Inflationary Stage Research Articles

The two stages of inflation with non-canonical scalar fields

The two stages of inflation with non-canonical scalar fields

Generalising axion-like particle as the curvaton: sourcing primordial density perturbation and non-Gaussianities

We investigate the non-perturbatively generated axion-like particle (ALP) potential, involving fermions in the dark sector that couple to the ALP, in an early universe cosmological inflationary stage with the ALP being a spectator field. The potential here deviates from the standard cosine nature due to the presence of the two dark sector fermion masses mu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_u$$\\end{document} and md\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_d$$\\end{document} which couple to the ALP. The ALP is a spectator field during inflation but it starts to oscillate and dominates the energy density of the universe after inflation ends, thereby sourcing isocurvature perturbations, while standard curvature fluctuations from the inflaton are assumed to be sub-dominant. Subsequently the ALP decays converting the isocurvature perturbations to adiabatic perturbations thereby acting as the origin of the primordial density perturbations. We identify the parameter space involving the axion decay constant fϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{\\phi }$$\\end{document}, scale of confinement Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}, ALP mass m and the masses of the fermions, mu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_u$$\\end{document} and md\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_d$$\\end{document} where it can satisfactorily behave as the curvaton and source the observed primordial density perturbation. We also predict local non-Gaussianity signals for bi-spectrum and tri-spectrum fNL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{NL}$$\\end{document} and gNL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{NL}$$\\end{document}, as a function of the ratio mu/md\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_u/m_d$$\\end{document}, which are within the allowed range in the latest Planck observations and are detectable with future observations. Particularly we find that the value of fNL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{NL}$$\\end{document} and gNL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{NL}$$\\end{document} are dependent on the ratio of mu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_u$$\\end{document} and md\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_d$$\\end{document}: fNL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{NL}$$\\end{document} is more or less positive for all scenarios except mu=md\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_u = m_d$$\\end{document} and gNL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{NL}$$\\end{document} is always positive irrespective of the ratio between mu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_u$$\\end{document} and md\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_d$$\\end{document}. The results of our analysis in the limit mu=md\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_u = m_d$$\\end{document} resembles vanilla curvaton scenario while in the limit mu≫md\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_u \\gg m_d$$\\end{document} resembles pure axion cosine potential. This is because the model has the unique feature where the extra matter in the dark sector determines the nature and shape of the potential.

Climbing over the potential barrier during inflation via null energy condition violation

The violation of the null energy condition (NEC) may play a crucial role in enabling a scalar field to climb over high potential barriers, potentially significant in the very early universe. We propose a single-field model where the universe sequentially undergoes a first stage of slow-roll inflation, NEC violation, and a second stage of slow-roll inflation. Through the NEC violation, the scalar field climbs over high potential barriers, leaving unique characteristics on the primordial gravitational wave power spectrum, including a blue-tilted nature in the middle-frequency range and diminishing oscillation amplitudes at higher frequencies. Additionally, the power spectrum exhibits nearly scale-invariant behavior on both large and small scales.

Production of ultralight dark matter from inflationary spectator fields

We investigate inflationary particle production associated with a spectator ultralight scalar field, which has recently been proposed as a plausible dark matter candidate. In this framework, we select the Starobinsky potential to drive the inflationary epoch, also discussing the case of a nonminimally coupled inflaton field fueled by a quartic symmetry-breaking potential. We focus on particle production arising from spacetime perturbations, which are induced by inflaton fluctuations during the quasi–de Sitter stage of inflation. In particular, we construct the first-order Lagrangian describing interaction between inhomogeneities and the spectator field, quantifying superhorizon particle production during slow-roll. We then compare this mechanism with gravitational particle production associated with an instantaneous transition from inflation to the radiation dominated era. We show that the number of particles obtained from perturbations is typically non-negligible, and it is significantly enhanced on super-Hubble scales by the nonadiabatic inflationary expansion. Possible implications for primordial entanglement generation are also debated. Published by the American Physical Society 2024

Primordial Black Holes from Null Energy Condition Violation during Inflation.

Primordial black holes (PBHs) and the violation of the null energy condition (NEC) have significant implications for our understanding of the very early Universe. We present a novel approach to generate PBHs via the NEC violation in a single-field inflationary scenario. In our scenario, the Universe transitions from a first slow-roll inflation stage with a Hubble parameter H=H_{inf1} to a second slow-roll inflation stage with H=H_{inf2}≫H_{inf1}, passing through an intermediate stage of NEC violation. The NEC violation naturally enhances the primordial scalar power spectrum at a certain wavelength, leading to the production of PBHs with masses and abundances of observational interest. We also investigate the phenomenological signatures of scalar-induced gravitational waves resulting from the enhanced density perturbations. Our work highlights the potential of utilizing a combination of PBHs, scalar-induced gravitational waves, and primordial gravitational waves as a valuable probe for studying NEC violation during inflation, opening up new avenues for exploring the early Universe.

Enhanced curvature perturbation and primordial black hole formation in two-stage inflation with a break

We investigate a model of R2-gravity with a non-minimally coupled scalar field that gives rise to two-stage inflation with a break, that is, with an intermediate stage where inflation momentarily halts. We find that the power spectrum of the primordial curvature perturbation is significantly enhanced at the break scale, which can account for the primordial black hole (PBH) formation, without affecting the CMB constraint on large scales. The behavior of the curvature perturbation is carefully analyzed and we find a few notable new features in the spectrum. In particular, we find that the k3 growth of the spectrum of toward the end of the first stage of inflation. We argue that this is a universal feature common to all two-stage models where the field dominating the second stage is heavy during the first stage. By appropriately tuning the model parameters, we find that our model can realize the scenario of PBHs as the cold dark matter of the Universe. We also find that we can choose the parameters so that the spectrum of the induced gravitational waves from the enhanced curvature perturbation fits the NANOGrav-15yr data of pulsar timing array observation.

Constraints on inflation with null energy condition violation from advanced LIGO and advanced Virgo's first three observing runs

The null energy condition (NEC) is a cornerstone of general relativity, and its violation could leave observable imprints in the cosmic gravitational wave spectrum. Theoretical models suggest that NEC violations during inflation can amplify the primordial tensor power spectrum, leading to distinct features in the stochastic gravitational wave background (SGWB). In this work, we search for these NEC-violating signatures in the SGWB using data from Advanced LIGO and Advanced Virgo's first three observing runs. Our analysis reveals no statistically significant evidence of such signals, allowing us to place stringent upper limits on the tensor power spectrum amplitude, P T,2, during the second inflationary stage. Specifically, we find that P T,2 ≲ 0.15 at a 95% confidence level. Notably, this upper limit is consistent with constraints derived from pulsar timing array observations, reinforcing the hypothesis that NEC violations during inflation could explain the signal detected by pulsar timing arrays. Our findings contribute to a deeper understanding of the early Universe and highlight the potential of current and future gravitational wave experiments in probing the physics of inflation and NEC violations.

Fuzzy bounces

We observe that the energy and the enthalpy densities can be smeared by two fudge factors that are constrained by the contracted Bianchi identities. Depending on the analytic properties of the smearing functions the underlying cosmological solutions belong to two physically different classes, namely the bounces of the scale factor and the curvature bounces. While the curvature bounces are naturally compatible with a stage of accelerated expansion, the bounces of the scale factor demand an early phase of accelerated contraction even if a short inflationary stage may arise prior to the decelerated regime. Despite the regularity of the underlying solutions, gradient instabilities and singularities do occasionally appear in the evolution of curvature inhomogeneities. After deducing the specific criteria behind these occurrences, the background-independent conclusions are corroborated by a series of concrete examples associated with different forms of the smearing functions. The evolution of the curvature inhomogeneities restricts the ranges of the solutions that turn out to be unsuitable even for a limited description of the pre-inflationary initial data. The same observation holds in the case of the gauge-invariant evolution of the matter density contrast. It is however not excluded that a class of scenarios (mainly associated with the curvature bounces) could indeed avoid the potential instabilities. All in all the present analysis explore a general approach whose results are relevant in all the contexts where bouncing solutions are invoked either as complementary or as alternative to the conventional inflationary scenarios.

Reproduction of grass carp (Ctenopharyngodon idella) in the Maumee River, Ohio: Part 2—Optimal river conditions for egg and larval drift

This study uses a one-dimensional steady-state hydraulic model and the Fluvial Egg Drift Simulator (FluEgg) to model the drift and dispersion of grass carp eggs and larvae in the Maumee River, Ohio, for 180 scenarios representing different combinations of 10 river flows, 6 water temperatures, and 3 spawning locations. The FluEgg simulations were used to quantify in-river suspended hatching rates (the percentage of eggs that hatch within the river and in suspension) and in-river larval retention rates (the percentage of larvae that reach the gas bladder inflation stage within the river after hatching in suspension), and identify which scenarios produce the highest likelihood of recruitment. The simulations indicate that at low flows, in-river suspended hatching and larval retention rates in the Maumee River are limited by the capacity of the flow to keep fertilized eggs in suspension, whereas at high flows, the limiting factor is the distance available for the eggs/larvae to drift in the river. A wide range of scenarios result in eggs hatching within the river, but all larvae drift into Maumee Bay prior to the gas bladder inflation stage when flows exceed the mean annual flow. The simulations were assessed in the context of the hydraulic conditions that trigger spawning and maximize egg fertilization and the nursery habitat requirements for larval grass carp. The results indicate that the Maumee River, although suitable for grass carp spawning, may not be an ideal setting for recruitment unless Maumee Bay provides adequate nursery habitat for larvae.

Gravitational Waves and gravitino mass in No-Scale Supergravity inflation with Polonyi term

We study a No-Scale supergravity inflation model which has a non-minimal deformation of the Kähler potential and a Wess-Zumino superpotential extended by the inclusion of a Polonyi mass term. The non-minimal structure of the Kähler potential is responsible for an inflexion point that can lead to the production of gravitational waves at late stages of inflation, while the Polonyi term breaks supersymmetry at the end of inflation, generating a non-vanishing gravitino mass. After a thorough parameter space scan, we identify promising points for gravitational wave production. We then study the resulting gravitational wave energy density for this set of points, and we observe that the gravitational waves should be observable in the next generation of both space-based and ground-based interferometers. Finally, we show how the presence of the Polonyi term can be used to further boost the gravitational wave energy density, which is correlated with the gravitino mass. The code used for the scan and the numerical analysis is provided at https://gitlab.com/miguel.romao/gw-and-m32-no-scale-inflation-polonyi.

Study of Nonlinear Evolution of Spacetime Fluctuations in Quantum Gravity Inflation for Deriving Primordial Spectrum

We study the evolution of quantum fluctuations of gravity around an inflationary solution in renormalizable quantum gravity, in which the initial scalar-fluctuation dominance is shown by the background-free nature expressed by a special conformal invariance. Inflation ignites at the Planck scale and continues until spacetime phase transition occurs at a dynamical scale of about 1017 GeV. We show that during inflation, the initially large scale-invariant fluctuations reduce in amplitude to the appropriate magnitude suggested by tiny CMB anisotropies. The goal of this research is to derive the spectra of scalar fluctuations at the phase transition point, that is, the primordial spectra. A system of nonlinear evolution equations for the fluctuations is derived from the quantum gravity effective action. The running coupling constant is then expressed by a time-dependent average following the spirit of the mean field approximation. In this paper, we determine and examine various nonlinear terms, not treated in previous studies such as the exponential factor of the conformal mode. These contributions occur during the early stage of inflation when the amplitude is still large. Moreover, in order to verify their effects concretely, we numerically solve the evolution equation by making a simplification to extract the most contributing parts of the terms in comoving momentum space. The result indicates that they serve to maintain the initial scale invariance over a wide range beyond the comoving Planck scale. This is a challenge toward the derivation of the precise primordial spectra, and we expect in the future that it will lead to the resolution of the tensions that have arisen in cosmology.

Physical mechanisms controlling a vapor bubble collapse and formation of a liquid jet during a laser-induced subcooled boiling near the end face of a thin waveguide

Laser-induced subcooled boiling near the tip of thin waveguide immersed in a liquid which temperature is less than the saturation temperature (subcooled liquid) can produce intensive liquid jets finding promising applications in medicine. Individual act of the boiling process consists of successive stages of the bubble inflation, bubble collapse and formation of the jet. In this paper we investigate the contribution of different physical mechanisms to the characteristics of these stages. Simplified mathematical model introducing evaporation and condensation processes in the fully controlled manner allows manipulation of these processes by varying model parameters. Depending on the evaporation intensity or disequilibrity of the bubble inflation stage three regimes of laser-induced subcooled boiling can be distinguished, that are the pressure driven regime, transition regime and condensation driven regime. Distinctive features of these regimes are discussed and ranges of evaporation intensity and disequilibrity index typical for each regime are determined. The validity of incompressible gas assumption for description of different regimes is estimated.

The scaling of primordial gauge fields

The large-scale magnetic fields arising from the quantum mechanical fluctuations of the hypercharge are investigated when the evolution of the gauge coupling is combined with a sufficiently long inflationary stage. In this framework the travelling waves associated with the quantum mechanical initial conditions turn asymptotically into standing waves which are the gauge analog of the Sakharov oscillations. Even if the rate of dilution of the hypermagnetic and hyperelectric fields seems to be superficially smaller than expected from the covariant conservation of the energy-momentum tensor, the standard evolution for wavelengths larger than the Hubble radius fully accounts for this anomalous scaling which is anyway unable to increase the amplitude of the magnetic power spectra after symmetry breaking. An effective amplification of the gauge power spectra may instead occur when the post-inflationary expansion rate is slower than radiation. We stress that the modulations of the gauge power spectra freeze as soon as the relevant wavelengths reenter the Hubble radius and not at the end of inflation. After the Mpc scale crosses the comoving Hubble radius the scaling of the magnetic power spectrum follows from the dominance of the conductivity. From these two observations the late-time values of the magnetic power spectra are accurately computed in the case of a nearly scale-invariant slope and contrasted with the situation where the phases of Sakharov oscillations are not evaluated at horizon crossing but at the end of inflation, i.e. when all the wavelengths relevant for magnetogenesis are still larger than the comoving horizon.

Possible relationship between initial conditions for inflation and past geodesic incompleteness of the inflationary spacetime

According to the Borde-Guth-Vilenkin (BGV) theorem an expanding region of spacetime cannot be extended to the past beyond some boundary ℬ. Therefore, the inflationary universe must have had some kind of beginning. However, the BGW theorem says nothing about the boundary conditions on ℬ, or even about its location. Here we present a single-scalar field model of the Two-Measure Theory, where the non-Riemannian volume element Υ d 4 x is present in the action. As a result of the model dynamics, an upper bound φ 0 of admissible values of the scalar field φ appears, which sets the position of ℬ in the form of a spacelike hypersurface Υ(x) = 0 with a boundary condition: Υ → 0+ as φ → φ 0 -. A detailed study has established that if the initial kinetic energy density ρ kin (in) prevails over initial gradient energy density ρ grad (in) then there is an interval of initial values φ in (min) ≤ φ in < φ 0, where ρ kin (in) and ρ grad (in) cannot exceed the potential energy density and hence the initial conditions necessary for the onset of inflation are satisfied. It is shown that under almost all possible left-handed boundary conditions on ℬ, that is where Υ → 0-, the metric tensor in the Einstein frame has a jump discontinuity on ℬ, so the Christoffel connection coefficients are not defined on the spacelike hypersurface Υ = 0. Thus, if φ in (min) ≤ φ in < φ 0 and ρ kin (in) > ρ grad (in), then there was an inflationary stage in the history of our Universe and the congruence of timelike geodesics cannot be extended to the past beyond the hypersurface Υ = 0.

Mechanical model for geomechanical pumped storage in horizontal fluid‐filled lenses

AbstractPumped subsurface energy storage entails pumping fluid into fluid‐filled lenses in subterranean rock formations during times of peak power production, and then later producing the fluid back to the surface to drive a turbine. A new mechanical model is developed for lens behavior during flowback (production), shut‐in, and inflation (storage) stages. The model couples elastic deformation of the lens with Darcy–Weisbach fluid flow spanning the laminar to turbulent regimes. It includes an energy‐based inlet boundary condition governing fluid flow rate out of the lens and up to the Earth's surface. It also introduces pressure‐dependent leakoff of fluid to the surrounding rock and the impact of intact rock bridges, which can arise from the lens having multiple petals or lobes, on lens compliance. The model is then used to illustrate the transition from early‐time gradual decline in wellhead pressure and flow rate to eventual pinching of the lens width at the wellbore, leading to rapid decline of pressure and flow rate. The model demonstrates the feasibility of efficient storage cycles that generate a desired amount of power over a desired time while avoiding pinching. Maximizing efficiency is shown to have at least two contrasting regimes depending on whether the fluid leakoff rate to the host rock is dependent on the fluid pressure. The development of this model is therefore an essential step in deployment of subsurface energy storage by providing a mechanical basis for storage lens design.

The alteration of the Schwinger effect on radiatively corrected Higgs inflationary magneto-genesis by axial coupling

We study the alteration of the Schwinger effect on radiatively corrected Higgs inflationary magneto-genesis by axial coupling function. The conformal invariance of Maxwell action should be broken by axial coupling with the inflaton field. We use the potential of [M. Kamarpour, Gen. Relativ. Gravit. 53 (2021) 53, doi:10.1007/s10714-021-02824-0; M. Kamarpour, Gen. Relativ. Gravit. 54 (2022) 32, doi:10.1007/s10714-022-02920-9] with the simplest coupling function [Formula: see text] in which [Formula: see text] is a dimensionless coupling parameter. In comparison to our previous work (in which we used curvature-based coupling or so-called nonminimal coupling function to gravity to break conformal invariance of action) of [M. Kamarpour, Gen. Relativ. Gravit. 54 (2022) 32, doi:10.1007/s10714-022-02920-9] we find that the Schwinger effect does alter magneto-genesis and is considerable. In fact, in comparison to our previous work of [M. Kamarpour, Gen. Relativ. Gravit. 54 (2022) 32, doi:10.1007/s10714-022-02920-9] we obtain that for some certain values of coupling parameter [Formula: see text] the Schwinger effect does alter magneto-genesis (see [M. Kamarpour, Gen. Relativ. Gravit. 53 (2021) 53, doi:10.1007/s10714-021-02824-0]) and the energy density of created charged particles during the Schwinger effect becomes considerable and of course comparable to the energy density of inflaton field. Therefore, the Schwinger effect decreases the value of the electric field, so that it helps to finish the inflation stage. Then the universe enters the stage of preheating. The Schwinger effect produces charged particles, imposing the Schwinger reheating framework even before the ending of last oscillations of the inflaton field.

Hypermagnetic power spectra and the phases of Sakharov oscillations

If the gauge fields are amplified from the inflationary vacuum, the quantum mechanical initial data correspond to travelling waves that turn asymptotically into standing waves whose phases only depend on the evolution of the gauge coupling. We point out that these gauge analogs of the Sakharov oscillations are exchanged by the duality symmetry and ultimately constrain both the relative scaling of the hypermagnetic power spectra and their final asymptotic values. Unlike the case of the density contrasts in a relativistic plasma, the standing oscillations never develop since they are eventually overdamped by the finite value of the conductivity as soon as the corresponding modes are comparable with the expansion rates after inflation. We show that the late-time value of the magnetic field is not determined at radiation dominance (and in spite of the value of the wavenumber) but it depends on the moment when the wavelengths (comparable with the Mpc) get of the order of the Hubble radius before equality. This means that the magnetogenesis requirements are only relaxed if the post-inflationary expansion rate is slower than radiation but the opposite is true when the plasma expands faster than radiation and the corresponding power spectra are further suppressed. After combining the present findings with the evolution of the gauge coupling we show that these results are consistent with a magnetogenesis scenario where the gauge coupling is always perturbative during the inflationary stage while, in the dual case, the same requirements cannot be satisfied.

Eliminating the Hubble Tension in the Presence of the Interconnection between Dark Energy and Matter in the Modern Universe

It is accepted in modern cosmology that the scalar field responsible for the inflationary stage of the early Universe is completely transformed into matter. It is assumed that the accelerated expansion is currently driven by dark energy (DE), which is likely determined by Einstein’s cosmological constant, unrelated to the scalar field responsible for inflation. We consider a cosmological model in which DE can currently have two components, one of which is Einstein’s constant (Λ) and the other, smaller dark energy variable component DEV (ΛV), is associated with the remnant of the scalar field that caused inflation after the main part of the scalar field has turned into matter. We consider only the stages of evolution of the Universe after recombination (z=1100), where dark matter (DM) is the predominant component of matter. It is assumed that the transformation of the scalar field into matter continues at the present time and is accompanied by the reverse process of the transformation of DM into a scalar field. The interconnection between DM and DEV, which leads to a linear relationship between the energy densities of these components after recombination ρDM=αρDEV, is considered. Variants with a dependence of the coefficient α(z) on the redshift z are also considered. One of the problems that have arisen in modern cosmology, called Hubble Tension (HT), is the discrepancy between the present values of the Hubble constant (H0) measured from observations of the Universe at small redshifts (z≲1) and the values found from fluctuations of the cosmic microwave background in the Universe at large redshifts (z≈1100). In the model under consideration, this discrepancy can be explained by the deviation of the existing cosmological model from the conventional Λ cold dark matter (CDM) model of the flat Universe by the action of the additional dark energy component DEV at the stages after recombination. Within this extended model, we consider various α(z) functions that can eliminate the HT. To maintain the ratio of DEV and DM energy densities close to constant over the interval 0⩽z≲1100, it is necessary to assume the existence of a wide spectrum of dark matter particle masses.

Eliminating the Hubble Tension in the Presence of the Interconnection between Dark Energy and Matter in the Modern Universe

It is accepted in modern cosmology that the scalar field responsible for the inflationary stage of the early Universe is completely transformed into matter. It is assumed that the accelerated expansion is currently driven by dark energy (DE), which is likely determined by Einstein’s cosmological constant, unrelated to the scalar field responsible for inflation. We consider a cosmological model in which DE can currently have two components, one of which is Einstein’s constant ( $$\Lambda $$ ) and the other, smaller dark energy variable component DEV ( $${{\Lambda }_{V}}$$ ), is associated with the remnant of the scalar field that caused inflation after the main part of the scalar field has turned into matter. We consider only the stages of evolution of the Universe after recombination ( $$z \lesssim 1100$$ ), where dark matter (DM) is the predominant component of matter. It is assumed that the transformation of the scalar field into matter continues at the present time and is accompanied by the reverse process of the transformation of DM into a scalar field. The interconnection between DM and DEV, which leads to a linear relationship between the energy densities of these components after recombination $${{\rho }_{{{\text{DM}}}}} = \alpha {\kern 1pt} {{\rho }_{{{\text{DEV}}}}}$$ , is considered. Variants with a dependence of the coefficient $$\alpha (z)$$ on the redshift $$z$$ are also considered. One of the problems that have arisen in modern cosmology, called Hubble Tension (HT), is the discrepancy between the present values of the Hubble constant ( $${{H}_{0}}$$ ) measured from observations of the Universe at small redshifts ( $$z \lesssim 1$$ ) and the values found from fluctuations of the cosmic microwave background in the Universe at large redshifts ( $$z \approx 1100$$ ). In the model under consideration, this discrepancy can be explained by the deviation of the existing cosmological model from the conventional $$\Lambda $$ cold dark matter (CDM) model of the flat Universe by the action of the additional dark energy component DEV at the stages after recombination. Within this extended model, we consider various $$\alpha {\kern 1pt} (z)$$ functions that can eliminate the HT. To maintain the ratio of DEV and DM energy densities close to constant over the interval $$0 \leqslant z \lesssim 1100$$ , it is necessary to assume the existence of a wide spectrum of dark matter particle masses.

The nonlinear anisotropic model of the Universe with the linear potential

In the Bianchi I cosmology some subclasses of the Horndeski theory allow for the non-standard anisotropy behavior. For example, the anisotropy is damped near the initial singularity instead of tending to infinity. In this article, we analyze the nonlinear anisotropic model with the linear potential.We have considered an example of such theory, for which the anisotropy is always finite. The anisotropy reaches its a maximum value at the initial moment. The anisotropy suppression occurs during the inflationary stage, and it approaches zero at later times. This cosmological model does not contain the singular point.