Jordan and Einstein Frames Hamiltonian Analysis for FLRW Brans-Dicke Theory

We analyze the Hamiltonian equivalence between Jordan and Einstein frames considering a mini-superspace model of the flat Friedmann–Lemaître–Robertson–Walker (FLRW) Universe in the Brans–Dicke theory. Hamiltonian equations of motion are derived in the Jordan, Einstein, and anti-gravity (or anti-Newtonian) frames. We show that, when applying the Weyl (conformal) transformations to the equations of motion in the Einstein frame, we did not obtain the equations of motion in the Jordan frame. Vice-versa, we re-obtain the equations of motion in the Jordan frame by applying the anti-gravity inverse transformation to the equations of motion in the anti-gravity frame.

f(R) dual theories of quintessence: expansion-collapse duality

The accelerated expansion of the universe demands presence of an exotic matter, namely the dark energy. Though the cosmological constant fits this role very well, a scalar field minimally coupled to gravity, or quintessence, can also be considered as a viable alternative for the cosmological constant. We study f(R) gravity models which can lead to an effective description of dark energy implemented by quintessence fields in Einstein gravity, using the Einstein frame-Jordan frame duality. For a family of viable quintessence models, the reconstruction of the f(R) function in the Jordan frame consists of two parts. We first obtain a perturbative solution of f(R) in the Jordan frame, applicable near the present epoch. Second, we obtain an asymptotic solution for f(R), consistent with the late time limit of the Einstein frame if the quintessence field drives the universe. We show that for certain class of viable quintessence models, the Jordan frame universe grows to a maximum finite size, after which it begins to collapse back. Thus, there is a possibility that in the late time limit where the Einstein frame universe continues to expand, the Jordan frame universe collapses. The condition for this expansion-collapse duality is then generalized to time varying equations of state models, taking into account the presence of non-relativistic matter or any other component in the Einstein frame universe. This mapping between an expanding geometry and a collapsing geometry at the field equation level may have interesting potential implications on the growth of perturbations therein at late times.

Kalb-Ramond backgrounds in α′-complete cosmology

We study the matter-coupled equations of motion for cosmological NS massless fields including all α′ corrections in an O(d, d) duality invariant approach, with emphasis on the Kalb-Ramond two-form field B(2) and its source. Solutions for the vacuum and matter cases are found and the corresponding Einstein frame cosmologies are discussed. We also show that the ansatz for B(2) required by the duality invariant framework implies that the two-form is non-isotropic.

Cosmology at the top of the α′ tower

The cosmology of the fully α′-corrected duality-invariant action for the Neveu-Schwarz sector of string theory is revisited, with special emphasis on its coupling to matter sources. The role of the duality covariant pressure and dilatonic charge of the matter sector is explored in various contexts, from the low-curvature regime to non-perturbative solutions in α′. We comment on how an infinite tower of α′ corrections allows for fixed-dilaton de Sitter solutions, even in vacuum. We further investigate the necessary conditions for accelerated expansion in the Einstein frame, as well as for non-singular bounces that could resolve the big bang singularity. In particular, explicit examples are constructed, which show that the tower of α′ corrections may support an Einstein-frame non-singular cosmological bouncing background, even when the matter sector respects the null energy condition.

Renormalization group equations of Higgs-R2 inflation

We derive one- and two-loop renormalization group equations (RGEs) of Higgs-R2 inflation. This model has a non-minimal coupling between the Higgs and the Ricci scalar and a Ricci scalar squared term on top of the standard model. The RGEs derived in this paper are valid as long as the energy scale of interest (in the Einstein frame) is below the Planck scale. We also discuss implications to the inflationary predictions and the electroweak vacuum metastability.

Higgs potential from Weyl conformal gravity

We consider Weyl’s conformal gravity coupled to a complex matter field in Weyl geometry. It is shown that a Higgs potential naturally arises from a [Formula: see text] term in moving from the Jordan frame to the Einstein frame. A massless Nambu–Goldstone boson, which stems from spontaneous symmetry breakdown of the Weyl gauge invariance, is absorbed into the Weyl gauge field, thereby the gauge field becoming massive. We present a model where the gravitational interaction generates a Higgs potential whose form is a perfect square. Finally, we show that a theory in the Jordan frame is gauge-equivalent to the corresponding theory in the Einstein frame via the BRST formalism.

Dynamically Generated Inflationary ΛCDM

Our primary objective is to construct a plausible, unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, wherein all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the formalism of non-Riemannian spacetime volume-elements. The non-Riemannian volume element in the initial scalar field action leads to a hidden, nonlinear Noether symmetry which produces an energy-momentum tensor identified as the sum of a dynamically generated cosmological constant and dust-like dark matter. The non-Riemannian volume-element in the initial Einstein–Hilbert action upon passage to the physical Einstein-frame creates, dynamically, a second scalar field with a non-trivial inflationary potential and with an additional interaction with the dynamically generated dark matter. The resulting Einstein-frame action describes a fully dynamically generated inflationary model coupled to dark matter. Numerical results for observables such as the scalar power spectral index and the tensor-to-scalar ratio conform to the latest 2018 PLANCK data.

Dynamically Generated Inflationary Lambda-CDM

Our primary objective is to construct a plausible unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, where all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the formalism of non-Riemannian spacetime volume-elements. The non-Riemannian volume element in the initial scalar field action leads to a hidden nonlinear Noether symmetry which produces energy-momentum tensor identified as a sum of a dynamically generated cosmological constant and a dust-like dark matter. The non-Riemannian volume-element in the initial Einstein-Hilbert action upon passage to the physical Einstein-frame creates dynamically a second scalar field with a non-trivial inflationary potential and with an additional interaction with the dynamically generated dark matter. The resulting Einstein-frame action describes a fully dynamically generated inflationary model coupled to dark matter. Numerical results for observables such as the scalar power spectral index and the tensor-to-scalar ratio conform to the latest 2018 PLANCK data.

Quasi-normal modes of static spherically symmetric black holes in f(R) theory

We study the quasi-normal modes (QNMs) of static, spherically symmetric black holes in f(R) theories. We show how these modes in theories with non-trivial f(R) are fundamentally different from those in general relativity. In the special case of $$f(R) = \alpha R^2$$f(R)=αR2 theories, it has been recently argued that iso-spectrality between scalar and vector modes breaks down. Here, we show that such a break down is quite general across all f(R) theories, as long as they satisfy $$f''(0)/(1+f''(0)) \ne 0$$f′′(0)/(1+f′′(0))≠0, where a prime denotes derivative of the function with respect to its argument. We specifically discuss the origin of the breaking of isospectrality. We also show that along with this breaking the QNMs receive a correction that arises when $$f''(0)/(1+f'(0)) \ne 0$$f′′(0)/(1+f′(0))≠0 owing to the inhomogeneous term that it introduces in the mode equation. We discuss how these differences affect the “ringdown” phase of binary black hole mergers and the possibility of constraining f(R) models with gravitational-wave observations. We also find that even though the iso-spectrality is broken in f(R) theories, in general, nevertheless in the corresponding scalar-tensor theories in the Einstein frame it is unbroken.