End Of Inflation Research Articles

Relic gravitons at intermediate frequencies and the expansion history of the Universe

The early expansion history of the Universe is constrained by combining the most recent limits on the cosmic gravitons in the audio band and the claimed evidences of the nHz domain. The simplest scenario stipulates that between the end of inflation and the formation of light nuclei the evolution consists of a single phase expanding at a rate that is either faster or slower than the one of radiation. If there are instead multiple postinflationary stages evolving at different rates, then the spectral energy density always undershoots the signals potentially attributed to relic gravitons by the pulsar timing arrays at intermediate frequencies but ultimately develops a local maximum. After examining further complementary possibilities (like the presence of a secondary stage of inflation at low scales), we analyze the early modifications of the effective expansion rate and argue that if the refractive index of the relic gravitons increases during a conventional inflationary epoch, then the spectral energy density is blue above the fHz and then flattens out in the $\ensuremath{\mu}\mathrm{Hz}$ region. In this instance the signal is compatible with the unconfirmed nHz observations, with the most recent limits of the wide-band interferometers and with the further constraints customarily imposed on the backgrounds of relic gravitons produced during inflation.

Stochastic effects in axion inflation and primordial black hole formation

We revisit the model of axion inflation in the context of stochastic inflation and investigate the effects of the stochastic noises associated to the electromagnetic fields. Because of the parity violating interaction, one polarization of the gauge field is amplified inducing large curvature perturbation power spectrum. Taking into account the stochastic kicks arising from the short modes at the time of horizon crossing we obtain the corresponding Langevin equations for the long modes of the electromagnetic and axion fields. It is shown that a mean-reverting process governs the dynamics of the electromagnetic fields such that the tachyonic growth of the gauge fields is balanced by the diffusion forces. As the instability parameter grows towards the end of inflation, the large curvature perturbations induced from gauge field perturbations lead to copious production of small mass primordial black holes (PBHs). It is shown that the produced PBHs follow a Gaussian statistics. Imposing the observational constraints on PBHs formation relaxes the previous bounds on the instability parameter by about fifty percents.

Gravitational wave nonlinearities and pulsar-timing array angular correlations

Several pulsar-timing array (PTA) collaborations are finding tantalizing hints for a stochastic gravitational wave background signal in the nano-Hertz regime. So far, though, no convincing evidence for the expected Hellings-Downs quadrupolar correlations has been found. While this issue might get fixed at the light of more accurate, forthcoming data, it is important to keep an eye open on different possibilities and explore scenarios able to produce different types of PTA angular correlations. We point out that a stationary non-Gaussian component to the gravitational wave background can modulate the two-point PTA overlap reduction function, adding contributions that can help in fitting the angular distribution of PTA data. We discuss possible sources for such non-Gaussian signal in terms of cosmological processes occurring after inflation ends, and we investigate further tests for this idea.

Viscous absorption of ultra-high-frequency gravitons

The high-frequency gravitons can be absorbed by the first and second viscosities of the post-inflationary plasma as the corresponding wavelengths reenter the Hubble radius prior to big-bang nucleosynthesis. When the total sound speed of the medium is stiffer than radiation the rate of expansion still exceeds the shear rate but the bulk viscosity is not negligible. Depending on the value of the entropy density at the end of inflation the spectral energy density of the relic gravitons gets modified in comparison with the inviscid result when the frequency ranges between the kHz band and the GHz region. In the nHz domain the spectrum inherits a known suppression due to neutrino free-streaming but also a marginal spike potentially caused by a sudden outbreak of the bulk viscosity around the quark-hadron phase transition, as suggested by the hadron spectra produced in the collisions of heavy ions.

Dynamical torsion suppression in Brans–Dicke inflation and Lorentz violation

Paul and SenGupta (Eur Phys J C 79:591, 2019) have recently shown that the reason why torsion effects are not present in today s universe is that they are suppressed in the bulk of a 5D braneworld. In this case only curvature effects remain. In this paper our goals are to investigate how this idea applies in the 4D Brans–Dicke inflation in two cases: First in the spin-torsion energy density scaling as sim {a^{-6}}, whereas matter density scales at a^{-3}. Here a(t) is the cosmic evolution parameter in the cosmic time t. In this case when a is given by the de Sitter expansion spin-torsion density it is highly suppressed. the second is the inflation in the framework of Einstein–Cartan–Brans–Dicke (ECBD) gravity used here, to build an effective inflaton potential and computing the number of its e-folds. Spin-torsion density contributes to a decrease on the number of e-folds when the ratio of spin-torsion density to matter density is not suppressed as in Early Universe. At present universe it is easy to show that by the end of inflation, spin-torsion density is suppressed with respect to matter-curvature density with a ratio of a^{-3} or t^{-3} by the end of inflation. When torsion possesses dynamical degrees of freedom, contortion is also shown to be suppressed by the end of BD inflation. The Kalb–Ramond fields in the 5D braneworld are equivalent to torsion. At present universe we find Ksim {10^{-39}~hbox {GeV}} for contortion. Such an estimate is much more stringent than the value found by Russell et al. (Phys Rev Lett 100, 2008) from torsion Lorentz violation (LV) with dual masers experiment.

Particle physics and cosmology of the string derived no-scale flipped SU(5)

In a recent paper, we identified a cosmological sector of a flipped SU(5) model derived in the free fermionic formulation of the heterotic superstring, containing the inflaton and the goldstino superfields with a superpotential leading to Starobinsky type inflation, while SU(5){times }U(1) is still unbroken. Here, we study the properties and phenomenology of the vacuum after the end of inflation, where the gauge group is broken to the Standard Model. We identify a set of vacuum expectation values, triggered by the breaking of an anomalous U(1)_A gauge symmetry at roughly an order of magnitude below the string scale, that solve the F and D-flatness supersymmetric conditions up to 6th order in the superpotential which is explicitly computed, leading to a successful particle phenomenology. In particular, all extra colour triplets become superheavy guaranteeing observable proton stability, while the Higgs doublet mass matrix has a massless pair eigenstate with realistic hierarchical Yukawa couplings to quarks and leptons. The supersymmetry breaking scale is constrained to be high, consistent with the non observation of supersymmetry signals at the LHC.

Astrophysical chiral dynamos and strain-torsioned Weyl materials

Our goal in this paper is two-fold: First we show that in the absence of four-fermion interactions, from Einstein–Cartan–Maxwell (ECM) anisotropy cosmology, one may derive instabilities in chiral dynamo equations from magnetic perturbations. They are obtained from a model, where the spinning-fluid does not couple directly to the Einstein–Maxwell model. Instead spin fluid enter into the evolution equation of density perturbations. Chiral dynamo equation is obtained from magnetic perturbations in the particular case where the perturbations in the chiral magnetized plasma can be neglected in second order of perturbations. The vanishing of the Nieh–Yan (NY) topological density in this Bianchi type-I model is also investigated. In the second example, use of the magnetic and torsion perturbations are given by the technique of encoding the magnetic perturbations in the metric constrained by teleparallelism. We consider non-uniform chiral chemical potential in the chiral flipping equation in order to obtain the magnetic field dynamo amplification. Dynamo effects are obtained from current perturbations expressed in terms of chiral chemical potential when number density of left-handed chiral particles is approximately zero. The damping found in magnetic field by the end of inflation, may help to explain why so weak galactic dynamo seeds are found at present universe. Furthermore, damping depends upon the strain–torsion relation of the Weyl topological materials. Though in general, torsion does not couple to electromagnetic fields, it influences the magnetic field through strain–torsion pseudo-magnetic potential.

Characterizing the postinflationary reheating history: Single daughter field with quadratic-quadratic interaction

We study the evolution of the energy distribution and equation of state of the Universe from the end of inflation until the onset of either radiation domination (RD) or a transient period of matter domination (MD). We use both analytical techniques and lattice simulations. We consider two-field models where the inflaton $\Phi$ has a monomial potential after inflation $V(\Phi) \propto |\Phi - v|^p$ ($p\geq2$), and is coupled to a daughter field $X$ through a quadratic-quadratic interaction $g^2\Phi^2 X^2$. We consider two situations, depending on whether the potential has a minimum at $i)$ $v = 0$, or $ii)$ $v > 0$. In the scenario $i)$, the final energy transferred to $X$ is independent of $g^2$ and entirely determined by $p$: it is negligible for $p < 4$, and of order $\sim 50\%$ for $p \geq 4$. The system goes to MD at late times for $p = 2$, while it goes to RD for $p > 2$. In the later case, we can calculate exactly the number of e-folds until RD as a function of $g^2$, and hence predict accurately inflationary observables like the scalar tilt $n_s$ and the tensor-to-scalar ratio $r$. In the scenario $ii)$, the energy is always transferred completely to $X$ for $p>2$, as long as its effective mass $m_X^2 = g^2(\Phi-v)^2$ is not negligible. For $p=2$, the final ratio between the energy densities of $X$ and $\Phi$ depends strongly on $g^2$. For all $p \ge 2$, the system always goes to MD at late times.

Dark photon dark matter from a rolling inflaton

We study in detail a recently proposed mechanism for producing non-thermal dark photon dark matter at the end of inflation in the mass range μ eV≲ m ≲ 10 TeV. A tachyonic instability induced by a rolling inflaton leads to the coherent production of dark (abelian) gauge bosons with a peak in the power spectrum corresponding to the Hubble scale at the end of inflation. As the Universe expands after inflation the dark photons redshift and, at some point in their cosmic evolution, they obtain a mass. We focus in particular on the case where the dark photons are relativistic at the time their mass is generated and examine the associated cosmic evolution to compute the relic abundance today. We also examine the late time power spectrum demonstrating explicitly that it preserves the peak generated at the end of inflation. We show that the peak corresponds to small physical scales today, ℓtoday∼ cm-100 km, with large density fluctuations at ℓtoday leading to a clumpy nature for the dark photon dark matter. We also discuss potential phenomenology and future directions, briefly commenting on the non-relativistic case.

Dependence of the amplitude of gravitational waves from preheating on the inflationary energy scale

Stochastic gravitational wave backgrounds receive increasing attention and provide a new possibility to directly probe the early Universe. In the preheating process at the end of inflation, parametric resonance can generate large energy density perturbations and efficiently produce gravitational waves (GWs) which carry unique information about inflation. Since the peak frequency of such GWs is approximately proportional to the inflationary energy scale, ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$, GWs from preheating are expected to be observed by interferometer GW detectors in low-scale inflationary models. We investigate a class of preheating models where the effective potential has a quadratic minimum, and the dependence of the amplitude of such GWs on ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$, then find that the present energy spectrum of these GWs does not depend on ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$ except in the case where ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$ is above a critical value ${\mathrm{\ensuremath{\Lambda}}}_{c}$---a parameter depending on the resonance strength. We numerically obtain ${\mathrm{\ensuremath{\Lambda}}}_{c}$ in terms of the model parameters in a linear approximation and then conduct lattice simulations to verify this result. For ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}\ensuremath{\lesssim}{\mathrm{\ensuremath{\Lambda}}}_{c}$, the amplitude of GWs quickly decreases with ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$ and becomes challenging to observe. In turn, observing such GWs in interferometer detectors also helps to determine ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$ and the resonance strength during the preheating.

Inflation in a scalar–vector–tensor theory

In this work, we study inflation in a particular scalar-vector-tensor theory of gravitation without the $U(1)$ gauge symmetry. The model is constructed from the more general action introduced in Heisenberg et al. (Phys Rev D 98:024038, 2018) using certain specific choices for the Lagrangians and the coupling functions. Also, for this model we build the explicit form for the action, and from it, we derive the general equations: the energy-momentum tensor and the equations of motion, and using the flat FLRW background, we have analyzed if it's possible to obtain an inflationary regime with it. Additionally, using particular choices for the potential, the coupling functions, suitable dimensionless coupling constants and initial conditions, it was possible verify numerically that this model of inflation is viable. In this sense, we could verify that the introduction of the coupling function $f(\phi)$ in our model of inflation, allows us to reach a suitable amount of $e$-foldings $N$ for sufficient inflation. This is a remarkable result, since without the coupling function contribution, the amount of $e$-foldings is smaller at the end of inflation, as has been demonstrated in Heisenberg et al. (2018). Also, the no-ghosts and stability conditions that the model during inflation must satisfy, i.e., absence of ghosts and Laplacian instabilities of linear cosmological perturbations were obtained, furthermore these conditions were verified numerically too.

Hybrid inflation and waterfall field in string theory from D7-branes

We present an explicit string realisation of a cosmological inflationary scenario we proposed recently within the framework of type IIB flux compactifications in the presence of three magnetised D7-brane stacks. Inflation takes place around a metastable de Sitter vacuum. The inflaton is identified with the volume modulus and has a potential with a very shallow minimum near the maximum. Inflation ends due to the presence of “waterfall” fields that drive the evolution of the Universe from a nearby saddle point towards a global minimum with tuneable vacuum energy describing the present state of our Universe.

Subcritical hybrid inflation in a generalized superconformal model

We study a generalized superconformal model that gives rise to a subcritical regime of $D$-term hybrid inflation. Exhibiting the model both in a Jordan frame and in the Einstein frame, the effective potential of the subcritical regime is derived in the Einstein frame. It turns out the inflaton-waterfall field dynamics leads to various types of inflaton potential. Consequently the tensor-to-scalar ratio is found to range from $10^{-4}$ ($10^{-3}$) to $0.1$ for getting 60 (50) $e$-folds before the end of inflation.

The relationship between headline, core, and energy inflation: A wavelet investigation

This paper investigates if core inflation, the measure of price growth obtained excluding the more volatile items such as energy and food prices, is a good approximation of headline inflation that considers the entire bundle. Starting from the mid-90s, our answer is negative. From a monetary policy perspective, this raises the issue of whether controlling core inflation is still useful to anchor medium-run inflation. Using the wavelet methodology, our analysis suggests that starting from the end of the 90s core inflation is weakly correlated with headline inflation especially at the lower frequencies. Energy inflation is strongly correlated with headline inflation at a broad range of frequencies, casting doubt on its exclusion from a trend inflation measure.

Lattice simulations of inflation

The scalar field theory of cosmological inflation constitutes nowadays one of the preferred scenarios for the physics of the early universe. In this paper we aim at studying the inflationary universe making use of a numerical lattice simulation. Various lattice codes have been written in the last decades and have been extensively used for understating the reheating phase of the universe, but they have never been used to study the inflationary phase itself far from the end of inflation (i.e. about 50 e-folds before the end of inflation). In this paper we use a lattice simulation to reproduce the well-known results of some simple models of single-field inflation, particularly for the scalar field perturbation. The main model that we consider is the standard slow-roll inflation with an harmonic potential for the inflaton field. We explore the technical aspects that need to be accounted for in order to reproduce with precision the nearly scale invariant power spectrum of inflaton perturbations. We also consider the case of a step potential, and show that the simulation is able to correctly reproduce the oscillatory features in the power spectrum of this model. Even if a lattice simulation is not needed in these cases, that are well within the regime of validity of linear perturbation theory, this sets the basis to future work on using lattice simulations to study more complicated models of inflation.

Reheating after inflation by supersymmetry breaking

We study reheating after the end of inflation in models where the inflaton is the superpartner of goldstino and is charged under a gauged U(1) R-symmetry. We consider two classes of models – one is small field characterized by an almost flat Kähler space, and the other large field characterized by a hyperbolic Kähler space SU(1, 1)/U(1), while in both cases the inflaton superpotential is linear due to the R-symmetry. The inflationary observables of our models fit within 2sigma CMB values. Upon coupling the inflaton sector to the (supersymmetric) Standard Model, we compute the MSSM parameters, mass spectrum, and decay modes of the inflaton, with the resulting reheating temperature around 10^8 GeV. We also find that both models can accommodate superheavy LSP dark matter, depending on the parameter choice.

Non-equilibrium dynamics of a scalar field with quantum backreaction

We study the dynamical evolution of coupled one- and two-point functions of a scalar field in the 2PI framework at the Hartree approximation, including backreaction from out-of-equilibrium modes. We renormalize the 2PI equations of motion in an on-shell scheme in terms of physical parameters. We present the Hartree-resummed renormalized effective potential at finite temperature and critically discuss the role of the effective potential in a non-equilibrium system. We follow the decay and thermalization of a scalar field from an initial cold state with all energy stored in the potential, into a fully thermalized system with a finite temperature. We identify the non-perturbative processes of parametric resonance and spinodal instability taking place during the reheating stage. In particular we study the unstable modes in the region where the vacuum 1PI effective action becomes complex and show that such spinodal modes can have a dramatic effect on the evolution of the one-point function. Our methods can be easily adapted to simulate reheating at the end of inflation.

Gravity waves and primordial black holes in scalar warm little inflation

In warm inflation, dissipation due to the interactions of the inflaton field to other light degrees of freedom leads naturally to the enhancement of the primordial spectrum during the last 10-20 efolds of inflation. We study this effect in a variant of the Warm Little Inflaton model, where the inflaton couples to light scalars, with a quartic chaotic potential. These large fluctuations on re-entry will form light, evaporating Primordial Black Holes, with masses lighter than 106 g. But at the same time they will act as a source for the tensors at second order. The enhancement is maximal near the end of inflation, which result in a spectral density of Gravitational Waves (GW) peaked at frequencies f ∼ O(105-106) Hz today, and with an amplitude ΩGW ∼ 10-9. Although the frequency range is outside the reach of present and planned GW detectors, it might be reached in future high-frequency gravitational waves detectors, designed to search for cosmological stochastic GW backgrounds above MHz frequencies.

Gravitational wave from axionlike particle inflation

In this paper, we investigate the Axion-like Particle inflation by applying the multi-nature inflation model, where the end of inflation is achieved through the phase transition (PT). The events of PT should not be less than $200$, which results in the free parameter $n\geq404$. Under the latest CMB restrictions, we found that the inflation energy is fixed at $10^{15} \rm{GeV}$. Then, we deeply discussed the corresponding stochastic background of the primordial gravitational wave (GW) during inflation. We study the two kinds of $n$ cases, i.e., $n=404, 2000$. We observe that the magnitude of $n$ is negligible for the physical observations, such as $n_s$, $r$, $\Lambda$, and $\Omega_{\rm{GW}}h^2$. In the low-frequency regions, the GW is dominated by the quantum fluctuations, and this GW can be detected by Decigo at $10^{-1}~\rm{Hz}$. However, GW generated by PT dominates the high-frequency regions, which is expected to be detected by future 3DSR detector.

Cosmic strings, inflation, and gravity waves

We investigate the impact of Coleman-Weinberg inflation on the stochastic gravity wave background spectrum emitted by intermediate scale cosmic strings. The string network is partially inflated and re-enters the horizon at later times after the end of inflation, such that the short string loops are not produced. This leads to a significant modification of the gravity wave spectrum that we explore in detail. We find that Coleman-Weinberg inflation can help to satisfy the Parkes Pulsar Timing Array (PPTA) bound for dimensionless string tension values in the range $G\mu > 1.1\times 10^{-10}$. We also identify the modified gravity wave spectra which, in the case of inflation, are compatible with the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) data. We then discuss the formation of monopoles and strings at the same breaking scale and the compatibility of the Monopole, Astrophysics and Cosmic Ray Observatory (MACRO) bound with the PPTA bound, and also with the NANOGrav data. Finally, an example of a realistic non-supersymmetric $E_6$ model incorporating successful Coleman-Weinberg inflation is presented in which monopoles and strings both survive inflation and are present at an observable level.