Starobinsky-like Inflation Research Articles

Induced gravitational waves from flipped SU(5) superstring theory at nHz

The no-scale flipped SU(5) superstring framework constitutes a very promising paradigm for physics below the Planck scale providing us with a very rich cosmological phenomenology in accordance with observations. In particular, it can accommodate Starobinsky-like inflation, followed by a reheating phase, which is driven by a light “flaton” field, and during which the GUT phase transition occurs. In this Letter, we extract for the first time a gravitational-wave (GW) signal which naturally arises in the context of the flipped SU(5) cosmological phenomenology and is related to the existence of an early matter era (eMD) driven by the flaton field. Specifically, we study GWs non-linearly induced by inflationary perturbations and which are abundantly produced during a sudden transition from the flaton-driven eMD era to the late-time radiation-dominated era. Remarkably, we find a GW signal with a characteristic peak frequency fGW,peak depending only on the string slope α′ and reading as fGW,peak∝10−9(α′α⁎′)4Hz, where α⁎′ is the fiducial string slope being related directly to the reduced Planck scale MPl as α⁎′=8/MPl2. Interestingly enough, fGW,peak lies within the nHz frequency range; hence rendering this primordial GW signal potentially detectable by SKA, NANOGrav and PTA probes at their very low frequency region of their detection bands.

Supergravity Model of Inflation and Explaining IceCube HESE Data via PeV Dark Matter Decay

We construct a unified model of inflation and PeV dark matter with an appropriate choice of no-scale Kähler potential, superpotential, and gauge kinetic function in terms of MSSM fields and hidden sector Polonyi field. The model is consistent with the CMB observations and can explain the PeV neutrino flux observed at IceCube HESE. A Starobinsky-like Higgs-sneutrino plateau inflation is obtained from the D-term SUGRA potential while F-term being subdominant during inflation. To get PeV dark matter, SUSY breaking at PeV scale is achieved through Polonyi field. This sets the scale for soft SUSY breaking parameters m0,m1/2,A0 at the GUT scale in terms of the parameters of the model. The low-energy particle spectrum is obtained by running the RGEs. We show that the ~125 GeV Higgs and the gauge coupling unification can be obtained in this model. The 6 PeV bino-type dark matter is a subdominant fraction (~11%) of the relic density, and its decay gives the PeV scale neutrino flux observed at IceCube by appropriately choosing the couplings of the R-parity violating operators. Also, we find that there is degeneracy in scalar field parameters γ,β and coupling ζ value in producing the correct amplitude of CMB power spectrum. However, the value of parameter tanβ=1.8, which is tightly fixed from the requirement of PeV scale SUSY breaking, removes the degeneracy in the values of the scalar field parameters to provide a unique solution for inflation. In this way, it brings the explanation for dark matter, PeV neutrinos, and inflation within the same framework.

Consistent inflationary cosmology from quadratic gravity with dynamical torsion

The idea of gauge theories of gravity predicts that there should exist not only the massless graviton but also massive particles carrying the gravitational force. We study the cosmology in a quadratic gravity with dynamical torsion where gravity may be interpreted as a gauge force associated with the Poincaré group. In addition to the massless spin-2 graviton, the model contains four non-ghost massive particle species: a couple of spin-0, a spin-1 and a spin-2. Supposing the restoration of the local Weyl invariance in the UV limit and the parity invariance, we find the most general minisuperspace action describing a homogeneous and isotropic universe with a flat spatial geometry. We then transform the minisuperspace action to a quasi-Einstein frame in which the field space is a hyperboloid and the field potential is a combination of those of a Starobinsky-like inflation and a natural inflation. Remarkably, thanks to the multi-field dynamics, the Starobinsky-like inflationary trajectory can be realized even if the initial condition is away from the top of the Starobinsky-like potential. We also study linear tensor perturbations and find qualitatively different features than the Starobinsky inflation, spontaneous parity violation and mixing of the massless and massive spin-2 modes, which might reveal the underlying nature of gravity through inflationary observables.

Volkov\u2013Akulov\u2013Starobinsky supergravity revisited

We find new realizations of Volkov–Akulov–Starobinsky supergravity, i.e. Starobinsky inflationary models in supergravity coupled to a nilpotent superfield describing Volkov–Akulov goldstino. Our constructions are based on the no-scale Kähler potential K=-3log (T+overline{T}) for the inflaton field, and can describe de Sitter vacuum after inflation where supersymmetry is broken by the goldstino auxiliary component. In fact, we show that a more general class of models with K=-alpha log (T+overline{T}) for 3le alpha lesssim 6.37 can accomodate Starobinsky-like inflation with the universal prediction n_ssimeq 1-frac{2}{N_e} and rsimeq frac{4alpha }{(alpha -2)^2N_e^2}, while for 6.37lesssim alpha lesssim 7.23 viable hilltop inflation is possible (with n_s and r close to the above expressions). We derive the full component action and the masses of sinflaton, gravitino, and inflatino that are generally around the inflationary Hubble scale. Finally, we show that one of our models can be dualized into higher-derivative supergravity with constrained chiral curvature superfield.

Inflation and leptogenesis in high-scale supersymmetry

No-scale supergravity provides a successful framework for Starobinsky-like inflation models. Two classes of models can be distinguished depending on the identification of the inflaton with the volume modulus, $T$ (C-models), or a matter-like field, $\phi$ (WZ-models). When supersymmetry is broken, the inflationary potential may be perturbed, placing restrictions on the form and scale of the supersymmetry breaking sector. We consider both types of inflationary models in the context of high-scale supersymmetry. We further distinguish between models in which the gravitino mass is below and above the inflationary scale. We examine the mass spectra of the inflationary sector. We also consider in detail mechanisms for leptogenesis for each model when a right-handed neutrino sector, used in the seesaw mechanism to generate neutrino masses, is employed. In the case of C-models, reheating occurs via inflaton decay to two Higgs bosons. However, there is a direct decay channel to the lightest right-handed neutrino which leads to non-thermal leptogenesis. In the case of WZ-models, in order to achieve reheating, we associate the matter-like inflaton with one of the right-handed sneutrinos whose decay to the lightest right handed neutrino simultaneously reheats the Universe and generates the baryon asymmetry through leptogenesis.

Superstring-inspired particle cosmology: inflation, neutrino masses, leptogenesis, dark matter & the SUSY scale

We develop a string-inspired model for particle cosmology, based on a flipped SU(5)×U(1) gauge group formulated in a no-scale supergravity framework. The model realizes Starobinsky-like inflation, which we assume to be followed by strong reheating, with the GUT symmetry being broken subsequently by a light `flaton' field whose decay generates a second stage of reheating. We discuss the production of gravitinos and the non-thermal contribution made by their decays to the density of cold dark matter, which is assumed to be provided by the lightest neutralino. We also discuss the masses of light and heavy neutrinos and leptogenesis. As discussed previously [1], a key rôle is played by a superpotential coupling between the inflaton, matter and GUT Higgs fields, called λ6. We scan over possible values of λ6, exploring the correlations between the possible values of observables. We emphasize that the release of entropy during the GUT transition allows large regions of supersymmetry-breaking parameter space that would otherwise lead to severe overdensity of dark matter. Furthermore, we find that the Big Bang nucleosynthesis lower limit on the reheating temperature of ∼ 1 MeV restricts the supersymmetry-breaking scale to a range \U0001d4aa(10) TeV that is consistent with the absence of supersymmetric particles at the LHC.

Unified no-scale attractors

We have presented previously a general treatment of Starobinsky-like inflation in no-scale supergravity where the tensor-to-scalar ratio r = 3(1 − ns)2, and ns is the tilt of the scalar perturbations. In particular, we have shown how this scenario can be unified with modulus fixing, supersymmetry breaking and a small cosmological constant. In this paper we extend these constructions to inflationary models based on generalized no-scale structures. In particular, we consider alternative values of the curvature parameter, α < 1, as may occur if not all the complex Kähler moduli contribute to driving inflation, as well as α > 1, as may occur if complex structure moduli also contribute to driving inflation. In all cases, we combine these α-Starobinsky inflation models with supersymmetry breaking and a present-day cosmological constant, allowing for additional contributions to the vacuum energy from stages of gauge symmetry breaking.

Cosmology with a master coupling in flipped SU(5)×U(1): The λ6 universe

We propose a complete cosmological scenario based on a flipped SU(5)×U(1) GUT model that incorporates Starobinsky-like inflation, taking the subsequent cosmological evolution carefully into account. A single master coupling, λ6, connects the singlet, GUT Higgs and matter fields, controlling 1) inflaton decays and reheating, 2) the gravitino production rate and therefore the non-thermal abundance of the supersymmetric cold dark matter particle, 3) neutrino masses and 4) the baryon asymmetry of the Universe.

Unified no-scale model of modulus fixing, inflation, supersymmetry breaking, and dark energy

We present a minimal SU(2,1)/SU(2) x U(1) no-scale model that incorporates in an economical way modulus fixing, Starobinsky-like inflation, an adjustable scale for supersymmetry breaking and the possibility of a small cosmological constant, a.k.a. dark energy.

Starobinsky-like inflation and soft-SUSY breaking

We study a version of Starobinsky-like inflation in no-scale supergravity (SUGRA) where a Polonyi term in the hidden sector breaks supersymmetry (SUSY) after inflation, providing a link between the gravitino mass and inflation. We extend the theory to the visible sector and calculate the soft-SUSY breaking parameters depending on the modular weights in the superpotential and choice of Kähler potential. We are led to either no-scale SUGRA or pure gravity mediated SUSY breaking patterns, but with inflationary constraints on the Polonyi term setting a strict upper bound on the gravitino mass m3/2< 103 TeV. Since gaugino masses are significantly lighter than m3/2, this suggests that SUSY may be discovered at the LHC or FCC.

Symmetry breaking and reheating after inflation in no-scale flipped SU(5)

No-scale supergravity and the flipped SU(5)×U(1) gauge group provide an ambitious prototype string-inspired scenario for physics below the string scale, which can accommodate the Starobinsky-like inflation favoured by observation when the inflaton is associated with one of the singlet fields associated with neutrino mass generation. During inflation, the vacuum remains in the unbroken GUT phase, and GUT symmetry breaking occurs later when a field with a flat direction (the flaton) acquires a vacuum expectation value. Inflaton decay and the reheating process depend crucially on GUT symmetry breaking, as decay channels open and close, depending on the value of the flaton vacuum expectation value. Here, we consider the simultaneous cosmological evolution of both the inflaton and flaton fields after inflation. We distinguish weak, moderate and strong reheating regimes, and calculate in each case the entropy produced as all fields settle to their global minima. These three reheating scenarios differ in the value of a Yukawa coupling that introduces mass mixing between the singlets and the 10s of SU(5). The dynamics of the GUT transition has an important impact on the production of gravitinos, and we also discuss the pattern of neutrino masses we expect in each of the three cases. Finally, we use recent CMB limits on neutrino masses to constrain the reheating models, finding that neutrino masses and the cosmological baryon asymmetry can both be explained if the reheating is strong.

Starobinsky inflation and dark energy and dark matter effects from quasicrystal like spacetime structures

The goal of this work on mathematical cosmology and geometric methods in modified gravity theories, MGTs, is to investigate Starobinsky-like inflation scenarios determined by gravitational and scalar field configurations mimicking quasicrystal, QC, like structures. Such spacetime aperiodic QCs are different from those discovered and studied in solid state physics but described by similar geometric methods. We prove that a inhomogeneous and locally anisotropic gravitational and matter field effective QC mixed continuous and discrete “ether” can be modelled by exact cosmological solutions in MGTs and Einstein gravity. The coefficients of corresponding generic off-diagonal metrics and generalized connections depend (in general) on all spacetime coordinates via generating and integration functions and, certain smooth and discrete parameters. Imposing additional nonholonomic constraints, prescribing symmetries for generating functions and solving the boundary conditions for integration functions and constants, we can model various nontrivial torsion QC structures or extract cosmological Levi-Civita configurations with diagonal metrics reproducing de Sitter (inflationary) like and other type homogeneous inflation and acceleration phases. Finally, we speculate how various dark energy and dark matter effects can be modelled by off-diagonal interactions and deformations of a nontrivial QC like gravitational vacuum structure and analogous scalar matter fields.

Inflation and high-scale supersymmetry with an EeV gravitino

We consider inflation and supersymmetry breaking in the context of a minimal model of supersymmetry in which the only "low" energy remnant of supersymmetry is the gravitino with a mass of order an EeV. In this theory, the supersymmetry breaking scale is above the inflaton mass, m ~ 3 x 10^{13} GeV, as are all sfermion and gaugino masses. In particular, for a no-scale formulation of Starobinsky-like inflation using the volume modulus T, we show that inflation can be accommodated even when the supersymmetry breaking scale is very large. Reheating is driven through a gravitational coupling to the two Higgs doublets and is enhanced by the large mu-parameter. This leads to gravitino cold dark matter where the mass is constrained to be in the range 0.1 EeV $\lesssim m_{3/2} \lesssim 1000$ EeV.

Starobinsky-like inflation, supercosmology and neutrino masses in no-scale flipped SU(5)

We embed a flipped SU(5) × U(1) GUT model in a no-scale supergravity framework, and discuss its predictions for cosmic microwave background observables, which are similar to those of the Starobinsky model of inflation. Measurements of the tilt in the spectrum of scalar perturbations in the cosmic microwave background, ns, constrain significantly the model parameters. We also discuss the model's predictions for neutrino masses, and pay particular attention to the behaviours of scalar fields during and after inflation, reheating and the GUT phase transition. We argue in favor of strong reheating in order to avoid excessive entropy production which could dilute the generated baryon asymmetry.

Starobinsky-like inflation in no-scale supergravity Wess-Zumino model with Polonyi term

We propose a simple modification of the no-scale supergravity Wess-Zumino model of Starobinsky-like inflation to include a Polonyi term in the superpotential. The purpose of this term is to provide an explicit mechanism for supersymmetry breaking at the end of inflation. We show how successful inflation can be achieved for a gravitino mass satisfying the strict upper bound m3/2< 103 TeV, with favoured values {m}_{3/2}lesssim mathcal{O}(1) TeV. The model suggests that SUSY may be discovered in collider physics experiments such as the LHC or the FCC.

The conformal limit of inflation in the era of CMB polarimetry

We argue that the non-detection of primordial tensor modes has taught us a great deal about the primordial universe. In single-field slow-roll inflation, the current upper bound on the tensor-to-scalar ratio, r<0.07 (95% CL), implies that the Hubble slow-roll parameters obey ε≪η , and therefore establishes the existence of a new hierarchy. We dub this regime the conformal limit of (slow-roll) inflation, and show that it includes Starobinsky-like inflation as well as all viable single-field models with a sub-Planckian field excursion. In this limit, all primordial correlators are constrained by the full conformal group to leading non-trivial order in slow-roll. This fixes the power spectrum and the full bispectrum, and leads to the ``conformal'' shape of non-Gaussianity. The size of non-Gaussianity is related to the running of the spectral index by a consistency condition, and therefore it is expected to be small. In passing, we clarify the role of boundary terms in the ζ action, the order to which constraint equations need to be solved, and re-derive our results using the Wheeler-deWitt formalism.

Starobinsky-like inflation and neutrino masses in a no-scale SO(10) model

Using a no-scale supergravity framework, we construct an SO(10) model that makes predictions for cosmic microwave background observables similar to those of the Starobinsky model of inflation, and incorporates a double-seesaw model for neutrino masses consistent with oscillation experiments and late-time cosmology. We pay particular attention to the behaviour of the scalar fields during inflation and the subsequent reheating.

Higgs inflation, reheating and gravitino production in no-scale Supersymmetric GUTs

We extend our previous study of supersymmetric Higgs inflation in the context of no-scale supergravity and grand unification, to include models based on the flipped SU(5) and the Pati-Salam group. Like the previous SU(5) GUT model, these yield a class of inflation models whose inflation predictions interpolate between those of the quadratic chaotic inflation and Starobinsky-like inflation, while avoiding tension with proton decay limits. We further analyse the reheating process in these models, and derive the number of e-folds, which is independent of the reheating temperature. We derive the corresponding predictions for the scalar tilt and the tensor-to-scalar ratio in cosmic microwave background perturbations, as well as discussing the gravitino production following inflation.

Starobinsky-Like Inflation and Running Vacuum in the Context of Supergravity

We describe the primeval inflationary phase of the early Universe within a quantum field theoretical (QFT) framework that can be viewed as the effective action of vacuum decay in the early times. Interestingly enough, the model accounts for the “graceful exit” of the inflationary phase into the standard radiation regime. The underlying QFT framework considered here is supergravity (SUGRA), more specifically an existing formulation in which the Starobinsky-type inflation (de Sitter background) emerges from the quantum corrections to the effective action after integrating out the gravitino fields in their (dynamically induced) massive phase. We also demonstrate that the structure of the effective action in this model is consistent with the generic idea of re-normalization group (RG) running of the cosmological parameters; specifically, it follows from the corresponding RG equation for the vacuum energy density as a function of the Hubble rate, ρ Λ ( H ) . Overall, our combined approach amounts to a concrete-model realization of inflation triggered by vacuum decay in a fundamental physics context, which, as it turns out, can also be extended for the remaining epochs of the cosmological evolution until the current dark energy era.

Spotting deviations from R2 inflation

We discuss the soundness of inflationary scenarios in theories beyond the Starobinsky model, namely a class of theories described by arbitrary functions of the Ricci scalar and the K-essence field. We discuss the pathologies associated with higher-order equations of motion which will be shown to constrain the stability of this class of theories. We provide a general framework to calculate the slow-roll parameters and the corresponding mappings to the theory parameters. For paradigmatic gravitational models within the class of theories under consideration we illustrate the power of the Planck/Bicep2 latest results to constrain such gravitational Lagrangians. Finally, bounds for potential deviations from Starobinsky-like inflation are derived.