End Of Inflation Research Articles

Computation of gravitational particle production using adiabatic invariants

Analytic and numerical techniques are presented for computing gravitational production of scalar particles in the limit that the inflaton mass is much larger than the Hubble expansion rate at the end of inflation. These techniques rely upon adiabatic invariants and time modeling of a typical inflaton field which has slow and fast time variation components. A faster computation time for numerical integration is achieved via subtraction of slowly varying components that are ultimately exponentially suppressed. The fast oscillatory remnant results in production of scalar particles with a mass larger than the inflationary Hubble expansion rate through a mechanism analogous to perturbative particle scattering. An improved effective Boltzmann collision equation description of this particle production mechanism is developed. This model allows computation of the spectrum using only adiabatic invariants, avoiding the need to explicitly solve the inflaton equations of motion.

Gravitational particle production of superheavy massive particles in quintessential inflation: A numerical analysis

We compute numerically the reheating temperature due to the gravitational production of conformally coupled superheavy particles during the phase transition from the end of inflation to the beginning of kination in two different Quintessential Inflation (QI) scenarios, namely Lorentzian Quintessential Inflation (LQI) and $\alpha$-attractors in the context of Quintessential Inflation ($\alpha$-QI). Once these superheavy particles have been created, they must decay into lighter ones to form a relativistic plasma, whose energy density will eventually dominate the one of the inflaton field in order to reheat after inflation our universe with a very high temperature, in both cases greater than $10^7$ GeV, contrary to the usual belief that heavy masses suppress the particle production and, thus, lead to an inefficient reheating temperature. Finally, we will show that the over-production of Gravitational Waves (GWs) during this phase transition, when one deals with our models, does not disturb the Big Bang Nucleosynthesis (BBN) success.

Achieving the highest temperature during reheating with the Higgs condensate

We study the role of the Standard Model Higgs condensate, formed during cosmological inflation, in the epoch of reheating that follows. We focus on the scenario where the inflaton decays slowly and perturbatively, so that there is a long period between the end of inflation and the beginning of radiation domination. The Higgs condensate decays nonperturbatively during this period, and we show that it heats the primordial plasma to much higher temperatures than would result from the slowly decaying inflaton alone. We discuss the effect of this hot plasma on the thermalization of the inflaton's decay products, and study its phenomenological implications for the formation of cosmological relics like dark matter, with associated isocurvature fluctuations, and the restoration of the electroweak and Peccei-Quinn symmetries.

Chaotic inflation and reheating in generalized scalar-tensor gravity

In the present work, we study slow-roll inflation in scalar-tensor gravity theories in the presence of both the non-minimal coupling between the scalar field and curvature, and the Galileon self-interaction of the scalar field. Furthermore, we give predictions for the duration of reheating as well as for the reheating temperature after inflation. After working out the expressions for the power spectra of scalar and tensor perturbations in the case of a general non-minimal coupling function that depends solely on the scalar field and a general scalar potential, we focus on the special cases of the power-law coupling function and chaotic quadratic inflation. Thus, under the slow-roll approximation we confront the predictions of the model with the current PLANCK constraints on the spectral index n s and the tensor-to-scalar ratio r using the n s-r plane. We found that the combination of the non-minimal coupling and Galileon self-interaction effects allows us to obtain better results for r than in the case in which each effect is considered separately. Particularly, we obtained that the predictions of the model are in agreement with the current observational bounds on n s and r within the 95 % C.L region and also slightly inside the 68 % C.L region. Also, we investigate the oscillatory regime after the end of inflation by solving the full background equations, and then we determine the upper bound for the Galileon and non-minimal coupling parameters under the condition that the scalar field oscillates coherently during reheating. Finally, after approximating reheating by a constant equation of state, we derive the relations between the reheating duration, the temperature at the end of reheating, its equation of state, and the number of e-folds of inflation and then we relate them all to the inflationary observables.

A Review of Quintessential Inflation

Some of the most important quintessential inflation scenarios, such as the Peebles–Vilenkin model, are described in detail. These models are able to explain the early- and late-time accelerated expansions of our universe, and the phase transition from the end of inflation to the beginning of kination where the adiabatic evolution of the universe was broken in order to produce enough particles to reheat the universe with a viable temperature, thereby aligning with the Hot Big Bang universe. In addition, while considering the reheating to be due to the gravitational production of superheavy particles conformally coupled to gravity, we checked that the considered scenarios do not suffer problems due to the overproduction of gravitational waves at the end of inflation, and thus the validity of Big Bang nucleosynthesis is preserved.

ΔN and the stochastic conveyor belt of ultra slow-roll inflation

We analyze field fluctuations during an ultra slow-roll phase in the stochastic picture of inflation and the resulting non-Gaussian curvature perturbation, fully including the gravitational backreaction of the field's velocity. By working to leading order in a gradient expansion, we first demonstrate that consistency with the momentum constraint of general relativity prevents the field velocity from having a stochastic source, reflecting the existence of a single scalar dynamical degree of freedom on long wavelengths. We then focus on a completely level potential surface, $V={V}_{0}$, extending from a specified exit point ${\ensuremath{\phi}}_{\mathrm{e}}$, where slow roll resumes or inflation ends, to $\ensuremath{\phi}\ensuremath{\rightarrow}+\ensuremath{\infty}$. We compute the probability distribution in the number of $e$-folds $\mathcal{N}$ required to reach ${\ensuremath{\phi}}_{\mathrm{e}}$, which allows for the computation of the curvature perturbation. We find that, if the field's initial velocity is high enough, all points eventually exit through ${\ensuremath{\phi}}_{\mathrm{e}}$ and a finite curvature perturbation is generated. On the contrary, if the initial velocity is low, some points enter an eternally inflating regime despite the existence of ${\ensuremath{\phi}}_{\mathrm{e}}$. In that case, the probability distribution for $\mathcal{N}$, although normalizable, does not possess finite moments, leading to a divergent curvature perturbation.

Gauge-field-induced torsion and cosmic inflation

In this paper, inflation in the framework of Einstein–Cartan theory is revisited. Einstein–Cartan theory is a natural extension of the General Relativity with nonvanishing torsion. The connection on Riemann–Cartan space–time is only compatible with the cosmological principal for a particular form of torsion. We also show this form to be compatible with gauge invariance principle for non-Abelian and Abelian gauge fields under a certain deviced coupling procedure. We adopt an Abelian gauge field in the form of “cosmic triad”. The dynamical field equations are obtained and shown to sustain cosmic inflation with a large number of e-folds. We emphasize that at the end of inflation, torsion vanishes and the theory of Einstein–Cartan reduces to the General Relativity with the usual FRW geometry.

Baryogenesis via gauge field production from a relaxing Higgs

We show that the baryon asymmetry of the universe can be explained in modelswhere the Higgs couples to the Chern-Simons term of the hypercharge groupand is away from the late-time minimum of its potential during inflation. The Higgs then relaxes toward this minimum once inflation ends which leads to the production of (hyper)magnetic helicity. We discuss the conditions under which this helicity can be approximately conserved during its joint evolution with the thermal plasma. At the electroweak phase transition the helicity is then converted into a baryon asymmetry by virtue of the chiral anomaly in the standard model. We propose a simple model which realizes this mechanism and show that the observed baryon asymmetry of the universe can be reproduced.

Cosmological consequences of a scalar field with oscillating equation of state. III. Unifying inflation with dark energy and small tensor-to-scalar ratio

We investigate the inflationary consequences of the oscillating dark energy model proposed by Ti\'an [\href{https://doi.org/10.1103/PhysRevD.101.063531}{Phys. Rev. D {\bf 101}, 063531 (2020)}], which aims to solve the cosmological coincidence problem with multi-accelerating Universe (MAU). We point out that the inflationary dynamics belong to slow-roll inflation. The spectral index of scalar perturbations and the tensor-to-scalar ratio $r$ are shown to be consistent with current \textit{Planck} measurements. Especially, this model predicts $r\sim10^{-7}$, which is far below the observation limits. This result motivates us to explore the smallness of $r$ in the general MAU. We propose a quintessential generalization of the original model and prove $r<0.01$ in general. The null detection to date of primordial gravitational waves provides a circumstantial evidence for the MAU. After the end of inflation, the scalar field rolls toward infinity instead of a local minimum, and meanwhile its equation of state is oscillating with an average value larger than $1/3$. In this framework, we show that gravitational particle creation at the end of inflation is capable of reheating the Universe.

States of low energy in bouncing inflationary scenarios in loop quantum cosmology

In generic Friedmann-Lema\^itre-Robertson-Walker spacetimes, States of Low Energy (SLEs) are defined to minimize the regularized energy density smeared along the time-like curve of an isotropic observer, which is specified via a smearing function. For every smearing function, SLEs are unique (up to a phase) and are shown to be exact Hadamard states. In this work, we investigate the viability of SLEs as the vacuum for cosmological perturbations in hybrid Loop Quantum Cosmology, motivated by the fact that SLEs have been shown to provide suitable vacua in models where a period of kinetic dominance precedes inflation. We find that there are two classes of smearing functions that can be seen as natural choices within this context, for which the corresponding SLEs and the resulting power spectra at the end of inflation are quite insensitive to the exact shape and support of the smearing function. Furthermore, a preliminary analysis of the tensor-to-scalar ratio and of the spectral index indicates as good an agreement with observations as that of standard cosmology.

Examining the end of inflation with primordial black hole mass distribution and gravitational waves

We explicitly construct a double-field inflationary model, which satisfies the latest Planck constraints at the cosmic microwave background (CMB) scales and produces the whole dark matter energy density as primordial black holes (PBHs), in the mass range ${10}^{\ensuremath{-}17}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}\ensuremath{\lesssim}{M}_{\mathrm{PBH}}\ensuremath{\lesssim}{10}^{\ensuremath{-}13}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. The PBHs can be produced after the end of slow-roll inflation from the bubbles of true vacuum that nucleate during the course of inflation. Obtaining PBHs in this mass range enforces the scale of inflation to be extremely low, ${10}^{\ensuremath{-}7}\ensuremath{\lesssim}H\ensuremath{\lesssim}{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{GeV}$, which makes the efforts to observe gravitational waves at the CMB scales futile, although it is high enough to allow for a successful big bang nucleosynthesis. We will show that the shape of the mass distribution of the PBHs is dependent on how inflation ends and the Universe settles from the metastable direction to the true one. End of inflation can also be probed by examining the gravitational waves spectrum. In particular, we show that if exit from the rolling metastable direction to the true vacuum of the potential happens through a first-order phase transition after the end of slow-roll inflation, it leaves behind a stochastic gravitational wave background (SGWB), which is potentially observable by the Laser Interferometer Space Antenna. Examining the mass distribution of PBHs and possible SGWB from the end of inflation, we may be able to gain invaluable information about the end of inflation.

Inflation and scale-invariant R2 gravity

In scale-invariant models of fundamental physics, mass scales are generated by spontaneous symmetry breaking. In this work, we study inflation in scale-invariant $R^2$ gravity, in which the Planck mass is generated by a scalar field, which is responsible for spontaneous breaking of scale--symmetry. If the self-interactions of the scalar field are non-zero, a cosmological constant is generated, which can be potentially quite large. To avoid fine-tuning at late times, we introduce another scalar field which drives the classical cosmological constant to zero during inflation. Working in the Einstein-frame, we find that due to a conserved Noether current the corresponding three-field inflationary model (consisting of the two scalar fields plus the scalaron) becomes effectively a two-field model. The prize to be paid for introducing the field which cancels the classical cosmological constant at the end of inflation is that the running of the spectral index and the running of the running can be quite large due to entropy perturbations during inflation, making the model testable with future cosmological experiments.

Inflationary magnetogenesis in the perturbative regime

While during inflation a phase of increasing gauge coupling allows for a scale-invariant hyperelectric spectrum, when the coupling decreases a flat hypermagnetic spectrum can be generated for typical wavelengths larger than the effective horizon. After the gauge coupling flattens out the late-time hypermagnetic power spectra outside the horizon in the radiation epoch are determined by the hyperelectric fields at the end of inflation whereas the opposite is true in the case of decreasing coupling. Instead of imposing an abrupt freeze after inflation, we consider a smooth evolution of the mode functions by positing that the gauge couplings and their conformal time derivatives are always continuous together with the background extrinsic curvature. The amplified gauge power spectra are classified according to their transformation properties under the duality symmetry. After clarifying the role of the comoving and of the physical spectra in the formulation of the relevant magnetogenesis constraints, the parameter space of the scenario is scrutinized. It turns out that a slightly blue hyperelectric spectrum during inflation may lead to a quasi-flat hypermagnetic spectrum prior to matter radiation equality and before the relevant wavelengths reenter the effective horizon. In this framework the gauge coupling is always perturbative but the induced large-scale magnetic fields can be of the order of a few hundredths of a nG and over typical length scales between a fraction of the Mpc and 100 Mpc prior to the gravitational collapse of the protogalaxy.

Chiral anomaly in SU(2)R-axion inflation and the new prediction for particle cosmology

Upon embedding the axion-inflation in the minimal left-right symmetric gauge extension of the SM with gauge group SU(2)L × SU(2)R × U(1)B−L, [1] proposed a new particle physics model for inflation. In this work, we present a more detailed analysis. As a compelling consequence, this setup provides a new mechanism for simultaneous baryogenesis and right-handed neutrino creation by the chiral anomaly of WR in inflation. The lightest right-handed neutrino is the dark matter candidate. This setup has two unknown fundamental scales, i.e., the scale of inflation and left-right symmetry breaking SU(2)R × U(1)B−L→ U(1)Y. Sufficient matter creation demands the left-right symmetry breaking scale happens shortly after the end of inflation. Interestingly, it prefers left-right symmetry breaking scales above 1010 GeV, which is in the range suggested by the non-supersymmetric SO(10) Grand Unified Theory with an intermediate left-right symmetry scale. Although WR gauge field generates equal amounts of right-handed baryons and leptons in inflation, i.e. B − L = 0, in the Standard Model sub-sector B − LSM ≠ 0. A key aspect of this setup is that SU(2)R sphalerons are never in equilibrium, and the primordial B − LSM is conserved by the Standard Model interactions. This setup yields a deep connection between CP violation in physics of inflation and matter creation (visible and dark); hence it can naturally explain the observed coincidences among cosmological parameters, i.e., ηB ≃ 0.3Pζ and ΩDM ≃ 5ΩB. The new mechanism does not rely on the largeness of the unconstrained CP-violating phases in the neutrino sector nor fine-tuned masses for the heaviest right-handed neutrinos. The SU(2)R-axion inflation comes with a cosmological smoking gun; chiral, non-Gaussian, and blue-tilted gravitational wave background, which can be probed by future CMB missions and laser interferometer detectors.

Preheating from target space curvature and unitarity violation: Analysis in field space

We study particle production and unitarity violation caused by a curved target space right after inflation. We use the inflaton field value instead of cosmic time as the time variable, and derive a semiclassical formula for the spectrum of produced particles. We then derive a simple condition for unitarity violation during preheating, which we confirm by our semiclassical method and numerical solution. This condition depends not only on the target space curvature but also on the height of the inflaton potential at the end of inflation. This condition tells us, for instance, that unitarity is violated in running kinetic inflation and Higgs inflation, while unitarity is conserved in $\alpha$-attractor inflation and Higgs-Palatini inflation.

The upper bound on the tensor-to-scalar ratio consistent with quantum gravity

We consider the polynomial inflation with the tensor-to-scalar ratio as large as possible which can be consistent with the quantum gravity (QG) corrections and effective field theory (EFT). To get a minimal field excursion Δϕ for enough e-folding number N, the inflaton field traverses an extremely flat part of the scalar potential, which results in the Lyth bound to be violated. We get a CMB signal consistent with Planck data by numerically computing the equation of motion for inflaton ϕ and using Mukhanov–Sasaki formalism for primordial spectrum. Inflation ends at Hubble slow-roll parameter or . Interestingly, we find an excellent practical bound on the inflaton excursion in the format , where a is a tiny real number and b is at the order 1. To be consistent with QG/EFT and suppress the high-dimensional operators, we show that the concrete condition on inflaton excursion is . For n s = 0.9649, N e = 55, and , we predict that the tensor-to-scalar ratio is smaller than 0.0012 for such polynomial inflation to be consistent with QG/EFT.

Testing hilltop supernatural inflation with gravitational waves

The scale of small-field inflation cannot be constrained via primordial gravitational waves through measurement of tensor-to-scalar ratio r.In this study, I show that if cosmic strings are produced after symmetry breaking at the end of hilltop supernatural inflation, this small-field inflation model can be tested through the production of gravitational waves from cosmic strings. Future experiments of gravitational wave detectors will determine or further constrain the parameter space in the model.

Power spectrum in stochastic inflation

We compute the power spectrum of curvature perturbations in stochastic inflation. This combines the distribution of first crossing times through the end-of-inflation surface, which has been previously studied, with the distribution of the fields value at the time when a given scale crosses out the Hubble radius during inflation, which we show how to compute. This allows the stochastic-δ N formalism to make concrete contact with observations. As an application, we study how quantum diffusion at small scales (arising e.g. in models leading to primordial black holes) affects the large-scale perturbations observed in the cosmic microwave background. We find that even if those sets of scales are well separated, large effects can arise from the distortion of the classical relationship between field values and wavenumbers brought about by quantum diffusion near the end of inflation. This shows that cosmic microwave background measurements can set explicit constraints on the entire inflationary potential down to the end of inflation.

Quintessential inflation in Palatini gravity

We study a model of quintessential inflation in the context of Palatini gravity. As a representative example, we consider the Peebles-Vilenkin model of quintessential inflation with a small non-minimal coupling to gravity, which is consistent with the most recent Planck measurements. At the end of inflation, the inflaton field passes through a tachyonic region and it leads to explosive particle production through the tachyonic preheating process. After preheating, the Universe becomes dominated by the kinetic energy of the inflaton and enters a period of kination. Eventually, the total energy density of the Universe becomes dominated by radiation, resulting in reheating. We find that the model predicts the reheating temperature values TRH∼\U0001d4aa(103 - 108) GeV, which is significantly above the temperature of Big Bang Nucleosynthesis. Following reheating, the inflaton field rolls down the quintessence potential until it freezes. Since the quintessence remains frozen until the present day, the residual potential energy density at this field value explains the observed dark energy density.

Inflationary cosmology- A new approach using Non-linear electrodynamics

We explore a new kind of NLED field as a source of gravity, which can accelerate the Universe during the inflationary era. We propose a new type of NLED lagrangian which is characterised by two parameters: α (dimensionless parameter) and β (dimensionful parameter). We investigate the classical stability and the causality aspects of this model of inflationary expansion by demanding that the speed of the sound wave and . Corresponding to , we find for α = 0.1(1.0). The equation of state parameter ω = −1/3 requires corresponding to . We find that the Universe is accelerating i.e. (which results in the deceleration parameter q < 0 (i.e. ω > −1/3)), provided . During inflation, the energy density is found to be maximum and is given by . The magnetic field necessary to trigger the inflation is found to be , where is the energy density of the Universe during the inflationary expansion. Our model also predicts the e-fold number that the magnetic field at the end of inflation is about B = 10−10 (10−4) Gauss corresponding to z = 0(1000) and this agrees quite well with the experimental prediction of the e-fold number. With α = 0.3(1.0) and , we find the scalar spectral index n s = 0.9649, consistent with the PLANCK 2018 CMB data. Further, with , we predicts the tensor-to-scalar ratio r = 0.1417(0.1449) and the tensorial spectral index .