Inflaton Rolling Research Articles

Fitting Power Spectrum of Scalar Perturbations for Primordial Black Hole Production during Inflation

A simple phenomenological fit for the power spectrum of scalar (curvature) perturbations during inflation is proposed to analytically describe slow roll of inflaton and formation of primordial black holes (PBH) in the early universe, in the framework of single-field models. The fit is given by a sum of the power spectrum of slow-roll inflation, needed for a viable description of the cosmic microwave background (CMB) radiation in agreement with Planck/BICEP/Keck measurements, and the log-normal (Gaussian) fit for the power spectrum enhancement (peak) needed for efficient PBH production, in the leading (model-independent) approximation. The T-type α-attractor models are used to get the simple CMB power spectrum depending upon the e-folds as the running variable. The location and height of the peak are chosen to yield the PBH masses in the asteroid-size window allowed for the whole (current) dark matter. We find the restrictions on the peak width.

Challenges in string and supersymmetric cosmology

We discuss the possibility that inflation is driven by supersymmetry breaking with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton. Imposing an R-symmetry allows to satisfy easily the slow-roll conditions, avoiding the so-called [Formula: see text]-problem, and leads to an interesting class of small field inflation models, characterized by an inflationary plateau around the maximum of the scalar potential near the origin, where R-symmetry is restored with the inflaton rolling down to a minimum describing the present phase of the Universe. Inflation can be driven by either an [Formula: see text]- or a [Formula: see text]-term, while the minimum has a positive tuneable vacuum energy. The models agree with cosmological observations and in the simplest case predict a rather small tensor-to-scalar ratio of primordial perturbations.

Constant roll warm inflation in high dissipative regime

Constant-roll warm inflation is introduced in this work. A novel approach to finding an exact solution for Friedman equations in the constant-roll framework is presented for cold inflation and is extended to warm inflation with the constant dissipative parameter Q=Γ/3H. The evolution of the primordial inhomogeneities of a scalar field in a thermal bath is also studied. The 1σ consistency between the theoretical predictions of the model and observational constraints has been proven for a range of Q and β=−ϕ̈/(3Hϕ) (constant rate of inflaton roll). In addition, we briefly investigate the possible enhancement of super-horizon perturbations beyond the slow-roll approximation.

Real-time corrections to the effective potential

Non-perturbatively generated effective potentials play an extremely useful and often critical role in string and inflationary model building. These potentials are typically computed by methods that assume the system is in equilibrium. For systems out of equilibrium, like an inflaton rolling down its potential, there are corrections to the semi-classical evolution due to transient phenomena. We provide a new qualitative and quantitative understanding of non-perturbative effects in real time for a wide class of toy quantum mechanical models. We derive an effective Schrödinger equation that does not rely on any notion of equilibrium and captures the low-energy dynamics supposedly described by the effective potential. We find that there are potentially large corrections to this potential that are not captured by standard equilibrium techniques, and quantify when these corrections significantly alter the effective dynamics.

Challenges in Supersymmetric Cosmology

We discuss the possibility that inflation is driven by supersymmetry breaking with the scalar component of the goldstino superfield (sgoldstino) playing the role of the inflaton and charged under a gauged U ( 1 ) R-symmetry. Imposing a linear superpotential allows us to satisfy easily the slow-roll conditions, avoiding the so-called η -problem, and leads to an interesting class of small field inflation models, characterised by an inflationary plateau around the maximum of the scalar potential near the origin, where R-symmetry is restored with the inflaton rolling down to a minimum describing the present phase of the Universe. Inflation can be driven by either an F- or a D-term, while the minimum has a positive tuneable vacuum energy. The models agree with cosmological observations and in the simplest case predict a rather small tensor-to-scalar ratio of primordial perturbations. We propose a generalisation of Fayet-Iliopoulos model as a microscopic model leading to this class of inflation models at low energy.

Backreaction of electromagnetic fields and the Schwinger effect in pseudoscalar inflation magnetogenesis

We study magnetogenesis in axionlike inflation driven by a pseudoscalar field $\phi$ coupled axially to the electromagnetic (EM) field $(\beta/M_{p})\phi F_{\mu\nu}\tilde{F}^{\mu\nu}$ with dimensionless coupling constant $\beta$. A set of equations for the inflaton field, scale factor, and expectation values of quadratic functions of the EM field is derived. These equations take into account the Schwinger effect and the backreaction of generated EM fields on the Universe expansion. It is found that the backreaction becomes important when the EM energy density reaches the value $\rho_{\rm EM}\sim (\sqrt{2\epsilon}/\beta)\rho_{\rm inf}$ ($\epsilon$ is the slow-roll parameter and $\rho_{\rm inf}$ is the energy density of the inflaton) slowing down the inflaton rolling and terminating magnetogenesis. The Schwinger effect becomes relevant when the electric energy density exceeds the value $\rho_{E}\sim \alpha_{\rm EM}^{-3} (\rho_{\rm tot}^{2}/M_{p}^{4})$, where $\rho_{\rm tot}=3H^{2}M_{p}^{2}$ is the total energy density and $\alpha_{\rm EM}$ is the EM coupling constant. For large $\beta$, produced charged particles could constitute a significant part of the Universe energy density even before the preheating stage. Numerically studying magnetogenesis in the $\alpha$-attractor model of inflation, we find that it is possible to generate helical magnetic fields with the maximal strength $10^{-15}\,{\rm G}$, however, only with the correlation length of order $1\,{\rm pc}$ at present.

Inflation from Supersymmetry Breaking

I discuss the possibility that inflation is driven by supersymmetry breaking, with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton. Imposing an R-symmetry to satisfy the slow-roll conditions, avoiding the so-called η -problem, leads to an interesting class of small field inflation models, characterised by an inflationary plateau around the maximum of scalar potential near the origin, where R-symmetry is restored with the inflaton rolling down to a minimum, describing the present phase of the Universe. Inflation can be driven by either an F- or a D-term, while the minimum has a positive tuneable vacuum energy. The models agree with cosmological observations and, in the simplest case, predict a rather small tensor-to-scalar ratio of primordial perturbations. This talk is an extended version of an earlier review (Antoniadis, 2018).

Scale hierarchies, supersymmetry and cosmology

I discuss a general class of models where the inflation is driven by supersymmetry breaking with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton. Imposing an R-symmetry allows to satisfy easily the slow-roll conditions, avoiding the so-called [Formula: see text]-problem, and leads to two different classes of small field inflation models; they are characterized by an inflationary plateau around the maximum of the scalar potential, where R-symmetry is either restored or spontaneously broken, with the inflaton rolling down to a minimum describing the present phase of our universe. Inflation can be driven by either an F- or a D-term, while the minimum has a positive tuneable vacuum energy. The models agree with cosmological observations and in the simplest case predict a tensor-to-scalar ratio of primordial perturbations [Formula: see text] and an inflation scale [Formula: see text].

Inflation from supersymmetry breaking

I discuss a general class of models where the inflation is driven by supersymmetry breaking with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton. Imposing an R-symmetry allows to satisfy easily the slow-roll conditions, avoiding the so-called [Formula: see text]-problem, and leads to two different classes of small field inflation models; they are characterized by an inflationary plateau around the maximum of the scalar potential, where R-symmetry is either restored or spontaneously broken, with the inflaton rolling down to a minimum describing the present phase of our Universe. Inflation can be driven by either an F- or a D-term, while the minimum has a positive tunable vacuum energy. The models agree with cosmological observations and in the simplest case predict a tensor-to-scalar ratio of primordial perturbations [Formula: see text] and an inflation scale [Formula: see text].

New perspectives on constant-roll inflation

We study constant-roll inflation using the β-function formalism. We show that the constant rate of the inflaton roll is translated into a first order differential equation for the β-function which can be solved easily. The solutions to this equation correspond to the usual constant-roll models. We then construct, by perturbing these exact solutions, more general classes of models that satisfy the constant-roll equation asymptotically. In the case of an asymptotic power law solution, these corrections naturally provide an end to the inflationary phase. Interestingly, while from a theoretical point of view (in particular in terms of the holographic interpretation) these models are intrinsically different from standard slow-roll inflation, they may have phenomenological predictions in good agreement with present cosmological data.

Inflation from supersymmetry breaking

We explore the possibility that inflation is driven by supersymmetry breaking with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton. Moreover, we impose an R-symmetry that allows one to satisfy easily the slow-roll conditions, avoiding the so-called eta -problem, and leads to two different classes of small-field inflation models; they are characterised by an inflationary plateau around the maximum of the scalar potential, where R-symmetry is either restored or spontaneously broken, with the inflaton rolling down to a minimum describing the present phase of our Universe. To avoid the Goldstone boson and be left with a single (real) scalar field (the inflaton), R-symmetry is gauged with the corresponding gauge boson becoming massive. This framework generalises a model studied recently by the present authors, with the inflaton identified by the string dilaton and R-symmetry together with supersymmetry restored at weak coupling, at infinity of the dilaton potential. The presence of the D-term allows a tuning of the vacuum energy at the minimum. The proposed models agree with cosmological observations and predict a tensor-to-scalar ratio of primordial perturbations and an inflation scale GeV. H_* may be lowered up to electroweak energies only at the expense of fine-tuning the scalar potential.

Inflation with a constant rate of roll

We consider an inflationary scenario where the rate of inflaton roll defined by ̈ϕ/H ϕ̇ remains constant. The rate of roll is small for slow-roll inflation, while a generic rate of roll leads to the interesting case of ‘constant-roll’ inflation. We find a general exact solution for the inflaton potential required for such inflaton behaviour. In this model, due to non-slow evolution of background, the would-be decaying mode of linear scalar (curvature) perturbations may not be neglected. It can even grow for some values of the model parameter, while the other mode always remains constant. However, this always occurs for unstable solutions which are not attractors for the given potential. The most interesting particular cases of constant-roll inflation remaining viable with the most recent observational data are quadratic hilltop inflation (with cutoff) and natural inflation (with an additional negative cosmological constant). In these cases even-order slow-roll parameters approach non-negligible constants while the odd ones are asymptotically vanishing in the quasi-de Sitter regime.

Cosmological evolution in a two-brane warped geometry model

We study an effective 4-dimensional scalar–tensor field theory, originated from an underlying brane–bulk warped geometry, to explore the scenario of inflation. It is shown that the inflaton potential naturally emerges from the radion energy–momentum tensor which in turn results in an inflationary model of the Universe on the visible brane that is consistent with the recent results from the Planck's experiment. The dynamics of modulus stabilization from the inflaton rolling condition is demonstrated. The implications of our results in the context of recent BICEP2 results are also discussed.

Sculpting the extra dimensions: inflation from codimension-2 brane back-reaction

We construct an inflationary model in 6D supergravity that is based on explicit time-dependent solutions to the full higher-dimensional field equations, back-reacting to the presence of a 4D inflaton rolling on a space-filling codimension-2 source brane. Fluxes in the bulk stabilize all moduli except the `breathing' modulus (that is generically present in higher-dimensional supergravities). Back-reaction to the inflaton roll causes the 4D Einstein-frame on-brane geometry to expand, a(t)∝tp, as well as exciting the breathing mode and causing the two off-brane dimensions to expand, r(t)∝tq. The model evades the general no-go theorems precluding 4D de Sitter solutions, since adjustments to the brane-localized inflaton potential allow the power p to be dialed to be arbitrarily large, with the 4D geometry becoming de Sitter in the limit p → ∞ (in which case q = 0). Slow-roll solutions give accelerated expansion with p large but finite, and q = ½. Because the extra dimensions expand during inflation, the present-day 6D gravity scale can be much smaller than it was when primordial fluctuations were generated — potentially allowing TeV gravity now to be consistent with the much higher gravity scale required at horizon-exit for observable primordial gravity waves. Because p >> q, the 4 on-brane dimensions expand more quickly than the 2 off-brane ones, providing a framework for understanding why the observed four dimensions are presently so much larger than the internal two. If uplifted to a 10D framework with 4 dimensions stabilized, the 6D evolution described here could describe how two of the six extra dimensions evolve to become much larger than the others, as a consequence of the enormous expansion of the 4 large dimensions we can see.