinuity and the change in the potential shape. This feature produces oscillations of the spectrum and bispectrum around the comoving scale k=k0 that exits the horizon when the inflaton passes the discontinuity. We find that the effects on the spectrum and almost all configurations of the bispectrum including the squeezed limit depend on a single quantity which is a function of the two parameters defining the feature. This leads to a degeneracy, i.e. different features of the inflaton potential can produce the same observational effects. However, we find that the degeneracy in the bispectrum is removed at the equilateral limit around k=k0. This can be used to discriminate different models which give the same spectrum.

Series solutions of single-field models of inflation

We describe a generic method, first presented in Ref.[1], to find inflationary solutions without the need to be specific about the scalar potential. The method shows that single-field models of inflation can be classified in two groups according to their predictions of inflationary observables, we call these groups as Class I and Class II. We apply the method to the study of different scalar potentials and compare their results with recent observational data. We conclude that potentials belonging to Class I are in better agreement with observations mostly because they can provide large enough values of the spectral index of linear perturbations.

The decisive future of inflation

How much more will we learn about single-field inflationary models in the future? We address this question in the context of Bayesian design and information theory. We develop a novel method to compute the expected utility of deciding between models and apply it to a set of futuristic measurements. This necessarily requires one to evaluate the Bayesian evidence many thousands of times over, which is numerically challenging. We show how this can be done using a number of simplifying assumptions and discuss their validity. We also modify the form of the expected utility, as previously introduced in the literature in different contexts, in order to partition each possible future into either the rejection of models at the level of the maximum likelihood or the decision between models using Bayesian model comparison. We then quantify the ability of future experiments to constrain the reheating temperature and the scalar running. Our approach allows us to discuss possible strategies for maximising information from future cosmological surveys. In particular, our conclusions suggest that, in the context of inflationary model selection, a decrease in the measurement uncertainty of the scalar spectral index would be more decisive than a decrease in the uncertainty in the tensor-to-scalar ratio. We have incorporated our approach into a publicly available python class, foxi,1 that can be readily applied to any survey optimisation problem.

Inflationary predictions of double-well, Coleman-Weinberg, and hilltop potentials with non-minimal coupling

We discuss how the non-minimal coupling ξϕ2R between the inflaton and the Ricci scalar affects the predictions of single field inflation models where the inflaton has a non-zero vacuum expectation value (VEV) v after inflation. We show that, for inflaton values both above the VEV and below the VEV during inflation, under certain conditions the inflationary predictions become approximately the same as the predictions of the Starobinsky model. We then analyze inflation with double-well and Coleman-Weinberg potentials in detail, displaying the regions in the v-ξ plane for which the spectral index ns and the tensor-to-scalar ratio r values are compatible with the current observations. r is always larger than 0.002 in these regions. Finally, we consider the effect of ξ on small field inflation (hilltop) potentials.

Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis–Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et al. (2013) [21] for these Berry phases, which is resolved to yield agreement with our results.

Primordial black holes from polynomial potentials in single field inflation

Within canonical single field inflation models, we provide a method to reverse engineer and reconstruct the inflaton potential from a given power spectrum. This is not only a useful tool to find a potential from observational constraints, but also gives insight into how to generate a large amplitude spike in density perturbations, especially those that may lead to primordial black holes (PBHs). In accord with other works, we find that the usual slow-roll conditions need to be violated in order to generate a significant spike in the spectrum. We find that a way to achieve a very large amplitude spike in single field models is for the classical roll of the inflaton to over-shoot a local minimum during inflation. We provide an example of a quintic polynomial potential that implements this idea and leads to the observed spectral index, observed amplitude of fluctuations on large scales, significant PBH formation on small scales, and is compatible with other observational constraints. We quantify how much fine-tuning is required to achieve this in a family of random polynomial potentials, which may be useful to estimate the probability of PBH formation in the string landscape.

Running of the spectrum of cosmological perturbations in string gas cosmology

We compute the running of the spectrum of cosmological perturbations in String Gas Cosmology, making use of a smooth parametrization of the transition between the early Hagedorn phase and the later radiation phase. We find that the running has the same sign as in simple models of single scalar field inflation. Its magnitude is proportional to $(1 - n_s)$ ($n_s$ being the slope index of the spectrum), and it is thus parametrically larger than for inflationary cosmology, where it is proportional to $(1 - n_s)^2$.

CMB constraints on the inflaton couplings and reheating temperature in \u03b1-attractor inflation

We study reheating in α-attractor models of inflation in which the inflaton couples to other scalars or fermions. We show that the parameter space contains viable regions in which the inflaton couplings to radiation can be determined from the properties of CMB temperature fluctuations, in particular the spectral index. This may be the only way to measure these fundamental microphysical parameters, which shaped the universe by setting the initial temperature of the hot big bang and contain important information about the embedding of a given model of inflation into a more fundamental theory of physics. The method can be applied to other models of single field inflation.

Test the mergers of the primordial black holes by high frequency gravitational-wave detector

The black hole could have a primordial origin if its mass is less than 1M_odot . The mergers of these black hole binaries generate stochastic gravitational-wave background (SGWB). We investigate the SGWB in high frequency band 10^{8}–10^{10},mathrm {Hz}. It can be detected by high frequency gravitational-wave detector. Energy density spectrum and amplitude of the SGWB are derived. The upper limit of the energy density spectrum is around 10^{-7}. Also, the upper limit of the amplitude ranges from 10^{-31.5} to 10^{-29.5}. The fluctuation of spacetime origin from gravitational wave could give a fluctuation of the background electromagnetic field in a high frequency gravitational-wave detector. The signal photon flux generated by the SGWB in the high frequency band 10^{8}–10^{10},mathrm {Hz} is derived, which ranges from 1 to 10^2,mathrm {s^{-1}}. The comparison between the signal photon flux generated by relic gravitational waves (RGWs) and the SGWB is also discussed in this paper. It is shown that the signal photon flux generated by the RGW, which is predicted by the canonical single-field slow-roll inflation models, is sufficiently lower than the one generated by the SGWB in the high frequency band 10^{8}–10^{10},mathrm {Hz}. Our results indicate that the SGWB in the high frequency band 10^{8}–10^{10},mathrm {Hz} is more likely to be detected by the high frequency gravitational-wave detector.

Equation of State and Duration to Radiation Domination after Inflation.

We calculate the equation of state after inflation and provide an upper bound on the duration before radiation domination by taking the nonlinear dynamics of the fragmented inflaton field into account. A broad class of single-field inflationary models with observationally consistent flattening of the potential at a scale M away from the origin, V(ϕ)∝|ϕ|^{2n} near the origin, and where the couplings to other fields are ignored, is included in our analysis. We find that the equation of state parameter w→0 for n=1 and w→1/3 (after sufficient time) for n≳1. We calculate how the number of e-folds to radiation domination depends on both n and M when M∼m_{Pl}, whereas when M≪m_{Pl}, we find that the duration to radiation domination is negligible. Our results are explained in terms of a linear instability analysis in an expanding universe and scaling arguments, and are supported by 3+1-dimensional lattice simulations. We show that our upper bound on the postinflationary duration before radiation domination reduces the uncertainty in inflationary observables even when couplings to additional light fields are included (at least under the assumption of perturbative decay).