In this talk we will discuss how inflation can be embedded within a minimal extension of the Standard Model where the inflaton carries the Standard Model charges. There is no need of an ad-hoc scalar field to be introduced in order to explain the temperature anisotropy of the cosmic microwave background radiation, all the ingredients are present within a minimal supersymmetric Standard Model. The model is robust enough to provide a successful exit from inflation with all observed matter in the universe. This is a triumph for an inflationary paradigm which has always begged a simple question: can we identify the inflaton in a laboratory. We will briefly discuss how LHC can shed some insight into the inflaton.
Inflation, as currently understood, requires the presence of fields with very flat potentials. Supersymmetric models in which supersymmetry breaking is communicated by supergravity naturally yield such fields, but the scales are typically not suitable for obtaining both sufficient inflation and a suitable fluctuation spectrum. In the context of recent ideas about gauge mediation, there are new candidates for the inflaton. We present a simple model for slow-rollover inflation where the vacuum energy driving inflation is related to the same F-term responsible for the spectrum of supersymmetric p…
We compute the gluon and ghost propagators of Yang-Mills theory in linear covariant gauges from the coupled system of Dyson-Schwinger equations. For small values of the gauge fixing parameter $ξ\sim 0.1$, the deviations to the Landau gauge already become clearly visible. For the ghost dressing function, this is reflected in a logarithmic infrared suppression. Also, the gluon dressing function changes - but only quantitatively - and the gluon propagator remains finite at zero momentum. From the results, a running coupling is extracted.
We study the possibility that the Higgs and the inflaton are the same single field or cousins arising from the extra space components of some higher-dimensional gauge field. We take 5D supersymmetric gauge theory with a matter compactified on S^1 as a toy model and evaluate the one-loop contribution to the Higgs-inflaton potential. Our gauge-Higgs-inflaton unification picture applied to the gauge field of intermediate energy scale (\sim 10^{13} GeV) can explain the observed inflation parameters without fine-tuning.
The evolution of the inflaton field fluctuations from gauge-invariant metric fluctuations is discused. In particular, the case of a symmetric $ϕ_c$-exponential potential is analyzed.
The chirally symmetric Overlap quark propagator is explored in Coulomb gauge. This gauge is well suited for studying the relation between confinement and chiral symmetry breaking, since confinement can be attributed to the infrared divergent Lorentz-vector dressing function. Using quenched gauge field configurations on a $20^4$ lattice, the quark propagator dressing functions are evaluated, the dynamical quark mass is extracted and the chiral limit of these quantities is discussed. By removing the low-lying modes of the Dirac operator, chiral symmetry is artificially restored. Its effect on th…
The inflaton necessary to implement the mechanism of inflationary cosmology has natural candidates in quiver gauge theory. We discuss the dimensionless coefficients of quartic couplings and enumerate scalars which are singlet under the low-energy gauge group. The inflaton mass is generally predicted to be in the TeV region, close to 4 TeV for one specific unified model. A quartic inflaton potential, and a mutated hybrid inflation, are discussed. They can give adequate inflation and appropriate fluctuations but different spectral indices.
In the context of the Higgs model involving gauge and Yukawa interactions with the spontaneous gauge symmetry breaking, we consider $λϕ^4$ inflation with non-minimal gravitational coupling, where the Higgs field is identified as inflaton. Since the inflaton quartic coupling is very small, once quantum corrections through the gauge and Yukawa interactions are taken into account, the inflaton effective potential most likely becomes unstable. In order to avoid this problem, we need to impose stability conditions on the effective inflaton potential, which lead to not only non-trivial relations amo…
We construct a model of cosmological inflation and perturbation based on the higher-dimensional gauge theory. The inflaton and curvaton are the scalar fields arising from the extra space components of the gauge field living in more than four dimensions. We take the six-dimensional (6D) Yang-Mills theory compactified on $T^2$ as a toy model, and apply the one-loop effective potential of the inflaton and the curvaton to the curvaton scenario. We have found that the curvaton is subdominant for the linear curvature perturbation, but that a significant non-Gaussianity and a sizable tensor to scalar…
Cosmological inflation gives a natural answer for a variety of cosmological questions, including the horizon problem, the flatness problem, and others. However, inflation yields new questions relating to the flatness of the inflaton potential. Recent studies of ``little'' fields, a special class of pseudo-Goldstone bosons, have shown it is possible to protect the mass of a field while still yielding order one interactions with other fields. In this paper, we will show that ``little inflatons'' are natural candidates for the slow roll field of hybrid inflation models. We consider both supersymm…
We show that the `dressing' approach, which describes physical charges as gauge invariant composites of matter and clouds of gauge bosons, arises naturally in gauge theories. We give perturbative examples of dressings for both asymptotic charges and for states in which the fields are confined to a compact volume as is required, for example, by causality in pair creation. In QCD, we use dressed states to demonstrate explicitly how Gribov copies obstruct the non-perturbative construction of colour charges.
We analyze decay processes of the inflaton field, phi, during the coherent oscillation phase after inflation in f(phi)R gravity. It is inevitable that the inflaton decays gravitationally into gauge fields in the presence of f(phi)R coupling. We show a concrete calculation of the rate that the inflaton field decays into a pair of gauge fields via the trace anomaly. Comparing this new decay channel via the anomaly with the channels from the tree-level analysis, we find that the branching ratio crucially depends on masses and the internal multiplicities (flavor quantum number) of decay product pa…
We realize and study a model of hybrid inflation in the context of softly broken supersymmetry. The inflaton is taken to be a flat direction in the superfield space and, due to unsuppressed couplings, its soft supersymmetry breaking mass runs with scale. Both gauge and Yukawa couplings are taken into account and different inflationary scenarios are investigated depending on the relative strenght of the couplings and the mass spectrum.
We propose a model for cosmic inflation which is based on an effective description of strongly interacting, nonsupersymmetric matter within the framework of dynamical abelian projection and centerization. The underlying gauge symmetry is assumed to be SU(N) with N$\gg$1. Appealing to a thermodynamical treatment, the ground-state structure of the model is determined by a potential for the inflaton field (monopole condensate) which allows for nontrivially BPS saturated and thereby stable solutions. For $T<M_P$ this leads to an apparent decoupling of gravity from the inflaton dynamics. The ground…
We study the novel features in a model with Gauge Mediated Supersymmetry Breaking. If the messenger fields have positive R-parity, there will be new sources of flavor violations. We show that the dimension-5 operators will be quite important. When dressing these operators by wino-loops, the constraints on them by the present data are given.
Many controlled realizations of chaotic inflation employ pseudo-scalar axions. Pseudo-scalars ϕare naturally coupled to gauge fields through c ϕF \tilde{F}. In the presence of this coupling, gauge field quanta are copiously produced by the rolling inflaton. The produced gauge quanta, in turn, source inflaton fluctuations via inverse decay. These new cosmological perturbations add incoherently with the "vacuum" perturbations, and are highly nongaussian. This provides a natural mechanism to generate large nongaussianity in single or multi field slow-roll inflation. The resulting phenomenological…
The infrared behaviour of the gauge-invariant dressed fermion propagator in massless QED_3 is discussed for three choices of dressing. It is found that only the propagator with the isotropic (in three Euclidean dimensions) choice of dressing is acceptable as the physical fermion propagator. It is explained that the negative anomalous dimension of this physical fermion does not contradict any field-theoretical requirement.
The chirally symmetric overlap quark propagator is explored in Coulomb gauge for the first time. This gauge is especially well suited for studying the interrelation between confinement and chiral symmetry breaking, since confinement can be attributed to the infrared divergence of the vector dressing function of the inverse quark propagator. Using quenched gauge field configurations on a $20^4$ lattice, the dressing functions of the quark propagator as well as the dynamical quark mass function are evaluated, also in the chiral limit. Chiral symmetry is artificially restored by removing the low …
We perform an analytical study of the stability of the background solution of the model in which an inflaton, through an axionic coupling to a $U(1)$ gauge field, causes an amplification of the gauge field modes that strongly backreact on its dynamics. To this goal, we study the evolution of the gauge field modes coupled to the inflaton zero mode, treating perturbatively the deviation of the inflaton velocity from its mean-field value. As long as the system is in the strong backreaction regime we find that the inflaton velocity performs oscillations of increasing amplitude about the value it w…
We argue that all the necessary ingredients for successful inflation are present in the flat directions of the Minimally Supersymmetric Standard Model. We show that out of many gauge invariant combinations of squarks, sleptons and Higgses, there are two directions, ${\bf LLe}$, and ${\bf udd}$, which are promising candidates for the inflaton. The model predicts more than $10^3$ e-foldings with an inflationary scale of $H_{\rm inf}\sim {\cal O}(1-10)$ GeV, provides a tilted spectrum with an amplitude of $δ_H\sim 10^{-5}$ and a negligible tensor perturbation. The temperature of the thermalized p…
The $N=1$ supergravity models of cosmological inflation with inflaton belonging to a massive vector multiplet and spontaneous SUSY breaking after inflation are reformulated as the supersymmetric $U(1)$ gauge theories of a massless vector superfield interacting with the Higgs and Polonyi chiral superfields, all coupled to supergravity. The $U(1)$ gauge sector is identified with the $U(1)$ gauge fields of the super-GUT coupled to supergravity, whose gauge group has a $U(1)$ factor. A positive cosmological constant (dark energy) is included. The scalar potential is calculated, and its de Sitter v…
The slow roll inflation requires an extremely flat inflaton potential. The supersymmetry (SUSY) is not only motivated from the gauge hierarchy problem, but also from stabilizing that flatness of the inflaton potential against radiative corrections. However, it has been known that the Planck suppressed higher order terms in the Kähler potential receive large radiative corrections loosing the required flatness in the N = 1 supergravity. We propose to impose a global N = 2 SUSY on the inflaton sector. What we find is that the N = 2 SUSY Abelian gauge theory is exactly the same as the desired hybr…
We discuss inflaton decay in supergravity, taking account of the gravitational effects. It is shown that, if the inflaton has a nonzero vacuum expectation value, it generically couples to any matter fields that appear in the superpotential at the tree level, and to any gauge sectors through anomalies in the supergravity. Through these processes, the inflaton generically decays into the supersymmetry breaking sector, producing many gravitinos. The inflaton also directly decays into a pair of the gravitinos. We derive constraints on both inflation models and supersymmetry breaking scenarios for …
Using a semiclassical approach to Gravitoelectromagnetic Inflation (GEMI), we study the origin and evolution of seminal inflaton and electromagnetic fields in the early inflationary universe from a 5D vacuum state. We use simultaneously the Lorentz and Feynman gauges. Our formalism is naturally not conformal invariant on the effective 4D de Sitter metric, which make possible the super adiabatic amplification of electric and magnetic field modes during the early inflationary epoch of the universe on cosmological scales. This is the first time that solutions for the electric field fluctuations a…
It is shown that colour can only be defined on gauge invariant states. Since the ability to associate colour with constituent quarks is an integral part of the constituent quark model, this means that, if we want to extract constituent quarks from QCD, we need to dress Lagrangian quarks with gluons so that the result is gauge invariant. We further prove that gauge fixings can be used to construct such dressings. Gauge invariant dressed quark states are presented and a direct approach to the interquark potential is discussed. Some further aspects of dressing quarks are briefly discussed.
We study preheating in theories where the inflaton couples derivatively to scalar and gauge fields. Such couplings may dominate in natural models of inflation, in which the flatness of the inflaton potential is related to an approximate shift symmetry of the inflaton. We compare our results with previously studied models with non-derivative couplings. For sufficiently heavy scalar matter, parametric resonance is ineffective in reheating the universe, because the couplings of the inflaton to matter are very weak. If scalar matter fields are light, derivative couplings lead to a mild long-wavele…
A {\it gauge invariant} combination of LLe {\it sleptons} within the Minimal Supersymmetric Standard Model is one of the few inflaton candidates that can naturally explain population of the observable sector and creation of matter after inflation. After the end of inflation, the inflaton oscillates coherently about the minimum of its potential, which is a point of {\it enhanced gauged symmetry}. This results in bursts of non-perturbative production of the gauge/gaugino and (s)lepton quanta. The subsequent decay of these quanta is very fast and leads to an extremely efficient transfer of the in…
We calculate particle production during inflation and in the early stages of reheating after inflation in models with a charged scalar field coupled to Abelian and non-Abelian gauge fields. A detailed analysis of the power spectra of primordial electric fields, magnetic fields and charge fluctuations at the end of inflation and preheating is provided. We carefully account for the Gauss constraints during inflation and preheating, and clarify the role of the longitudinal components of the electric field. We calculate the timescale for the back-reaction of the produced gauge fields on the inflat…
We consider a scenario in which the inflaton $ϕ$ is a pseudoscalar field non-minimally coupled to gravity through a term of the form ${\cal X} R ϕ^2$. The pseudoscalar is also coupled to a $U(1)$ gauge field (or an ensemble of ${\cal N}$ gauge fields) through an axial coupling of the form $ϕF \tilde{F}$. After M. M. Anber and L. Sorbo, Phys. Rev. D 81, 043534 (2010), Ref. [1], it is well known that this axial coupling leads to a production of gauge particles which acts as a friction term in the dynamics of the inflaton, producing a slow-roll regime even in presence of a steep potential. A rema…
In a class of (pseudoscalar) inflation, inflationary phase is followed by a kination phase, where the Universe is dominated by the kinetic energy of the inflaton that runs away in a vanishing scalar potential. In this class of postinflationary evolution of the Universe, reheating of the Universe cannot be achieved by the inflaton particle decay, which requires its coherent oscillation in a quadratic potential. In this study, we explore the U(1) gauge field production through the Chern-Simons coupling between the pseudoscalar inflaton and the gauge field during the kination era and examine the …
The term `preheating' has been introduced recently to denote the process in which energy is transferred from a classical inflaton field into fluctuating field (particle) degrees of freedom without generating yet a real thermal ensemble. The models considered up to now include, besides the inflaton field, scalar or fermionic fluctuations. On the other hand the typical ingredient of an inflationary scenario is a nonabelian spontaneously broken gauge theory. So the formalism should also be developed to include gauge field fluctuations excited by the inflaton or Higgs field. We have chosen here, a…
We explore a possibility that an inflaton, which drives the cosmological inflation in the early Universe, can be detected by the recently approved FASER at the High-Luminosity LHC (HL-LHC). We consider nonminimal quartic inflation scenario in the minimal U(1)$_X$ extension of the Standard Model (SM) with the classical conformal invariance, where the inflaton is identified with the U(1)$_X$ Higgs field ($ϕ$). By virtue of the classical conformal invariance and the radiative U(1)$_X$ symmetry breaking via the Coleman-Weinberg mechanism, the inflationary predictions (in particular, the tensor-to-…
We show that, by adding a gauge singlet scalar S to the standard model which is nonminimally coupled to gravity, S can act both as the inflaton and as thermal relic dark matter. We obtain the allowed region of the (m_s, m_h) parameter space which gives a spectral index in agreement with observational bounds and also produces the observed dark matter density while not violating vacuum stability or nonperturbativity constraints. We show that, in contrast to the case of Higgs inflation, once quantum corrections are included the spectral index is significantly larger than the classical value (n = …
In order to gain new insights into the gauge field couplings in the early universe, we consider the constraints on gauge field production during inflation imposed by requiring that their effect on the CMB anisotropies are subdominant. In particular, we calculate systematically the bispectrum of the primordial curvature perturbation induced by the presence of vector gauge fields during inflation. Using a model independent parametrization in terms of magnetic non-linearity parameters, we calculate for the first time the contribution to the bispectrum from the cross correlation between the inflat…
Starting from the observation that colour charge is only well defined on gauge invariant states, we construct perturbatively gauge invariant, dynamical dressings for individual quarks. Explicit calculations show that an infra-red finite mass-shell renormalisation of the gauge invariant, dressed propagator is possible and, further, that operator product effects, which generate a running mass, may be included in a gauge invariant way in the propagator. We explain how these fields may be combined to form hadrons and show how the interquark potential can now be directly calculated. The onset of co…
If the inflaton is a pseudoscalar, then it naturally interacts with gauge fields via an axion-like coupling to $F_{μν} \tilde{F}^{μν}$. Through this coupling, the rolling inflaton produces quanta of the gauge field, that in their turn source the tensor components of the metric perturbations. Due to the parity-violating nature of the system, the right- and the left-handed tensor modes have different amplitudes. Such an asymmetry manifests itself in the form of non-vanishing TB and EB correlation functions in the Cosmic Microwave Background (CMB). We compute the amplitude of the parity-violating…
We study an approximate version of the Schwinger-Dyson equation that controls the nonperturbative behavior of the ghost-gluon vertex, in the Landau gauge. In particular, we focus on the form factor that enters in the dynamical equation for the ghost dressing function, in the same gauge, and derive its integral equation, in the "one-loop dressed" approximation. We consider two special kinematic configurations, which simplify the momentum dependence of the unknown quantity; in particular, we study the soft gluon case, and the well-known Taylor limit. When coupled with the Schwinger-Dyson equatio…
Supersymmetric theories often include the non-compact directions in the field space along which the tree level potential grows only up to a certain limited value (determined by the mass scale of the theory) and then stays constant for the arbitrarily large expectation value of the field parametrizing the direction. Above the critical value, the tree-level curvature is large and positive in the other directions. Such plateaux are natural candidates for the hybrid inflaton. The non-zero F-term density along the plateau spontaneously breaks SUSY and induces the one-loop logarithmic slope for the …
We study radiative plateau-like inflation \& Z$_{BL}$-portal freeze-in fermionic dark matter (DM) in a minimal B-L extended model. The U(1)$_{B-L}$ Higgs, responsible for heavy neutrino masses, also drives inflation in the early universe, thanks to radiative corrections from the heavy neutrinos \& the Z$_{BL}$ gauge boson. In our benchmark choice for the U(1)$_{B-L}$ gauge coupling $g_{B-L}\sim10^{-4}$, a light Z$_{BL}$ boson can be explored by current and future lifetime frontier experiments, such as FASER and FASER 2 at the LHC, SHiP, Belle II and LHCb. For the benchmark, the Hubble scale of…
We study a variant of the Chromo-Natural Inflation (CNI) mechanism in which the inflaton interacts only gravitationally with the CNI fields. Integrating out all the non-dynamical scalar fields of the model results in a coupling between the perturbations of the inflaton and of the CNI pseudo-scalar which is significantly greater than the one obtained in the absence of the gauge CNI dynamics. We compute how this greater coupling impacts the power spectrum of the inflaton perturbations that are sourced nonlinearly by the unstable (tensor) gauge CNI modes, and we require that the amplitude of thes…
We propose a new inflation model in which a gauge singlet inflaton turns into the Higgs condensate after inflation. The inflationary path is characterized by a moduli space of supersymmetric vacua spanned by the inflaton and Higgs field. The inflation energy scale is related to the soft supersymmetry breaking, and the Hubble parameter during inflation is smaller than the gravitino mass. The initial condition for the successful inflation is naturally realized by the pre-inflation in which the Higgs plays a role of the waterfall field.
We construct the simplest inflationary $α$-attractor models in supergravity: it has only one scalar, the inflaton. There is no sinflaton since the inflaton belongs to an orthogonal nilpotent superfield where the sinflaton depends on fermion bilinears. When the local supersymmetry is gauge-fixed, these models have only one single real scalar (the inflaton), a graviton and a massive gravitino. The sinflaton, sgoldstino and inflatino are all absent from the physical spectrum in the unitary gauge. The orthogonality condition leads to the simplest Kähler potential for the inflaton, while preserving…
We propose a model for cosmic inflation which is based on an effective description of strongly interacting, nonsupersymmetric matter within the framework of dynamical Abelian projection and centerization. The underlying gauge symmetry is assumed to be $SU(N+1)$ with $N \gg 1$. Appealing to a thermodynamical treatment, the ground-state structure of the model is classically determined by a potential for the inflaton field (dynamical monopole condensate) which allows for nontrivially BPS saturated and thereby stable solutions. For $T<M_P$ this leads to decoupling of gravity from the inflaton dyna…
We study the inflation due to the D-flat direction of an extra $U(1)$. This scenario is a hybrid of a right-handed sneutrino inflaton scenario and a gauge non-singlet inflaton scenario. The inflaton is a gauge non-singlet field which induces a right-handed neutrino mass spontaneously through an extra $U(1)$ D-flat direction. This right-handed neutrino mass can explain the solar neutrino problem. The reheating temperature resulting from the decay of the coherent oscillation of the right-handed sneutrino is sufficiently high so that the baryogenesis based on the lepton number asymmetry can be ap…
An inflation model based on dimensional (de)construction of a massive gauge theory is proposed. The inflaton in this model is the "zero-mode" of a component of the massive gauge field in the (de)constructed extra dimensions. The inflaton potential originates from the gauge invariant Stueckelberg potential. At low energy, the field range of the inflaton is enhanced by a factor $N^{\frac{d}{2}}$ compared to the field range of the original fields in the model, where $d$ is the number of the (de)constructed extra dimensions and $N$ is the number of the lattice points in each (de)constructed dimens…
The Standard Model Higgs boson, which has previously been shown to develop an effective vacuum expectation value during inflation, can give rise to large particle masses during inflation and reheating, leading to temporary blocking of the reheating process and a lower reheat temperature after inflation. We study the effects on the multiple stages of reheating: resonant particle production (preheating) as well as perturbative decays from coherent oscillations of the inflaton field. Specifically, we study both the cases of the inflaton coupling to Standard Model fermions through Yukawa interacti…
We study the process of primordial black hole (PBH) formation at the beginning of radiation era for the cosmological scenario in which the inflaton is a pseudo-Nambu-Goldstone boson (axion) and there is a coupling of the inflaton with some gauge field. In this model inflation is accompanied by the gauge quanta production and a strong rise of the curvature power spectrum amplitude at small scales (along with non-Gaussianity) is predicted. We show that data on PBH searches can be used for a derivation of essential constraints on the model parameters in such an axion inflation scenario. We compar…
Most successful models of inflation in supergravity have a shift symmetry for the inflaton and contain a stabilizer field coupled to the inflaton in a particular way. We argue that the natural interpretation of the stabilizer, from the viewpoint of the shift symmetry, is a three-form multiplet. Its coupling to the inflaton is uniquely determined by the shift symmetry and the invariance under three-form gauge transformations and has a natural string theory interpretation.
Usually one expectes the inflaton field to be coupled to some gauge-charged particles allowing for its decay during reheating. Such particles then play a role of the messengers for the gauge-mediated supersymmetry breaking during and (shortly) after the inflation and radiatively induce soft masses to all other $D$-flat directions. We show that during the preheating stage this gauge-mediated soft masses are typically much greater than the Hubble parameter during inflation. The dramatic role is played by the supersymmetry (SUSY) breaking due to the parametric resonance effect, which ensures that…
We show how we can implement chaotic inflation in the context of supergravity by conveniently selecting the functional form of a strong enough non-minimal coupling between the inflaton and the Ricci scalar curvature. The procedure can be applied when a gauge singlet or non-singlet inflaton is coupled to another singlet superfield within linear-quadratic, trilinear or bilinear superpotential terms. The tachyonic instability occurring along the direction of the accompanying non-inflaton field can be cured by expanding the kinetic part of the frame function up to the fourth order in powers of the…
We propose a simple model where a {\it gauge invariant inflaton} is responsible for cosmic inflation and generates the seed for structure formation, while its relic {\it thermal} abundance explains the missing matter of the universe in the form of cold dark matter. The inflaton self-coupling also explains the observed neutrino masses. All the virtues can be attained in a minimal extension of the Standard Model gauge group around the TeV scale. We can also unveil these properties of an inflaton in forthcoming space and ground based experiments.
In any realistic particle physics model of inflation, the inflaton can be expected to couple to other fields. We consider a model with a dilaton-like coupling between a U(1) gauge field and a scalar inflaton. We show that this coupling can result in observable non-gaussianity, even in the conventional regime where inflation is supported by a single scalar slowly rolling on a smooth potential: the time dependent inflaton condensate leads to amplification of the large-scale gauge field fluctuations, which can feed-back into the scalar/tensor cosmological perturbations. In the squeezed limit, the…
A model of inflation is presented where the inflaton field is a complex scalar field coupled to a U(1) gauge field. Due to the axial symmetry of the potential, the inflation is driven by the radial direction while the angular field is gauged by U(1). Due to the coupling of the inflaton to the gauge field, a time dependent mass term for the gauge field is generated dynamically and conformal invariance is broken. We study whether a significant amount of primordial magnetic fields can be generated during inflation by allowing a time-dependent U(1) gauge kinetic coupling.
