Refined swampland conjecture in deformed Starobinsky gravity

Journal of High Energy Physics, 2015

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form R 2(1−α) , with R the Ricci scalar and α a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes. We also suggest natural microscopic (non) gravitational sources of these corrections and demonstrate that they lead generally to a nonzero and positive α. Furthermore we argue, that within this framework, the tensor modes probe theories of grand unification with a large scalar field content.

Physical Review D

The goal of this work on mathematical cosmology and geometric methods in modifed gravity theories, MGTs, is to investigate Starobinsky-like infation 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 inhomogeneous and locally anisotropic gravitational and matter field effective QC mixed continuous and discrete "ether" can be modeled by exact cosmological solutions in MGTs and Einstein gravity. The coeffcients 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.

We study a single-fluid component in a flat like universe (FLU) governed by f (T ) gravity theories, where T is the teleparallel torsion scalar. The FLU model, regardless of the value of the spatial curvature k, identifies a special class of f (T ) gravity theories. Remarkably, FLU f (T ) gravity does not reduce to teleparallel gravity theory. In large Hubble spacetime the theory is consistent with the inflationary universe scenario and respects the conservation principle. The equation of state evolves similarly in all models k = 0, ±1. We study the case when the torsion tensor consists of a scalar field, which enables to derive a quintessence potential from the obtained f (T ) gravity theory. The potential produces Starobinsky-like model naturally without using a conformal transformation, with higher orders continuously interpolate between Starobinsky and quadratic inflation models. The slow-roll analysis shows double solutions, so that for a single value of the scalar tilt (spectral index) n s the theory can predict double tensor-to-scalar ratios r of E-mode and B-mode polarizations.

Fortschritte der Physik

An alternative refined de Sitter conjecture giving rise to a natural combination of the first and second derivatives of the scalar potential was proposed recently by David Andriot and Christoph Roupec (Fortsch. Phys. 67 (2019) no.1-2, 1800105). In this work, we study the inflation models in a general scalar-tensor theory with exponential and hyperbolic tangent forms of potential as well as model with quantum corrected potential and examine whether these three models of inflation can satisfy this further refining de Sitter swampland conjecture or not. Regarding our analysis with proper choices of parameters with proper choices of parameters a, b = 1 − a and q, we find that these three inflationary models can always satisfy this new refined swampland conjecture. Therefore, all three inflationary models might all be in "landscape" since the "further refining de Sitter swampland conjecture" is satisfied.

We discuss the instabilities appearing in the cosmological model with a quasi de Sitter phase following from a fourth-order gravity theory. Both the classical equation as well as the quantization in form of a Wheeler -De Witt equation are conformally related to the analogous model with Einstein's theory of gravity with a minimally coupled scalar field. Results are: 1. In the non-tachyonic case, classical fourth-order gravity is not more unstable than Einstein's theory itself. 2. The well-known classically valid conformal relation is also (at least for some typical cases) valid on the level of the corresponding Wheeler -De Witt equations, which turns out to be a non-trivial statement.

arXiv (Cornell University), 2018

Starobinsky has suggested an inflation model which is obtained from the vacuum Einstein's equations modified by the one-loop corrections due to quantized matter fields. Although the one-loop gravitational action is not known for a general FRW background, it can be obtained in a de Sitter space to give M 2 p R+αR 2 +βR 2 ln(R/M 2). Thus, one needs to investigate the inflationary behavior of this model compared to the Starobinsky model (i.e. β = 0). The coefficient α can be changed by varying the renormalization scale M 2 and β is obtained from the quantum anomaly which is related to the numbers of quantum fields. It has been assumed that α β. We investigate the viable values of α and β based on the CMB observation. We also scrutinize the reheating process in this model.

Journal of Cosmology and Astroparticle Physics

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.

Journal of Cosmology and Astroparticle Physics, 2017

We consider the classical energy conditions (strong, null and weak) in Starobinsky supergravity theories. We study in detail the simplest Starobinsky supergravity model in the "old-minimal" supergravity setup and find examples of violations of each energy condition for a certain range of the parameters due to extra scalar d.o.f. present in supergravity. We find the null and weak energy conditions to be preserved and the strong energy condition to be violated in the physically relevant examples such as inflation and dark energy.