New actions for modified gravity and supergravity

We extend the f (R) gravity action by including a generic dependence upon the Weyl tensor, and further generalize it to supergravity by using the super-curvature R and super-Weyl W chiral superfields in N = 1 chiral curved superspace. We argue that our (super)gravitational actions are the meaningful extensions of the phenomenological f(R) gravity and its locally supersymmetric generalization towards their UV completion and their embedding into superstring theories. The proposed actions can be used for study of cosmological perturbations and gravitational instabilities due to a nonvanishing Weyl tensor in gravity and supergravity

Modified born-infeld-dilaton-axion coupling in supersymmetry

We propose the supersymmetric extension of the modified Born–Infeld-axion-dilaton non-linear electrodynamics that has confined static abelian solutions used for describing the electromagnetic confinement in the presence of axion and dilaton fields, as well as charged matter. The supersymmetric extension also has the non-trivial scalar potential that implies the upper bounds on the matter fields

Modified Gravity in Higher Dimensions, Flux Compactification, and Cosmological Inflation

We review a possible origin of cosmological inflation from higher (D) spacetime dimensions in the context of modified gravity theory. It is demonstrated that it requires a spontaneous warped compactification of higher (D) spacetime dimensions together with the stabilization of extra (D?4) dimensions by Freund–Rubin mechanism. The relevant tools include an extra gauge (D/2?1) -form field with a non-vanishing flux in compact dimensions and a positive cosmological constant in D dimensions. Those features are illustrated on the specific example in eight spacetime dimensions compactified on a four-sphere with a warped factor and a flux, which leads to a viable Starobinsky-like inflationary model in four (non-compact) spacetime dimensions

General couplings of a vector multiplet in N = 1 supergravity with new FI terms

We propose new interactions of a (massive) vector multiplet with chiral multiplets and (D-type) spontaneously broken supersymmetry in four-dimensional N=1supergravity, due to the generalized Fayet-Iliopoulos (FI) terms. Our actions are invariant under linearly realized off-shell supersymmetry and Kähler-Weyl transformations. We compute the scalar potentials and pinpoint some physical restrictions arising in this approach

Multi-Field versus Single-Field in the Supergravity Models of Inflation and Primordial Black Holes

We review the models unifying inflation and Primordial Black Hole (PBH) formation, which are based on the modified (Starobinsky-type) supergravity. We begin with the basic (Starobinsky) inflationary model of modified gravity and its alpha-attractor-type generalizations for PBH production, and recall how all those single-field models can be embedded into the minimal supergravity. Then, we focus on the effective two-field models arising from the modified (Starobinsky-type) supergravity and compare them to the single-field models under review. Those two-field models describe double inflation whose first stage is driven by Starobinsky’s scalaron and whose second stage is driven by another scalar belonging to the supergravity multiplet. The power spectra are numerically computed, and it is found that the ultra-slow-roll regime gives rise to the enhancement (peak) in the scalar power spectrum leading to an efficient PBH formation. The resulting PBH masses and their density fraction (as part of dark matter) are found to be in agreement with cosmological observations. The PBH-induced gravitational waves, if any, are shown to be detectable by the ground-based and space-based gravitational interferometers under construction

On the superstring-inspired quantum correction to the Starobinsky model of inflation

Superstring/M-theory is the theory of quantum gravity that can provide the UV-completion to viable inflation models. We modify the Starobinsky inflation model by adding the Bel-Robinson tensor $T^{\mu\nu\lambda\rho}$ squared term proposed as the leading quantum correction inspired by superstring theory. The $(R+\frac{1}{6m^2}R^2 -\frac{\beta}{8m^6}T^2)$ model under consideration has two parameters: the inflaton mass $m$ and the string-inspired positive parameter $\beta$. We derive the equations of motion in the Friedmann-Lemaitre-Robertson-Walker universe and investigate its solutions. We find the physical bounds on the value of the parameter $\beta$ by demanding the absence of ghosts and consistency of the derived inflationary observables with the measurements of the cosmic microwave background radiation.Comment: 22 pages, 5 figures, LaTe

Gravitino condensate in N = 1 supergravity coupled to the N = 1 supersymmetric Born–Infeld theory

The $N=1$ supersymmetric Born-Infeld theory coupled to $N=1$ supergravity in four spacetime dimensions is studied in the presence of a cosmological term with spontaneous supersymmetry breaking. The consistency is achieved by compensating a negative contribution to the cosmological term from the Born-Infeld theory by a positive contribution originating from the gravitino condensate. This leads to an identification of the Born-Infeld scale with the supersymmetry breaking scale. The dynamical formation of the gravitino condensate in supergravity is reconsidered and the induced one-loop effective potential is derived. Slow roll cosmological inflation with the gravitino condensate as the inflaton (near the maximum of the effective potential) is viable against the Planck 2018 data and can lead to the inflationary (Hubble) scale as high as $10^{12}$ GeV. Uplifting the Minkowski vacuum (after inflation) to a de Sitter vacuum (dark energy) is possible by the use of the alternative Fayet-Iliopoulos term. Some major physical consequences of our scenario to reheating are briefly discussed also.Comment: 15 pages, 2 figures, LaTeX; section 2 revised, main results unchanged; comments added; misprints correcte

Beyond Starobinsky inflation

A supergravity extension of the (R+R2) gravity with the additional (Born-Infeld) structure of a massive vector multiplet gives rise to the specific F(R) gravity, whose structure is investigated in detail. The massive vector multiplet has an inflaton (scalaron), goldstino, and massive vector field as its field components. The model describes Starobinsky inflation and allows us to extrapolate the F(R) function beyond the inflationary scale (up to Planck scale). We observe some differences versus the (R+R2)gravity and several breaking patterns of the well-known correspondence between the F(R) gravity and the scalar-tensor gravity

Analytic extensions of Starobinsky model of inflation

We study several extensions of the Starobinsky model of inflation, which obey all observational constraints on the inflationary parameters, by demanding that both the inflaton scalar potential in the Einstein frame and the F(R) gravity function in the Jordan frame have the explicit dependence upon fields and parameters in terms of elementary functions. Our models are continuously connected to the original Starobinsky model via changing the parameters. We modify the Starobinsky (R + R 2) model by adding an R 3-term, an R 4-term, and an R 3/2-term, respectively, and calculate the scalar potentials, the inflationary observables and the allowed limits on the deformation parameters by using the latest observational bounds. We find that the tensor-to-scalar ratio in the Starobinsky model modified by the R 3/2-term significantly increases with raising the parameter in front of that term. On the other side, we deform the scalar potential of the Starobinsky model in the Einstein frame in powers of y = exp(-(2/3)φ/M Pl), where φ is the canonical inflaton (scalaron) field, calculate the corresponding F(R) gravity functions in the two new cases, and find the restrictions on the deformation parameters in the lowest orders with respect to the variable y that is physically small during slow-roll inflation

Minimal Starobinsky supergravity coupled to a dilaton-axion superfield

The minimal Starobinsky supergravity with inflaton (scalaron) and goldstino in a massive vector supermultiplet is coupled to the dilaton-axion chiral superfield with the no-scale Kahler potential and a superpotential. The Kachru-Kallosh-Linde-Trivedi-type superpotential with a constant term is used to stabilize dilaton and axion during inflation, but it is shown to lead to an instability. The instability is cured by adding the alternative Fayet-Iliopoulos (FI) term that does not lead to the gauged R symmetry. Other stabilization mechanisms, based on the Wess-Zumino-type superpotential, are also studied in the presence of the FI term. A possible connection to the D3-brane models is briefly discussed too