Starobinsky-like two-field inflation

Advances in High Energy Physics, 2017

We review the realization of Starobinsky-type inflation within induced-gravity supersymmetric (SUSY) and non-SUSY models. In both cases, inflation is in agreement with the current data and can be attained for sub-Planckian values of the inflation. The corresponding effective theories retain perturbative unitarity up to the Planck scale and the inflation mass is predicted to be 3·1013 GeV. The supergravity embedding of these models is achieved by employing two gauge singlet chiral superfields, a superpotential that is uniquely determined by a continuous R and a discrete Zn symmetry and several (semi)logarithmic Kähler potentials that respect these symmetries. Checking various functional forms for the noninflation accompanying field in the Kähler potentials, we identify four cases which stabilize it without invoking higher order terms.

Physical Review D, 2014

We study inflation induced by (power-low) scalar curvature corrections to General Relativity. The class of inflationary scalar potentials V (σ) ∼ exp[n σ], n general parameter, is investigated in the Einsein frame and the corresponding actions in the Jordan frame are derived. We found the conditions for which these potentials are able to reproduce viable inflation according with the last cosmological data and lead to large scalar curvature corrections which emerge only at a mass scale larger than the Planck mass. Cosmological constant may appear or be set equal to zero in the Jordan frame action without changing the behaviour of the model during inflation. Moreover, polynomial corrections to General Relativity are analyzed in detail. When de Sitter space-time emerges as an exact solution of the models, it is necessary to use perturbative equations in the Jordan framework to study their dynamics during the inflation. In this case, we demonstrate that the Ricci scalar decreases after a correct amount of inflation, making the models consistent with the observable evolution of the universe.

2020

We investigate the production of primordial black holes and their contribution to the presently observed dark matter in a dilaton two-field extension of Starobinsky's quadratic f(R) model of inflation. The model features a multi-field amplification mechanism which leads to the generation of a sharp peak in the inflationary power spectrum at small wavelengths responsible for the production of primordial black holes. This mechanism is significantly different from single-field models and requires a stochastic treatment during an intermediate phase of the inflationary dynamics. We find that the model leads to a successful phase of effective single-field Starobinsky inflation for wavelengths probed by the cosmic microwave background radiation and explains the observed cold dark matter content in the Universe by the formation of primordial black holes.

Physical Review D, 2006

It is believed that soon after the Planck era, space time should have a semi-classical nature. According to this, the escape from General Relativity theory is unavoidable. Two geometric counter-terms are needed to regularize the divergences which come from the expected value. These counter-terms are responsible for a higher derivative metric gravitation. Starobinsky idea was that these higher derivatives could mimic a cosmological constant. In this work it is considered numerical solutions for general Bianchi I anisotropic space-times in this higher derivative theory. The approach is "experimental" in the sense that there is no attempt to an analytical investigation of the results. It is shown that for zero cosmological constant Λ = 0, there are sets of initial conditions which form basins of attraction that asymptote Minkowski space. The complement of this set of initial conditions form basins which are attracted to some singular solutions. It is also shown, for a cosmological constant Λ > 0 that there are basins of attraction to a specific de Sitter solution. This result is consistent with Starobinsky's initial idea. The complement of this set also forms basins that are attracted to some type of singular solution. Because the singularity is characterized by curvature scalars, it must be stressed that the basin structure obtained is a topological invariant, i.e., coordinate independent.

A novel realization of the Starobinsky inflationary model within a moderate extension of the Minimal Supersymmetric Standard Model (MSSM) is presented. The proposed superpotential is uniquely determined by applying a continuous R and a Z_2 discrete symmetry, whereas the Kahler potential respects a no-scale-type SU(53,1)/SU(53)x U(1)_R x Z_2 symmetry too. The inflaton is identified with a Higgs-like modulus whose the vacuum expectation value controls the gravitational strength. Thanks to a strong enough coupling (with a parameter cT involved) between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton with cT>76 and the corresponding effective theory being valid up to the Planck scale. The inflationary observables turn out to be in agreement with the current data and the inflaton mass is predicted to be 3x10^13 GeV. At the cost of a relatively small superpotential coupling constant, the model offers also a resolution ...

International Journal of Modern Physics D, 2014

The recent CMB data from Planck and BICEP2 observations have opened a new window for inflationary cosmology. In this paper, we compare three Starobinsky-like inflationary scenarios: (i) The original Starobinsky proposal, (ii) a family of dynamically broken SUGRA models, and (iii) a class of "decaying" vacuum Λ(H) cosmologies. We then focus on the Λ(H) variant, which spans the complete cosmic history of the universe from an early inflationary stage, followed by the "graceful exit" into the standard radiation regime, the matter epoch and, finally, the late-time accelerated expansion. Computing the effective potential we find that the "running" Λ(H) models also provide a prediction for the tensor-to-scalar ratio of the CMB spectrum, r ≃ 0.16, which is compatible to within 1σ with the value [Formula: see text] recently measured by the BICEP2 collaboration.

International Journal of Modern Physics D, 2021

In this work, we study numerically one kind of generalization of the Starobinsky inflationary model (power-law type), which is characterized by the parameter [Formula: see text]. In order to find the parameter [Formula: see text] that fixes with observations, we compute the cosmological parameters [Formula: see text], [Formula: see text] and [Formula: see text] for several values of [Formula: see text]. We have found that the value of [Formula: see text] reproduces the value of [Formula: see text], [Formula: see text] and [Formula: see text] is in agreement with the current observational data.

2018

We review some recent trends in the inflationary model building, the supersymmetry (SUSY) breaking, the gravitino Dark Matter (DM) and the Primordial Black Holes (PBHs) production in supergravity. The Starobinsky inflation can be embedded into supergravity when the inflaton belongs to the massive vector multiplet associated with a (spontaneously broken) $U(1)$ gauge symmetry. The SUSY and R-symmetry can be also spontaneously broken after inflation by the (standard) Polonyi mechanism. Polonyi particles and gravitinos are super heavy and can be copiously produced during inflation via the Schwinger mechanism sourced by the Universe expansion. The overproduction and instability problems can be avoided, and the positive cosmological constant (dark energy) can also be introduced. The observed abundance of the Cold Dark Matter (CDM) composed of gravitinos can be achieved in our supergravity model too, thus providing the unifying framework for inflation, supersymmetry breaking, dark energy ...

International Journal of Modern Physics D, 2009

The Starobinsky model is a natural inflationary scenario in which inflation arises due to quantum effects of the massless matter fields. A modified version of the Starobinsky (MSt) model takes the masses of matter fields and the cosmological constant, Λ, into account. The equations of motion become much more complicated; however, approximate analytic and numeric solutions are possible. In the MSt model, inflation starts due to the supersymmetric (SUSY) particle content of the underlying theory, and the transition to the radiation-dominated epoch occurs due to the relatively heavy s-particles decoupling. For Λ = 0 the inflationary solution is stable until the last stage, just before decoupling. In the present paper we generalize this result for Λ ≠ 0, since Λ should be nonvanishing at the SUSY scale. We also take into account the radiative corrections to Λ. The main result is that the inflationary solution of the MSt model remains robust and stable.

ECU 2023

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

2020

We revisit inflation with non-canonical scalar fields by applying deformed-steepness exponential potentials. We show that the resulting scenario can lead to inflationary observables, and in particular to scalar spectral index and tensor-to-scalar ratio, in remarkable agreement with observations. Additionally, a significant advantage of the scenario is that the required parameter values, such as the non-canonicality exponent and scale, as well as the potential exponent and scale, do not need to acquire unnatural values and hence can accept a theoretical justification. Hence, we obtain a significant improvement with respect to alternative schemes, and we present distinct correlations between the model parameters that better fit the data, which can be tested in future probes. This combination of observational efficiency and theoretical justification makes the scenario at hand a good candidate for the description of inflation.

Journal of Cosmology and Astroparticle Physics, 2014

A novel realization of the Starobinsky inflationary model within a moderate extension of the Minimal Supersymmetric Standard Model (MSSM) is presented. The proposed superpotential is uniquely determined by applying a continuous R and a Z 2 discrete symmetry, whereas the Kähler potential is associated with a no-scale-type SU(54, 1)/ SU(54)×U(1) R ×Z 2 Kähler manifold. The inflaton is identified with a Higgs-like modulus whose the vacuum expectation value controls the gravitational strength. Thanks to a strong enough coupling (with a parameter c T involved) between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton with c T ≥ 76 and the corresponding effective theory being valid up to the Planck scale. The inflationary observables turn out to be in agreement with the current data and the inflaton mass is predicted to be 3 • 10 13 GeV. At the cost of a relatively small superpotential coupling constant, the model offers also a resolution of the µ problem of MSSM for c T ≤ 4500 and gravitino heavier than about 10 4 GeV. Supplementing MSSM by three right-handed neutrinos we show that spontaneously arising couplings between the inflaton and the particle content of MSSM not only ensure a sufficiently low reheating temperature but also support a scenario of non-thermal leptogenesis consistently with the neutrino oscillation parameters.

Journal of Cosmology and Astroparticle Physics, 2015

We compute corrections to the inflationary potential due to conformally coupled non-relativistic matter. We find that under certain conditions of the matter coupling, inflation may be interrupted abruptly. We display this in the superconformal Starobinsky model, where matter is conformally coupled to the Einstein frame metric. These corrections may easily stop inflation provided that there is an initial density of non-relativistic matter. Since these additional heavy degrees of freedom generically occur in higher dimension theories, for example as Kaluza-Klein modes, this effect can arise in multiple scenarios.

Physical Review D, 2006

We study the single field slow-roll inflation models that better agree with the available CMB and LSS data including the three years WMAP data: new inflation and hybrid inflation. We study these models as effective field theories in the Ginsburg-Landau context: a trinomial potential turns out to be a simple and well motivated model. The spectral index n s of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations and the running index dn s =d lnk are studied in detail. We derive explicit formulas for n s , r and dn s =d lnk and provide relevant plots. In new inflation, and for the chosen central value n s 0:95, we predict 0:03 < r < 0:04 and ÿ0:000 70 < dn s =d lnk < ÿ0:000 55. In hybrid inflation, and for n s 0:95, we predict r ' 0:2 and dn s =d lnk ' ÿ0:001. Interestingly enough, we find that in new inflation n s is bounded from above by n s max 0:961 528. .. and that r is a two valued function of n s in the interval 0:96 < n s < n s max. In the first branch we find r < r max 0:114 769. .. . In hybrid inflation we find a critical value 2 0 crit for the mass parameter 2 0 of the field coupled to the inflaton. For 2 0 < 0 M 2 Pl =192, where 0 is the cosmological constant, hybrid inflation yields a blue tilted n s > 1 behavior. Hybrid inflation for 2 0 > 0 M 2 Pl =192 fulfills all the present CMB LSS data for a large enough initial inflaton amplitude. Even if chaotic inflation predicts n s values compatible with the data, chaotic inflation is disfavored since it predicts a too high value r ' 0:27 for the ratio of tensor to scalar fluctuations. The model which best agrees with the current data and which best prepares the way to the expected data r & 0:1, is the trinomial potential with negative mass term: new inflation.

Symmetry

The latest released data from Planck in 2018 put up tighter constraints on inflationary parameters. In the present article, the in-built symmetry of the non-minimally coupled scalar-tensor theory of gravity is used to fix the coupling parameter, the functional Brans–Dicke parameter, and the potential of the theory. It is found that all the three different power-law potentials and one exponential pass these constraints comfortably, and also gracefully exit from inflation.