Inflaton Potential Research Articles

Tachyonic effects on Kähler moduli stabilized inflaton potential in type-IIB/F theory

We investigate the effects of inclusion of charged tachyonic open-string scalars in the perturbative and the non-perturbative Kähler moduli stabilizations in a geometry of three intersecting magnetized D7-brane stacks in type-IIB/F theory and also study the overall influence of this process on the inflaton potential, in a hybrid inflation scenario. We find that a tachyon lowers the minimum of the inflaton potential and assists to end the inflation. For simplicity, we have included one tachyon at a time in the present work and observe that this procedure preserves the features of slow-roll plateau of the potential. An interesting observation here is that the tachyonic part of the potential can be fine-tuned to get an almost zero minimum of the potential, thereby conforming to the small experimental value of the cosmological constant.

A generalized method of constraining Warm Inflation with CMB data

A thorough MCMC analysis of any inflationary model against the current cosmological data is essential for assessing the validity of such a model as a viable inflationary model. Warm Inflation, producing both thermal and quantum fluctuations, yield a complex form of scalar power spectrum, which, in general, cannot be directly written as a function of the comoving wavenumber k, an essential step to incorporate the primordial spectra into CAMB to do an MCMC analysis through CosmoMC/Cobaya. In this paper, we devised an efficient generalized methodology to mould the WI power spectra as a function of k, without the need of slow-roll approximation of the inflationary dynamics. The methodology is directly applicable to any Warm Inflation model, including the ones with complex forms of the dissipative coefficient and the inflaton potential.

Intermediate inflation in a generalized non-minimal derivative coupling model

In this work, we consider intermediate inflation in the context of the generalized non-minimal derivative coupling (GNMDC) model. In the GNMDC model, inflation is driven by a canonical scalar field that is coupled not only to gravity but also to the derivative of the scalar field. The model introduces new dynamics and features during the inflationary epoch. We find inflationary solutions with a power law scalar field for the power law coupling function. Additionally, we determine the inflaton potential that generates intermediate expansion of the scale factor. We also discuss the background equations in the high friction limit and derive constraints on the parameters of our model. Furthermore, we investigate the cosmological perturbations in the slow roll approximation within the GNMDC model, and we calculate the scalar and tensor spectral index and the tensor-to-scalar ratio during intermediate inflation. We compare the results of this model with observational data that can be used to test the model using cosmic microwave background radiation data. Overall, we establish conditions for the inflaton potential that ensure the continuation of accelerated expansion during slow roll inflation. We numerically analyze the power spectrum and spectral index for scalar and tensor modes in intermediate inflation in the high friction limit, and we use Planck 2018 data to obtain constraints on the parameters of the model. We demonstrate that intermediate inflation in the GNMDC model is successful in evaluation and explanation of background and perturbation quantities using observational data.

Leptogenesis, primordial gravitational waves, and PBH-induced reheating

We explore the possibility of producing the observed matter-antimatter asymmetry of the Universe uniquely from the evaporation of primordial black holes (PBHs) that are formed in an inflaton-dominated background. Considering the inflaton (ϕ) to oscillate in a monomial potential V(ϕ)∝ϕn, we show, it is possible to obtain the desired baryon asymmetry via vanilla leptogenesis from evaporating PBHs of initial mass ≲10 g. We find that the allowed parameter space is heavily dependent on the shape of the inflaton potential during reheating (determined by the exponent of the potential n), the energy density of PBHs (determined by β), and the nature of the coupling between the inflaton and the Standard Model. To complete the minimal gravitational framework, we also include in our analysis the gravitational leptogenesis setup through inflaton scattering via exchange of graviton, which opens up an even larger window for PBH mass, depending on the background equation of state. We finally illustrate that such gravitational leptogenesis scenarios can be tested with upcoming gravitational wave (GW) detectors, courtesy of the blue-tilted primordial GW with inflationary origin, thus paving a way to probe a PBH-induced reheating together with leptogenesis. Published by the American Physical Society 2024

Constraining the general oscillatory inflaton potential with freeze-indark matter and gravitational waves

The reheating phase after inflation is one of the least observationally constrained epochs in the evolution of the Universe. The forthcoming gravitational wave observatories will enable us to constrain at least some of the non-standard scenarios. For example, models where the radiation bath is produced by the perturbative inflaton decay that oscillates around a minimum of the potential of the form V ∝ ϕ 2n, with n > 2. In such scenarios a part of the inflationary gravitational wave spectrum becomes blue tilted, making it observable, depending on the inflation energy scale and the reheating temperature. The degeneracy between the latter two parameters can be broken if dark matter in the Universe is produced via the freeze-in mechanism. The combination of the independent measurement of dark matter mass with gravitational wave observations makes it possible to constrain the reheating temperature and the energy scale at the end of inflation, at least within some parameter ranges.

Role of cosmological gravitational particle production in baryogenesis

We investigate the generation of the baryon asymmetry within the framework of cosmological gravitational particle production, employing the Bogoliubov approach. We examine two well-known baryogenesis scenarios, namely baryogenesis in grand unified theories (GUT) and leptogenesis, while considering reheating temperatures sufficiently low for thermal processes to be negligible. Considering α–attractor T-models for the inflaton potential, we demonstrate that GUT baryogenesis from scalar decays can be successful across a large range of conformal couplings with gravity, without necessitating substantial levels of CP violation. In the case of leptogenesis, we find that the reheating temperature should be TRH≲106 GeV for right-handed neutrino masses M1≲6×1012 GeV to generate the observed asymmetry. Published by the American Physical Society 2024

Palatini [formula omitted]: A new framework for inflationary attractors

Palatini F(R) gravity proved to be a powerful tool in order to realize asymptotically flat inflaton potentials. Unfortunately, it also inevitably implies higher-order inflaton kinetic terms in the Einstein frame that might jeopardize the evolution of the system out of the slow-roll regime. We prove that a F(R+X) gravity, where X is the inflaton kinetic term, solves the issue. Moreover, when F is a quadratic function such a choice easily leads to a new class of inflationary attractors, fractional attractors, that generalizes the already well-known polynomial α-attractors.

Higgs inflation: Constraining the top quark mass and breaking the H0-σ8 correlation

Extending previous results, we explore aspects of the reheating mechanism for non-minimal Higgs inflation in the strong coupling regime. We constrain the radiative corrections for the inflaton's potential by considering the Coleman-Weinberg approximation and use the Renormalization Group Equations for the Higgs field to derive an upper limit on the top quark mass. Using the current Cosmic Microwave Background, Baryon Acoustic Oscillation, and Supernovae data, we obtain mt≤170.44 GeV, confirming the observational compatibility of the model with recent mt estimates reported by the CMS collaboration. We also analyze the breakdown of the well-known correlation involving the Hubble constant H0 and the clustering parameter σ8, which makes the model interesting in light of the cosmological tensions discussed over the last decade.

An analytical approximation of the evolution of the primordial curvature perturbation in the ultraslow-roll inflation: an extended study

Cosmic inflation can enter an ultraslow-roll (USR) stage, if there is a plateau on the inflaton potential. During this stage, the primordial curvature perturbation Rk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathscr {R}}}_k$$\\end{document} and its power spectrum PR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathscr {P}}}_{{\\mathscr {R}}}$$\\end{document} can be remarkably enhanced on small scales. In this work, an analytical approximation is provided to systematically study the evolution of Rk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathscr {R}}}_k$$\\end{document} in the USR inflation. We first discuss the asymptotic solutions of the moduli and arguments of Rk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathscr {R}}}_k$$\\end{document} and its time derivative Rk,N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathscr {R}}}_{k,N}$$\\end{document} on the sub- and super-horizon scales separately and find that all these solutions have simple exponential forms. Then, Rk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathscr {R}}}_k$$\\end{document} on five typical scales are investigated in order. Our analytical approximation predicts that Rk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathscr {R}}}_k$$\\end{document} first revolves around the origin in the complex plane, but if it crosses the horizon around the start of the USR stage, there appears a subsequent linear evolution towards or away from the origin. This behavior naturally explains the shape of PR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathscr {P}}}_{{\\mathscr {R}}}$$\\end{document} from the sharp dip to the peak and matches the numerical results perfectly. Moreover, the minimum of PR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathscr {P}}}_{{\\mathscr {R}}}$$\\end{document} is exactly proved to be nonvanishing. Our analytical approximation will help the model building in primordial black hole and gravitational wave physics.

Non-perturbative wavefunction of the universe in inflation with (resonant) features

We study the statistics of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential (resonant non-Gaussianity). We do so by deriving the wavefunction Ψ[ζ(x)] non-perturbatively in ζ, but at first order in the amplitude of the oscillations. The expression of the wavefunction of the universe (WFU) is explicit and does not require solving partial differential equations. One finds qualitative deviations from perturbation theory for |ζ| ≳ α−2, where α ≫ 1 is the number of oscillations per Hubble time. Notably, the WFU exhibits distinct behaviours for negative and positive values of ζ (troughs and peaks respectively). While corrections for ζ < 0 remain relatively small, of the order of the oscillation amplitude, positive ζ yields substantial effects, growing exponentially as eπα/2 in the limit of large ζ. This indicates that even minute oscillations give large effects on the tail of the distribution.

Beyond (and back to) Palatini quadratic gravity and inflation

We study single-field slow-roll inflation embedded in Palatini F(R) gravity where F(R) grows faster than R 2. Surprisingly, the consistency of the theory requires the Jordan frame inflaton potential to be unbounded from below. Even more surprisingly, this corresponds to an Einstein frame inflaton potential bounded from below and positive definite. We prove that for all such Palatini F(R)'s, there exists a universal strong coupling limit corresponding to a quadratic F(R) with the wrong sign for the linear term and a cosmological constant in the Jordan frame. In such a limit, the tensor-to-scalar ratio r does not depend on the original inflaton potential, while the scalar spectral index ns does. Unfortunately, the system is ill-defined out of the slow-roll regime. A possible way out is to upgrade to a F(R,X) model, with X the Jordan frame inflaton kinetic term. Such a modification essentially leaves the inflationary predictions unaffected.

Is natural inflation in agreement with CMB data?

Natural inflation is a well-motivated model for the early universe in which an inflaton potential of the pseudo-Nambu-Goldstone form, V(ϕ) = Λ4[1 + cos(ϕ/f)], can naturally drive a cosmic accelerated epoch. This paper investigates the observational viability of the minimally and non-minimally coupled natural inflation scenarios in light of current Cosmic Microwave Background (CMB) observations. We find that a small and negative coupling of the field with gravity can alleviate the well-known observational discrepancies of the minimally coupled model. We perform a Monte Carlo Markov Chain analysis of the Planck 2018 CMB and BICEP/Keck Array B-mode polarization data to estimate how strong the coupling ξ should be to achieve concordance with data. We also briefly discuss the impact of these results on the physical interpretation of the natural inflation scenario.

Dynamical inflation stimulated cogenesis

We propose a minimal setup that realises dynamical inflection point inflation, and, using the same field content, generates neutrino masses, a baryon asymmetry of the universe, and dark matter. A dark SU(2)D gauge sector with a dark scalar doublet playing the role of inflaton is considered along with several doublet and singlet fermions sufficient to realise multiple inflection points in the inflaton potential. The singlet fermions couple to SM leptons and generate neutrino masses via the inverse seesaw mechanism. Those fermions also decay asymmetrically and out of equilibrium, generating a baryon asymmetry via leptogenesis. Some of the fermion doublets are dark matter, and they are produced via inflaton decay and freeze-in annihilation of the same fermions that generate the lepton asymmetry. Reheating, leptogenesis, and dark matter are all at the TeV scale.

Observable gravitational waves from hyperkination in Palatini gravity and beyond

We consider cosmology with an inflaton scalar field with an additional quartic kinetic term. Such a theory can be motivated by Palatini R+R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R+R^2$$\\end{document} modified gravity. Assuming a runaway inflaton potential, we take the Universe to become dominated by the kinetic energy density of the scalar field after inflation. Initially, the leading kinetic term is quartic and we call the corresponding period hyperkination. Subsequently, the usual quadratic kinetic term takes over and we have regular kination, until reheating. We study, both analytically and numerically, the spectrum of primordial gravitational waves generated during inflation and re-entering the horizon during the subsequent eras. We demonstrate that the spectrum is flat for modes re-entering during radiation domination and hyperkination and linear in frequency for modes re-entering during kination: kinetic domination boosts the spectrum, but hyperkination truncates its peak. As a result, the effects of the kinetic period can be extended to observable frequencies without generating excessive gravitational waves, which could otherwise destabilise the process of Big Bang Nucleosynthesis. We show that there is ample parameter space for the primordial gravitational waves to be observable in the near future. If observed, the amplitude and ‘knee’ of the spectrum will provide valuable insights into the background theory.

Highly asymmetric probability distribution from a finite-width upward step during inflation

We study a single-field inflation model in which the inflaton potential has an upward step between two slow-roll regimes by taking into account the finite width of the step. We calculate the probability distribution function (PDF) of the curvature perturbation P[ℛ] using the δN formalism. The PDF has an exponential-tail only for positive ℛ whose slope depends on the step width. We find that the tail may have a significant impact on the estimation of the primordial black hole abundance. We also show that the PDF P[ℛ] becomes highly asymmetric on a particular scale exiting the horizon before the step, at which the curvature power spectrum has a dip. This asymmetric PDF may leave an interesting signature in the large scale structure such as voids.

Stochastic dynamics of multi-waterfall hybrid inflation and formation of primordial black holes

We show that a hybrid inflation model with multiple waterfall fields can result in the formation of primordial black holes (PBHs) with an astrophysical size, by using an advanced algorithm to follow the stochastic dynamics of the waterfall fields. This is in contrast to the case with a single waterfall field, where the wavelength of density perturbations is usually too short to form PBHs of the astrophysical scale (or otherwise PBHs are overproduced and the model is ruled out) unless the inflaton potential is tuned. In particular, we demonstrate that PBHs with masses of order 1020 g can form after hybrid inflation consistently with other cosmological observations if the number of waterfall fields is about 5 for the case of instantaneous reheating. Observable gravitational waves are produced from the second-order effect of large curvature perturbations as well as from the dynamics of texture or global defects that form after the waterfall phase transition.

Reheating after inflaton fragmentation

In the presence of self-interactions, the post-inflationary evolution of the inflaton field is driven into the non-linear regime by the resonant growth of its fluctuations. The once spatially homogeneous coherent inflaton is converted into a collection of inflaton particles with non-vanishing momentum. Fragmentation significantly alters the energy transfer rate to the inflaton's offspring during the reheating epoch. In this work we introduce a formalism to quantify the effect of fragmentation on particle production rates, and determine the evolution of the inflaton and radiation energy densities, including the corresponding reheating temperatures. For an inflaton potential with a quartic minimum, we find that the efficiency of reheating is drastically diminished after backreaction, yet it can lead to temperatures above the big bang nucleosynthesis limit for sufficiently large couplings. In addition, we use a lattice simulation to estimate the spectrum of induced gravitational waves, sourced by the scalar inhomogeneities, and discuss detectability prospects. We find that a Boltzmann approach allows to accurately predict some of the main features of this spectrum.

Mimetic inflation and self-reproduction

It is shown how self-reproduction can be easily avoided in the inflationary universe, even when inflation starts at Planck scales. This is achieved by a simple coupling of the inflaton potential with a mimetic field. In this case, the problem of fine-tuning of the initial conditions does not arise, while eternal inflation and the multiverse with all their widely discussed problems are avoided.

Effects of the inflaton potential on the primordial power spectrum in loop quantum cosmology scenarios

Effects of the inflaton potential on the primordial power spectrum in loop quantum cosmology scenarios

Novel CMB constraints on the α parameter in alpha-attractor models

Cosmological α-attractors are a compelling class of inflationary models. They lead to universal predictions for large-scale observables, broadly independent from the functional form of the inflaton potential. In this work we derive improved analytical predictions for the large-scale observables, whose dependence on the duration of reheating and the parameter α is made explicit. We compare these with Planck and BICEP/Keck 2018 data in the framework of a Bayesian study, employing uniform logarithmic and linear priors for α. Our improved universal predictions allow direct constraints on the duration of reheating. Furthermore, while it is well-known that CMB constraints on the tensor-to-scalar ratio can be used to place an upper bound on the α parameter, we demonstrate that including the α-dependence of the scalar spectral tilt yields novel constraints on α. In particular, for small α, the scalar spectral tilt scales with log10 α, regardless of the specific potential shape. For decreasing α, this eventually puts the models in tension with CMB measurements, bounding the magnitude of α from below. Therefore, in addition to the upper bound from the tensor-to-scalar ratio, we derive the first lower bound on the magnitude of α for α-attractor T-models, log10 α = -4.2+5.4 -8.6 at 95% C.L.