Inflaton Research Articles

The Ricci flow and the early universe

A framework of quantum spacetime reference frame is proposed and reviewed, in which the quantum spacetime at the Gaussian approximation is deformed by the Ricci flow. At sufficient large scale, the Ricci flow not only smooths out local small irregularities making the universe a homogeneous and isotropic Friedmann–Robertson–Walker metric, but also develops a local singularity at the physical-time origin. Due to the phenomenological suppression of the non-Gaussian primordial perturbations, we assume the validity of the Ricci flow applying to the high curvature region near the local singularity of the early universe. The no-local-collapsing theorem of Perelman ensures the existence of a canonical neighborhood around the large curvature pinching point, which resembles a gradient shrinking Ricci soliton (GSRS) solution of the Ricci flow. Without any inflaton field, the GSRS naturally reproduces an exact inflationary deSitter universe near the singularity at the leading order. Without any rolling-down behavior of inflaton, the deviation from exact deSitter described by the “slow roll parameters” can be calculated by a small deviation from the singular flow-time via the Ricci flow, and the primordial perturbations can also be studied on the GSRS background, the power spectrum of the scalar perturbation agrees with present observations, and the one of the tensor perturbation is predicted too small to be detectable than the standard inflation. The previous treatment of the cosmological constant and the effective gravity are also briefly reviewed in the framework. So we argue that the Ricci flow provides us a possible unified view and treatment of the late epoch accelerating expansion and early epoch inflation of the universe without introducing dark energy or inflaton (dark energy of the second kind).

Growth of curvature perturbations for PBH formation & detectable GWs in non-minimal curvaton scenario revisited

We revisit the growth of curvature perturbations in non-minimal curvaton scenario with a non-trivial field metric λ(ϕ) where ϕ is an inflaton field, and incorporate the effect from the non-uniform onset of curvaton's oscillation in terms of an axion-like potential. The field metric λ(ϕ) plays a central role in the enhancement of curvaton field perturbation δχ, serving as an effective friction term which can be either positive or negative, depending on the first derivative λ ,ϕ . Our analysis reveals that δχ undergoes the superhorizon growth when the condition η eff ≡ -2 √2ϵ M Pl λ ,ϕ /λ < -3 is satisfied. This is analogous to the mechanism responsible for the amplification of curvature perturbations in the context of ultra-slow-roll inflation, namely the growing modes dominate curvature perturbations. As a case study, we examine the impact of a Gaussian dip in λ(ϕ) and conduct a thorough investigation of both the analytical and numerical aspects of the inflationary dynamics. Our findings indicate that the enhancement of curvaton perturbations during inflation is not solely determined by the depth of the dip in λ(ϕ). Rather, the first derivative λ ,ϕ also plays a significant role, a feature that has not been previously highlighted in the literature. Utilizing the δ𝒩 formalism, we derive analytical expressions for both the final curvature power spectrum and the non-linear parameter f NL in terms of an axion-like curvaton's potential leading to the non-uniform curvaton's oscillation. Additionally, the resulting primordial black hole abundance and scalar-induced gravitational waves are calculated, which provide observational windows for PBHs.

PBHs and GWs from 𝕋2-inflation and NANOGrav 15-year data

In this paper, we propose a novel mechanism in 𝕋2-inflation to enhance the power spectrum large enough to seed primordial black holes (PBHs) formation. To accomplish this, we consider the coupling function between the inflaton field and 𝕋2 = TμνTμν term. PBHs formed within this scenario can contribute partially or entirely to dark matter (DM) abundance. Furthermore, the amplification in the scalar power spectrum will concurrently produce significant scalar-induced gravitational waves (SIGWs) as a second-order effect. In addition, the energy spectrum associated with SIGWs can be compatible with the recent NANOGrav 15-year stochastic gravitational wave detection and fall into the sensitivity range of other forthcoming GW observatories.

Quasi-de sitter solution, negative norm state and Krein space in cosmology

Recent observational data have shown two important results about cosmic inflation: First, the primordial power spectrum is approximately scale invariant. Secondly, the space–time geometry during inflation is quasi-de Sitter. In this paper, we study the background field method and the concept of negative norm states in the framework of Krein space to use in early universe cosmology. For the inflaton field equation, based on the observations and taking into account our studies, we suggest an alternative proposal. We will take the quasi-de Sitter solutions as the physical geometry with the positive norm and the pure de Sitter solutions as the background geometry with the negative norm. In the following, we review the consequences of applying the proposal to calculate some cosmological quantities.

Effect of dissipation on chromo-natural inflation

In this work, we examined chromo-natural inflation in the context of warm inflation with constant and variable dissipation coefficients. We studied the cosmological perturbation theory in this model and obtained the scalar and tensor power spectra in each case. The sources of density fluctuations in this model are mainly the thermal fluctuations of the inflaton field like a general warm inflationary model. Finally, cosmological observables, namely, the spectral index and tensor-to-scalar ratio are calculated. It is found that the cosmological observables are consistent with observational Planck 2018 and BICEP bounds for sub-Planckian values of axion decay constant [Formula: see text] in case of temperature–inflaton-dependent dissipation coefficient. In case of the constant and temperature-dependent dissipation coefficient, the values of axion decay constant [Formula: see text] can be lowered below the GUT scale.

Primordial non-Gaussianity in the warmk-inflation

This paper presents and investigates non-Gaussian perturbations for the warm $k$-inflation model that is driven by pure kinetic energy. The two complementary components of the overall non-Gaussianity are the three-point and four-point correlations. The intrinsic non-Gaussian component, denoted as the nonlinear parameter ${f}_{NL}^{\mathrm{int}}$, is rooted in the three-point correlation for the inflaton field. Meanwhile, the $\ensuremath{\delta}N$ part non-Gaussianity, denoted as ${f}_{NL}^{\ensuremath{\delta}N}$, is the contribution attributed to the four-point correlation function of the inflaton field. In this paper, the above two components in warm $k$-inflation are individually computed and analyzed under the condition that the dissipative coefficient in warm inflation is temperature independent. Then, comparisons and discussions between them are conducted, and the non-Gaussian theoretical results are compared with experimental observations to determine the range of model parameters within the allowable range of observation.

Numerical Studies of Back Reaction Effects in an Analog Model of Cosmological Preheating.

We theoretically propose an atomic Bose-Einstein condensate as an analog model of backreaction effects during the preheating stage of the early Universe. In particular, we address the out-of-equilibrium dynamics where the initially excited inflaton field decays by parametrically exciting the matter fields. We consider a two-dimensional, ring-shaped BEC under a tight transverse confinement whose transverse breathing mode and the Goldstone and dipole excitation branches simulate the inflaton and quantum matter fields, respectively. A strong excitation of the breathing mode leads to an exponentially growing emission of dipole and Goldstone excitations via parametric pair creation: Our numerical simulations of the BEC dynamics show how the associated backreaction effect results not only in an effective friction of the breathing mode, but also in a quick loss of longitudinal spatial coherence of the initially in-phase excitations. Implications of this result on the validity of the usual semiclassical description of backreaction are finally discussed.

Primordial black holes generated by the non-minimal spectator field

We improve and generalize the non-minimal curvaton model originally proposed in arXiv: 2112.12680 to a model in which a spectator field non-minimally couples to an inflaton field and the power spectrum of the perturbation of spectator field at small scales is dramatically enhanced by the sharp feature in the form of non-minimal coupling. At or after the end of inflation, the perturbation of the spectator field is converted into curvature perturbation and leads to the formation of primordial black holes (PBHs). Furthermore, for example, we consider three phenomenological models for generating PBHs with mass function peaked at ~ 10−12Mʘ and representing all the cold dark matter in our universe and find that the scalar induced gravitational waves generated by the curvature perturbation can be detected by the future space-borne gravitational-wave detectors such as Taiji, TianQin, and LISA.

The Warm Inflation Story

Warm inflation has normalized two ideas in cosmology, that in the early universe the initial primordial density perturbations generally could be of classical rather than quantum origin and that during inflation, particle production from interactions amongst quantum field, and its backreaction effects, can occur concurrent with inflationary expansion. When we first introduced these ideas, both were met with resistance, but today they are widely accepted as possibilities with many models and applications based on them, which is an indication of the widespread influence of warm inflation. Open quantum field theory, which has been utilized in studies of warm inflation, is by now a relevant subject in cosmology, in part due to this early work. In this review I first discuss the basic warm inflation dynamics. I then outline how to compute warm inflation dynamics from first-principles quantum field theory (QFT) and in particular how a dissipative term arises. Warm inflation models can have an inflaton mass bigger than the Hubble scale and the inflaton field excursion can remain sub-Planckian, thus overcoming the most prohibitive problems of inflation model building. I discuss the early period of my work in developing warm inflation that helped me arrive at these important features of its dynamics. Inflationary cosmology today is immersed in hypothetical models, which by now are acting as a diversion from reaching any endgame in this field. I discuss better ways to approach model selection and give necessary requirements for a well constrained and predictive inflation model. A few warm inflation models are pointed out that could be developed to this extent. I discuss how, at this stage, more progress would be made in this subject by taking a broader view on the possible early universe solutions that include not just inflation but the diverse range of options.

Analog simulations of early universe pre-heating and the back-reaction effect

We theoretically propose a ring-shaped, two-dimensional atomic Bose-Einstein condensate as analog model to investigate back-reaction effects during the pre-heating of the early universe. We study the out-of-equilibrium dynamics by which the inflaton field decays by parametrically exciting the vacuum fluctuations that initially populate the matter fields. By working at the level of the truncated Wigner approximation, our numerical simulations show how a signature of back-reaction beyond the semiclassical level is encoded in the effective friction experienced by the analog of the inflaton field, as well as in the spatial de-phasing of its oscillations and in the entanglement between the inflaton and matter fields degrees-of-freedoms.

On the constant roll complex scalar field inflationary models

In this paper we wish to point out the possibility of using a complex scalar field in a constant roll inflationary model, as needed for observational viability. We extend the idea of real field inflaton with constant rate of roll to a complex field, showing the feasibility of solving Einstein Klein-Gordon equations constrained by an appropriate form of constant roll definition. As compared to the well known (two-parametric class of) real field models, there is one more degree of flexibility in constant roll inflationary solutions which is represented by an arbitrary function of time, γ(t). We work with an arbitrary but constant function γ (where γ = 0 refers to the corresponding real field model) and find new inflationary class of potentials. In this class of models, the behavior of real and complex field models are similar in some aspects, for example the solutions with large constant roll parameter are not stable and should be considered as early time transients. These field solutions relax at late time on a dual attractor trajectory. However, complex fields phase space trajectories reach this stable regime after real fields. We performed the stability analysis on γ function space solutions and found that dynamically stable trajectories in phase space are stable under γ variations. We extended this study by considering multifield models of constant roll inflation with non-canonical kinetic terms. By enlarging the size of field space, we showed that a multifield constant roll model is dynamically a single field effective theory. If field space is parametrized by N non-canonical fields, there will be N free parameters in the potential that can be attributed to the interaction between the fields.

Leptogenesis via inflaton mass terms in nonminimally coupled inflation

We consider a model of baryogenesis based on adding lepton number-violating quadratic mass terms to the inflaton potential of a non-minimally coupled inflation model. The $L$-violating mass terms generate a lepton asymmetry in a complex inflaton field via the mass term Affleck-Dine mechanism, which is transferred to the Standard Model (SM) sector when the inflaton decays to right-handed (RH) neutrinos. The model is minimal in that it requires only the SM sector, RH neutrinos, and a non-minimally coupled inflaton sector. We find that baryon isocurvature fluctuations can be observable in metric inflation but are negligible in Palatini inflation. The model is compatible with reheating temperatures that may be detectable in the observable primordial gravitational waves predicted by metric inflation.

Constraining barrow entropy-based cosmology with power-law inflation

We study the inflationary era of the Universe in a modified cosmological scenario based on the gravity-thermodynamics conjecture with Barrow entropy instead of the usual Bekenstein–Hawking one. The former arises from the effort to account for quantum gravitational effects on the horizon surface of black holes and, in a broader sense, of the Universe. First, we extract modified Friedmann equations from the first law of thermodynamics applied to the apparent horizon of a Friedmann–Robertson–Walker Universe. Assuming a power-law behavior for the scalar inflaton field, we then investigate how the inflationary dynamics is affected in Barrow cosmological setup. We find that the inflationary era may phenomenologically consist of the slow-roll phase, while Barrow entropy is incompatible with kinetic inflation. By demanding observational consistency of the scalar spectral index and tensor-to-scalar ratio with recent Planck data, we finally constrain Barrow exponent to Delta lesssim mathcal {O}(10^{-4}), which is the most stringent bound in so-far literature.

Constant-roll inflation in modified f(R,phi ) gravity model using Palatini formalism

In this work, we study a constant-roll inflationary model in the Palatini formalism using modified gravity. Here our action consists a non-minimal coupling of a scalar field phi with Ricci scalar R in a general form of f(R,phi ). Using Palatini approach, we write its equivalent scalar-tensor form in the Einstein frame and then apply the constant-roll condition in the equation of motion for the inflaton field. Later the tensor-to-scalar ratio and the spectral index are calculated using the slow-roll parameters and the results obtained are matched with the Planck 2018 data. We found that the results agree nicely with the observations within the parameter regime under consideration.

Generation of primordial black holes from an inflation model with modified dispersion relation

A primordial black hole (PBH) is interesting to people for its ability of explaining dark matter as well as supermassive astrophysical objects. In the normal inflation scenario, the generation of PBHs usually requires an enhanced power spectrum of scalar perturbation at the end of inflation era, which is expected when the dispersion relation of the inflaton field gets modified. In this work, we study a kind of inflation model called the Dirac-Born-Infeld-inspired nonminimal kinetic coupling (DINKIC) model, where the dispersion relation is modified by a square root existing in the field Lagrangian. We discuss the enhancement of scalar power spectrum due to the modified dispersion relation, as well as the abundance of PBHs produced by the Press-Schechter collapse mechanism. We also discuss the formation of scalar-induced gravitational waves by linear scalar perturbations.

Hot Big Bang from inflation without the inflaton reheating

According to the standard lore, a prolonged inflation leaves a quantum field theory in a cold, low entropy state. Thus, some mechanism is needed to reheat this post-inflationary state, leaving a hot, thermal, radiation-dominated Universe. Typically, reheating is achieved coupling the inflaton field to the QFT degrees of freedom. We argue that the nonequilibrium dynamics of a non-conformal QFT in (post-)inflationary background space-time can produce hot quark-gluon plasma with the reheating temperature of order the inflationary Hubble scale, without the inflaton coupling.

Uniform rate inflation

In this work, I consider an inflation model with a quadratic potential and a negative cosmological constant. An analytical solution of the equation of motion for the inflaton field is found without slow-roll approximation. The result is that the inflation field is rolling at a constant speed. The prediction for cosmological perturbation is calculated.

Anisotropic warm inflation

Anisotropic inflation is a model that succeeded in explaining statistical anisotropy. Warm inflation is a model that succeeded in providing a mechanism of reheating during inflation. We study anisotropic warm inflation focusing on the cosmic no-hair conjecture. In the anisotropic warm inflation, the condition for making anisotropy survive is clarified. By assuming a constant value for the dissipation ratio, we find exact solutions of power-law anisotropic warm inflation, and investigate the phase space structure of general solutions. It turns out that whether the anisotropy during inflation survives or not depends on the competition of the potential that drives anisotropic inflation against dissipation of an inflaton field. Anisotropic warm inflation will be realized if the decaying process is not efficient.

A relativistic gas of inflatons as an initial state for inflation

The possibility of the resilience of the beginning of inflation under unfavourable conditions is examined by considering the initial state of the inflaton field to be in the form of a relativistic gas with some of its properties in close proximity to the black body spectrum. It is demonstrated that the initial potential energy budget in such an environment is suppressed beyond the minimal value required for inflation. This is the extension of our earlier work, where we have shown that the rare regions which happen to host favourable initial conditions for the beginning of inflation could come to dominate the late-time Universe only if they started out from above the so-called self-reproduction threshold.

Inflaton as a pseudo-Nambu-Goldstone boson

In the realistic model of cosmic inflation the inflaton potential should be flat and stable under quantum corrections. It is natural to imagine that there is some symmetry behind and an idea of the inflaton as a Nambu-Goldstone boson of spontaneous breaking of some symmetry has been examined. We give a general formulation of this idea using the non-linear realization of Nambu-Goldstone boson in low-energy effective theory with some explicit symmetry breaking to generate non-trivial potential. The potential is naturally a simple function, typically the mass term of inflaton, and the scenario of “warm inflation” should necessarily be applied under the present observational constraints. We investigate the generation mechanism of necessary thermal dissipation term in inflaton field equation for “warm inflation” without large thermal corrections to inflaton potential. A simple numerical analysis is given to investigate the viability of this scenario.