After reviewing the motivations for cosmological inflation formulated in the formalism of supersymmetry, we argue that the appropriate framework is that of no-scale supergravity. We then show how to construct within this framework inflationary models whose predictions for the tilt in the spectrum of scalar perturbations, $n_s$, and the ratio, $r$, of tensor and scalar perturbations coincide with those of the $R + R^2$ model of inflation proposed by Starobinsky. A more detailed study of no-scale supergravity reveals a structure that is closely related to that of $R^2$ modifications of the minimal Einstein-Hilbert action for general relativity, opening avenues for constructing no-scale de Sitter and anti-de Sitter models by combining pairs of Minkowski models, as well as generalizations of the original no-scale Starobinsky models of inflation. We then discuss the phenomenology of no-scale models of inflation, including inflaton decay and reheating, and then the construction of explicit scenarios based on SU(5), SO(10) and string-motivated flipped SU(5)$\times$U(1) GUT models. The latter provides a possible model of almost everything below the Planck scale, including neutrino masses and oscillations, the cosmological baryon asymmetry and cold dark matter, as well as $n_s$ and $r$.
Measurements of the cosmic microwave background (CMB) favour models of inflation with a small tensor-to-scalar ratio r, as predicted by the Starobinsky R + R^2 model. It has been shown previously that various models based on no-scale supergravity with different forms of superpotential make predictions similar to those of the Starobinsky model. In this paper we present a unified and general treatment of Starobinsky avatars of no-scale supergravity, using the underlying non-compact SU(2,1)/SU(2) x U(1) symmetry to demonstrate equivalences between different models, exhibiting 6 specific equivalen…
Higgs inflation and $R^2$-inflation (Starobinsky model) are two limits of the same quantum model, hereafter called Starobinsky-Higgs. We analyse the two-loop action of the Higgs-like scalar $ϕ$ in the presence of: 1) non-minimal coupling ($ξ$) and 2) quadratic curvature terms. The latter are generated at the quantum level with $ϕ$-dependent couplings ($\tildeα$) even if their tree-level couplings ($α$) are tuned to zero. Therefore, the potential always depends on both Higgs field $ϕ$ and scalaron $ρ$, hence multi-field inflation is a quantum consequence. The effects of the quantum (one- and tw…
We revisit the problem of generality of Starobinsky and Higgs inflation. The known results obtained in the Einstein frame are generalized for the case of an arbitrary initial energy of the scalar field. These results are compared with the results obtained directly in the Jordan frame, which, to our knowledge, has not been thoroughly explored in the literature previously. We demonstrate that the qualitative picture of initial conditions zone in the $(ϕ, \dot ϕ)$ plane, which leads to sufficient amount of inflation, is quite similar for both the frames in the case of Higgs inflation. For Starobi…
Based on the current experimental data, the Standard Model predicts that the current vacuum state of the Universe is metastable, leading to a non-zero rate of vacuum decay through nucleation of bubbles of true vacuum. Our existence implies that there cannot have been any such bubble nucleation events anywhere in our whole past lightcone. We consider a minimal scenario of the Standard Model together with Starobinsky inflation, using three-loop renormalization group improved Higgs effective potential with one-loop curvature corrections. We show that the survival of the vacuum state through infla…
Higgsino dark matter in the Starobinsky supergravity with the MSSM in light of the LUX-ZEPLIN event
Utrecht University（乌得勒支大学）；Dutch Institute for Emergent Phenomena（荷兰涌现现象研究所）；Tokyo Metropolitan University（东京都立大学）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study（理化学研究所 Kavli 宇宙粒子与宇宙线研究所（WPI），东京大学前沿研究综合中心）
In this work, we study unified picture of inflation and dark matter in the Higgs-Starobinsky (HS) model. As pointed out in the literature, Starobinsky $R^2$ inflation is induced by quantum correction effect from the large Higgs-curvature (graviton) coupling. We start with non-minimal coupling HS action in Jordan frame. We then transform the Jordan frame action into the Einstein one using the conformal transformation. The inflation potential is derived from the gravitational action of non-minimal-Higgs coupling and Starobinsky term in Einstein frame where the $R^2$ term is dominated in the infl…
The Starobinsky inflation model is one of the simplest inflation models that is consistent with the cosmic microwave background observations. In order to explain dark matter of the universe, we consider a minimal extension of the Starobinsky inflation model with introducing the dark sector which communicates with the visible sector only via the gravitational interaction. In Starobinsky inflation model, a sizable amount of dark-sector particle may be produced by the inflaton decay. Thus, a scalar, a fermion or a vector boson in the dark sector may become dark matter. We pay particular attention…
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 Schwing…
We single out the Starobinsky model and its extensions among generic $f(R)$ gravity as attractors at large field values for chaotic inflation. Treating a $R^3$ curvature term as a perturbation of the Starobinsky model, we impose the phenomenological bounds on the additional term satisfying the successful inflationary predictions. We find that the scalar spectral index can vary in both the red or blue tilted direction, depending on the sign of the coefficient of the $R^3$ term, whereas the tensor-to-scalar ratio is less affected in the Planck-compatible region. We also discuss the role of highe…
We study a model including a real scalar field $ϕ$ non-minimally coupled to $F({\cal R})$ gravity, which is conformally equivalent to an Einstein-Hilbert theory, involving two real scalar fields. We consider three special cases of the potential of the field $ϕ$ in the $F({\cal R})$-frame: a vanishing potential, a mass term and a Higgs potential. All these lead to non-trivial two-field potentials in the Einstein-frame which in particular directions resemble the well-known Starobinsky model. We find, that all these cases can yield viable inflationary models in complete agreement with current obs…
In the Starobinsky model of inflation, the observed dark matter abundance can be produced from the direct decay of the inflaton field only in a very narrow spectrum of close-to-conformal scalar fields and spinors of mass $\sim 10^7$ GeV. This spectrum can be, however, significantly broadened in the presence of effective non-renormalizable interactions between the dark and the visible sectors. In particular, we show that UV freeze-in can efficiently generate the right dark matter abundance for a large range of masses spanning from the keV to the PeV scale and arbitrary spin, without significant…
We study the stability of the electroweak vacuum during and after the Starobinsky inflation, assuming the existence of the non-minimal Higgs coupling to the Ricci scalar. In the Starobinsky inflation, there exists $R^2$ term (with $R$ being the Ricci scalar), which modifies the evolution equation of the Higgs field. We consider the case that the non-minimal coupling is sizable so that the quantum fluctuation of the Higgs field is suppressed and that the Higgs amplitude is settled near the origin during the inflation. In such a case, the Higgs amplitude may be amplified in the preheating epoch …
A Global Overview of Starobinsky Inflation beyond slow-roll with CMB-BAO data
Indian Institute of Science Education and Research Berhampur（印度科学教育研究所贝尔汉普尔分校）；Astronomisches Recheninstitut, Zentrum für Astronomie der Universität Heidelberg（海德堡大学天文学计算研究所）
The Starobinsky model, considered in the framework of the Palatini formalism, in contrast to the metric formulation, does not provide us with a model for inflation, due to the absence of a propagating scalar degree of freedom that can play the role of the inflaton. In the present article we study the Palatini formulation of the Starobinsky model coupled, in general nonminimally, to scalar fields and analyze its inflationary behavior. We consider scalars, minimally or nonminimally coupled to the Starobinsky model, such as a quadratic model, the induced gravity model or the standard Higgs-like i…
We perform the calculation for tree-level ultraviolet unitarity violation scales for scalar-$R^2$ inflation models by including an additional $R^2 |Φ|^2$-type term. Due to certain constraints, we resort to the Einstein frame for our calculations, where we separate our analysis between metric and Palatini formulations. We follow recent works in this line that debunk the naive predictions for unitarity violations in Higgs' inflation models to determine how to accurately estimate the behaviour of scattering amplitudes in the UV limit. Later, we work out different cases by assuming potentials corr…
Higgs boson mass and thermal wino dark matter from Starobinsky supergravity with the MSSM
Utrecht University（乌得勒支大学）；Dutch Institute for Emergent Phenomena（荷兰新兴现象研究所）；University of Southampton（南安普顿大学）；Rutherford Appleton Laboratory（卢瑟福·阿普尔顿实验室）；Tokyo Metropolitan University（东京都立大学）；International Institute of Physics, Natal（纳塔尔国际物理研究所）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study（东京大学基础研究院宇宙物质宇宙学前沿研究中心）
