End Of Inflation Research Articles

Vector dark matter production from inflation with symmetry breaking

We present a scenario of vector dark matter production from symmetry breaking at the end of inflation. In this model, the accumulated energy density associated with the quantum fluctuations of the dark photon accounts for the present energy density of dark matter. The inflaton is a real scalar field while a heavy complex scalar field, such as the waterfall of hybrid inflation, is charged under the dark gauge field. After the heavy field becomes tachyonic at the end of inflation, rolling rapidly towards its global minimum, the dark photon acquires mass via the Higgs mechanism. To prevent the decay of the vector field energy density during inflation, we introduce couplings between the inflaton and the gauge field such that the energy is pumped to the dark sector. The setup can generate the observed dark matter abundance for a wide range of the dark photon's mass and with the reheat temperature around $10^{12}$ GeV. The model predicts the formation of cosmic strings at the end of inflation with the tensions which are consistent with the CMB upper bounds.

Quantum Higgs inflation

The Higgs field is an attractive candidate for the inflaton because it is an observationally confirmed fundamental scalar field. Importantly, it can be modeled by the most general renormalizable scalar potential. However, if the classical Higgs potential is used in models of inflation, it is ruled out by detailed observations of the cosmic microwave background. Here, a new application of non-adiabatic quantum dynamics to cosmological models is shown to lead to a multi-field Higgs-like potential, consistent with observations of a slightly red-tilted power spectrum and a small tensor-to-scalar ratio, without requiring non-standard ingredients. These methods naturally lead to novel effects in the beginning of inflation, circumventing common fine-tuning issues by an application of uncertainty relations to estimate the initial quantum fluctuations in the early universe. Moreover, inflation ends smoothly as a consequence of the derived multi-field interactions.

Vacuum decay constraints on the Higgs curvature coupling from inflation

We derive lower bounds for the Higgs-curvature coupling from vacuum stability during inflation in three inflationary models: quadratic and quartic chaotic inflation, and Starobinsky-like power-law inflation. In contrast to most previous studies we take the time-dependence of the Hubble rate into account both in the geometry of our past light-cone and in the Higgs effective potential, which is approximated with three-loop renormalisation group improvement supplemented with one-loop curvature corrections. We find that in all three models, the lower bound is ξ≳ 0.051… 0.066 depending on the top quark mass. We also demonstrate that vacuum decay is most likely to happen a few e-foldings before the end of inflation.

Analytic formula for the dynamics around inflation end and implications on primordial gravitational waves

We argue that primordial gravitational waves have a spectral break andits information is quite useful for exploring the early universe.Indeed, such a spectral break can be a fingerprint of the end ofinflation, and the amplitude and the frequency at the break can tell usthe energy scale of inflation and the reheating temperaturesimultaneously. In order to investigate the spectral break, we give ananalytic formula for evolution of the Hubble parameter around the end ofinflation where the slow roll approximation breaks down. We alsoevaluate the spectrum of primordial gravitational waves around thebreak point semi-analytically using the analytic formula for theinflation dynamics.

Primordial black holes from metric preheating: mass fraction in the excursion-set approach

We calculate the mass distribution of Primordial Black Holes (PBHs) produced during metric preheating. After inflation, the oscillations of the inflaton at the bottom of its potential source a parametric resonant instability for small-scale scalar perturbations, that may collapse into black holes. After reviewing in a pedagogical way different techniques that have been developed in the literature to compute mass distributions of PBHs, we focus on the excursion-set approach. We derive a Volterra integral equation that is free of a singularity sometimes encountered, and apply it to the case of metric preheating. We find that if the energy density at which the instability stops, ρΓ, is sufficiently smaller than the one at which inflation ends, ρend, namely if ρΓ1/4/ρend1/4 < 10−5(ρend1/4/1016GeV)3/2, then PBHs dominate the universe content at the end of the oscillatory phase. This confirms the previous analysis of ref. [1]. By properly accounting for the “cloud-in-cloud” mechanism, we find that the mass distribution is more suppressed at low masses than previously thought, and peaks several orders of magnitude above the Hubble mass at the end of inflation. The peak mass ranges from 10 g to stellar masses, giving rise to different possible cosmological effects that we discuss.

Disformal dark matter

We generalize dark matter production to a two-metric framework whereby the physical metric, which couples to the Standard Model (SM), is conformally and/or disformally related to the metric governing the gravitational dynamics. We show that this setup is naturally present in many Ultra Violet (UV) constructions, from K\"ahler moduli fields to tensor-portal models, and from emergent gravity to supergravity models. In this setting we study dark matter production in the early Universe resulting from both scatterings off the thermal bath and the radiative decay of the inflaton. We also take into account noninstantaneous reheating effects at the end of inflation. In this context, dark matter emerges from the production of the scalar field mediating the conformal/disformal interactions with the SM, i.e., realizing a Feebly Interacting Matter Particle (FIMP) scenario where the suppression scale of the interaction between the scalar and the SM can be taken almost as high as the Planck scale in the deep UV.

Unrivaled quantum vacuum in the primordial universe

In a primordial universe pre- (post-)inflationary era, there could be phases of early universe made of cold gas baryons, radiation and early post-inflationary cosmological constant. I showed that in the baryonic epoch, the quantum vacuum is unique. By using the standard quantization scheme for a massive minimally coupled scalar field with maximal conformal symmetry in the classical space–time, I demonstrated that the scalar modes had an effective mass [Formula: see text] (or [Formula: see text]). This argument was validated when the conformal time [Formula: see text] kept so close to the inflation ending time [Formula: see text]. The energy density of the baryonic matter diverged at the inflation border and vanishes at the late time future. Furthermore, I argued that at very early accelerating epoch when the radiation was the dominant part in the close competition with the early time cosmological constant, fine-tuned mass of the scalar field [Formula: see text] also provided a unique quantum vacuum. The reason is that the effective mass eventually is vanished. A remarkable observation was that all the other possible vacuum states “squeezed” eternally.

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Gravitational wave constraints on the observable inflation

Gravitational waves (GW) produced in the early Universe contribute to the number of relativistic degrees of freedom, Neff, during Big Bang Nucleosynthesis (BBN) . By using the constraints on Neff, we present a new bound on how much the Universe could have expanded between horizon exit of the largest observable scales today and the end of inflation. We discuss the implications on inflationary models and show how the new constraints affect model selection. We also discuss the sensitivities of the current and planned GW observatories such as LIGO and LISA, and show that the constraints they could impose are always less stringent than the BBN bound.

Large r against Trans-Planckian censorship in scalar-tensor theory?

In this paper, we discuss about the possibility to enhance the tensor-to-scalar ratio r under the condition of Trans-Planckian censorship conjecture (TCC), thus r∼O(10−3) could be observable within the sensitivity of future experiments. We make use of the scalar-tensor theory where inflaton is nonminimally coupled to gravity. After demonstrating that the TCC condition could be modified in scalar-tensor theory, we show that due to the effects of modified gravity at the end of inflation, a large r∼O(10−3) could be allowed without violating the TCC. Moreover, the modification can give rise to a weak coupling of gravity to the inflation field. If such an effect has been present as early as inflation starts, it would imply that in our case, the Universe might have experienced an asymptotically safe period at its early time.

Fiber inflation and precision CMB data

Generic features of models of inflation obtained from string compactifications are the correlations between the model parameters and the postinflationary evolution of the universe. Thus, the postinflationary evolution depends on the inflationary model parameters and accurate inflationary predictions require that this be incorporated in the evolution of the primordial spectrum. The fibre inflation model is a promising model of inflation constructed in type IIB string theory. This model has two interesting features in its postinflationary evolution. The reheating temperature of the model is directly correlated with the model parameters. The model also necessarily predicts some dark radiation, which can be sizable for certain choices of discrete parameters in the model. We analyze this model in detail using publicly available codes - ModeChord and CosmoMC with the latest Planck+BICEP2/Keck array data to constrain the model parameters and $N_{\rm pivot}$ (the number of $e$-foldings between horizon exit of the CMB pivot mode and the end of inflation). We also carry out the same analysis using the publicly available code Cobaya. We find the results of both the analysis to be in agreement. Our analysis provides the basic methods necessary to extract precise inflationary prediction in string models incorporating correlations between model parameters and postinflationary evolution.

Crunching away the cosmological constant problem: dynamical selection of a small \u039b

We propose a novel explanation for the smallness of the observed cosmological constant (CC). Regions of space with a large CC are short lived and are dynamically driven to crunch soon after the end of inflation. Conversely, regions with a small CC are metastable and long lived and are the only ones to survive until late times. While the mechanism assumes many domains with different CC values, it does not result in eternal inflation nor does it require a long period of inflation to populate them. We present a concrete dynamical model, based on a super-cooled first order phase transition in a hidden conformal sector, that may successfully implement such a crunching mechanism. We find that the mechanism can only solve the CC problem up to the weak scale, above which new physics, such as supersymmetry, is needed to solve the CC problem all the way to the UV cutoff scale. The absence of experimental evidence for such new physics already implies a mild little hierarchy problem for the CC. Curiously, in this approach the weak scale arises as the geometric mean of the temperature in our universe today and the Planck scale, hinting at a new “CC miracle”, motivating new physics at the weak scale independent of electroweak physics. We further predict the presence of new relativistic degrees of freedom in the CFT that should be visible in the next round of CMB experiments. Our mechanism is therefore predictive and experimentally falsifiable.

Multi-Brid DBI Inflation

It is shown that it is possible to apply $\delta \cN$ to some special non-canonic cases. We extended the multi-brid idea to the multi-field separable model with a non-canonical kinetic term, mainly the DBI model. Assuming a specific surface for the end of inflation and introducing new fields, enable us to find an explicit expression for the number of e-folds in terms of the new fields. By using $\delta$N formalism, we arrived at the cosmological parameters. We considered the DBI model for two different limits, viz., speed limit and constant sound speed.

Non-minimally coupled quartic inflation with Coleman-Weinberg one-loop corrections in the Palatini formulation

We discuss how the non-minimal coupling ξϕ2R between the inflaton and the Ricci scalar affects the predictions of single field inflation models in the Palatini formalism. The inflaton field ϕ must interact with matter fields at the end of inflation in order to make a transition to the radiation dominated era. Interactions of the inflaton with other fields lead to radiative corrections to the inflationary potential. These radiative corrections can be explained at leading order by Coleman-Weinberg (CW) one-loop corrections. In this work, the effect of radiative corrections to the potential has been examined using two different prescriptions debated in the literature. Prescription I and Prescription II examine the coupling of the inflaton to bosons and fermions. We analyze the range of these coupling parameters for which the spectral index ns and the tensor-to-scalar ratio r are compatible with data taken by the Keck Array/BICEP2 and Planck collaborations. Finally, we show for all the considered potentials the behavior of the running of the spectral index α=dns/dln⁡k as a function of κ for selected ξ values.

Bianchi-I cosmology within f(T): Reconstruction method and dynamical study

This paper is fundamentally devoted to the cosmological reconstruction and dynamic studying in homogeneous BIANCHI-I space-time under the [Formula: see text] background. Its content is supported by the fact that in the General Relativity description of the standard cosmological paradigm, the evolution from an anisotropic universe into an Friedmann–Lemaitre–Robertson–Walker (FLRW) one can be achieved by a period of inflationary expansion. Nowadays, modified gravity theories like [Formula: see text] are widely accepted to provide a real description of some universe evolution phases like inflation era, matter-dominated era, etc. So, we aim to examine here what [Formula: see text] gravity model can accommodate with an anisotropic universe, an expanding universe and even the transition between both evolutions. To reach this goal, we use a reconstruction method based on dynamic equations in Bianchi-I space-time by assuming a particular form for the metric anisotropy and by specifying some time functions describing average scale factor. Most of the obtained models are consistent with certain known results in the literature but other add new results in this work. In the second part of this work, the dynamical behaviors of the Bianchi-I space-time are addressed through the reconstruction of an autonomous dynamical system. For an aleatory choice of anisotropic fluid, the numerical analysis of the system shows that the metric anisotropy decreases with expansion. Then, an attractor point is reached and becomes unstable by the end of inflation. Such interesting properties found in this work on Bianchi-I space-time are often interpreted as graceful exit from inflation which doesn’t occur in ordinary FLRW space-time.

Model independent results for the inflationary epoch and the breaking of the degeneracy of models of inflation

We address the problem of determining inflationary characteristics in a model independent way. We start from a recently proposed equation which allows to accurately calculate the value of the inflaton at horizon crossing ϕk. We then use an equivalent form of this equation to write a formula that relates the number of e-folds from horizon crossing to the pivot scale Nke+Nep with the tensor-to-scalar index r, hence a general bound for Nke+Nep follows. Nke is the number of e-folds from the scale factor ak during inflation to the end of inflation at ae and Nep is the number of e-folds from ae to the pivot scale factor ap. In particular, at present r < 0.063 implies Nke+Nep< 112.5 e-folds at k=kp and 128.1 e-folds at the present scale with wavenumber mode k0. We also give a lower bound to the size of the universe during the inflationary epoch that gave rise to the current observable universe. We also discussed the problem of degeneracy of inflationary models and argue that this degeneration can only be resolved by studying model predictions from the reheating epoch.

Two-phase reheating: CMB constraints on inflation and dark matter phenomenology

We propose a two-phase reheating scenario where the initial preheating dynamics is described by an effective dynamics followed by the standard perturbative reheating. Some of the important universal results of lattice simulation during preheating have been considered as crucial inputs in our two-phase dynamics. In this framework, detailed phenomenological constraints have been obtained on the inflaton couplings with reheating fields, and dark matter parameters in terms of CMB constrained inflationary scalar spectral index. It is observed that the conventional reheating scenario generically predicts the maximum reheating temperature $T_{re}^{max} \simeq 10^{15}$ GeV, corresponding to an almost instantaneous transition from the end of inflation to radiation domination. This fact will naturally lead to the problem of non-perturbative inflaton decay, which is in direct conflict with the perturbative reheating itself. Taking into account this by incorporating effective non-perturbative dynamics as the initial phase, our model of two-phase reheating scenarios also predicts model-independent maximum reheating temperature, which does not correspond to the instantaneous process. Further, $T_{re}^{max}$ is predicted to lie within $(10^{13}, 10^{10})$ GeV if CMB constraints on inflaton couplings with different reheating field are taken into account. We have further studied in detail the dark matter phenomenology in a model-independent manner and show how dark matter parameter space can be constrained through CMB parameters via the inflaton spectral index. Considering dark matter production during reheating via the Freeze-in mechanism, its parameter space has been observed to be highly constrained by our two-phase reheating than the constraints predicted by the conventional reheating scenarios, which are believed to theoretically incomplete.

Energy distribution and equation of state of the early Universe: Matching the end of inflation and the onset of radiation domination

We study the energy distribution and equation of state of the universe between the end of inflation and the onset of radiation domination (RD), considering observationally consistent single-field inflationary scenarios, with a potential ‘flattening’ at large field values, and a monomial shape V(ϕ)∝|ϕ|p around the origin. As a proxy for (p)reheating, we include a quadratic interaction g2ϕ2X2 between the inflaton ϕ and a light scalar ‘daughter’ field X, with g2>0. We capture the non-perturbative and non-linear nature of the system dynamics with lattice simulations, obtaining that: i) the final energy transferred to X depends only on p, not on g2; ii) the final transfer of energy is always negligible for 2≤p<4, and of order ∼50% for p≥4; iii) the system goes at late times to matter-domination for p=2, and always to RD for p>2. In the latter case we calculate the number of e-folds until RD, significantly reducing the uncertainty in the inflationary observables ns and r.

Dark matter from primordial quantum information

We suggest a general relation between the position of the cosmic microwave background temperature power spectrum peaks and the inflationary slow roll parameter ϵ. This relation is based on interpreting the variable setting the position of the peaks as the quantum distance between the end of inflation and recombination. This distance is determined by the primordial cosmological Fisher information introduced in [1]. The observational constraints set by cosmic microwave background temperature data lead to a very stringent prediction for the value of the tensor-to-scalar ratio: r=0.01 ± 0.002. Future polarization data of the cosmic microwave background should be able to measure this signal and corroborate or discard our model.

Rational nonlinear electrodynamics causes the inflation of the universe

The source of the universe inflation is electromagnetic fields obeying rational nonlinear electrodynamics proposed earlier. Within this model the singularities of the electric field at the center of charges, the Ricci scalar, the Ricci tensor squared and the Kretschmann scalar are absent. We consider the universe which is filled by stochastic magnetic fields. It is demonstrated that the inflation lasts approximately [Formula: see text] s with the reasonable [Formula: see text]-folding number [Formula: see text]. The inflation starts from de Sitter space–time and after the universe inflation end it decelerates approaching the radiation era.