In an attempt to generalize general relativity, we propose a new Hermitian theory of gravity. Space-time is generalized to space-time-momentum-energy and both the principles of general covariance and equivalence are extended. The theory is endowed with a Hermitian metric on a complex manifold. The Hermitian metric contains, apart from the symmetric metric, an anti-symmetric part, which describes dynamical torsion. The causality structure is changed in a way such that there is a minimal time for events to be in causal contact and a maximal radius for a non-local instantaneous causally related volume. The speed of light can exceed the conventional speed of light in non-inertial frames and accelerations are bounded. We have indications that the theory of Hermitian gravity yields general relativity at large scales and a theory equivalent to general relativity at very small scales, where the momenta and energies are very large. As an example, we study cosmology in Hermitian gravity, where matter is described by two scalar fields. While at late times Hermitian gravity reproduces the standard cosmological FLRW models, at early times it differs significantly: quite generically the Universe of Hermitian cosmology exhibits a bounce where a maximal expansion rate (Ricci curvature) is attained. Moreover, we prove that no cosmological constant is permitted at the classical level within our model of Hermitian cosmology.
Recently, Wang with Stankiewicz (Phys. Lett. B 800 (2020) 135106) opposed the widespread belief that due to quantization, the Big Bang singularity {\em must} necessarily get smeared and replaced by a non-singular "Big Bounce" process. Their claim is supported in a methodically independent manner in which just a highly schematic model (viz., the discrete and drastically simplified Wheeler-DeWitt equation) is considered. Our comparatively elementary argumentation is constructive, based on the assumption that the evolution of the Universe can fully consistently be described using an innovative, h…
Motivated by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with PT symmetry, we show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. The model is based on a classical complex Lagrangian of a scalar field. Specific symmetry properties analogous to PT in non-Hermitian quantum mechanics lead to purely real equation of motion.
Einstein-Strauss Hermitian gravity was recently formulated as a gauge theory where the tangent group is taken to be the pseudo-unitary group instead of the orthogonal group. A Higgs mechanism for massive gravity was also formulated. We generalize this construction to obtain massive Hermitian gravity with the use of a complex Higgs multiplet. We show that both the graviton and antisymmetric tensor acquire the same mass. At the linearized level, the theory is ghost free around Minkowski background and describes a massive graviton with five degrees of freedom and an antisymmetric field with three…
A class of Modified Gravity Models, consisting of inverse powers of linear combination of quadratic curvature invariants, is studied in the full parameter space. We find that singularity-free cosmological solutions, interpolating between an almost-Friedmann universe at Big Bang Nucleosynthesis and an accelerating universe today, exist only in a restricted parameter space. Furthermore, for all parameters of the models, there is an unstable scalar mode of the gravitational field. Therefore we conclude that this class of Modified Gravity Models is not viable.
We review some works of E M Lifshitz connected with gravity and cosmology and also some later works, connected with his ideas. The main topics of this review are the stochastic cosmology of an anisotropic universe and of an isotropic universe with the scalar field, the quasi-isotropic (gradient) expansion in cosmology and Horava-Lifshitz gravity and cosmology.
In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate the conditions that subsequently lead to slow-roll inflation. The consequences for this mechanism of various quantization ambiguities arising within loop quantum cosmology are considered. For the case of a quadratic potential, it is found that some quantization procedures are more likely to generate a phase of slow--roll inflation. In general, however, loop quantum cosmology is robust to ambiguities…
We explore cosmology of intersecting braneworlds with induced gravity on the branes. We find the cosmological equations that control the evolution of a moving codimension one brane and a codimension two brane that sits at the intersection. We study the Friedmann equation at the intersection, finding new contributions from the six dimensional bulk. These higher dimensional contributions allow us to find new examples of self-accelerating configurations for the codimension two brane at the intersection and we discuss their features.
We develop the general scheme for modified $f(R)$ gravity reconstruction from any realistic FRW cosmology. We formulate several versions of modified gravity compatible with Solar System tests where the following sequence of cosmological epochs occurs: a. matter dominated phase (with or without usual matter), transition from decceleration to acceleration, accelerating epoch consistent with recent WMAP data b. $Λ$CDM cosmology without cosmological constant. As a rule, such modified gravities are expressed implicitly (in terms of special functions) with late-time asymptotics of known type (for in…
Dimensional reductions of various higher dimensional (super)gravity theories lead to effectively two-dimensional field theories described by gravity coupled G/H nonlinear sigma-models. We show that a new set of complexified variables can be introduced when G/H is a Hermitian symmetric space. This generalizes an earlier construction that grew out of the Ashtekar formulation of two Killing vector reduced pure 4d general relativity. Apart from giving some new insights into dimensional reductions of higher dimensional (super)gravity theories, these Ashtekar-type variables offer several technical a…
We consider the cosmology of a brane-world scenario in the framework of teleparallel and $f(T)$ gravity in a way that matter is localized on the brane. We show that the cosmology of such branes is different from the standard cosmology in teleparallelism. In particular, we obtain a class of new solutions with a constant five-dimensional radius and cosmologically evolving brane in the context of constant torsion $f(T)$ gravity.
We argue that more cosmological solutions in massive gravity can be obtained if the metric tensor and the tensor $Σ_{μν}$ defined by Stückelberg fields take the homogeneous and isotropic form. The standard cosmology with matter and radiation dominations in the past can be recovered and $Λ$CDM model is easily obtained. The dynamical evolution of the universe is modified at very early times.
The general properties of the gravity wave backgrounds of cosmological origin are reviewed and briefly discussed, with emphasis on the relic background expected from an early pre-big bang phase typical of string cosmology models.
The Friedmann equations for a brane with induced gravity are analyzed and compared with the standard general relativity and Randall-Sundrum cases. Randall-Sundrum gravity modified the early universe dynamics, whereas induced gravity changes the late universe evolution. The early and late time limits are investigated. Induced gravity effects can contribute to late-universe acceleration. This conditions for this are found. Qualitative analysis is given for a range of scalar field potentials.
New Developments in String Gravity and String Cosmology are reported: 1-String driven cosmology and its Predictions. 2-The primordial gravitational wave background in string cosmology. 3-Non-singular string cosmologies from Exact Conformal Field Theories. 4-Quantum Field Theory, String Temperature and the String Phase of de Sitter space-time, 5-Hawking Radiation in String Theory and the String Phase of Black Holes. 6-New Dual Relation between Quantum Field Theory regimes and String regimes in Curved Backgrounds, and the 'QFT/String Tango'. 7- New Coherent String States and Minimal Uncertainty …
In this paper, we analyze the modified $f(\mathcal{R})$ gravity models in Friedmann--Lema\^ıtre--Robertson--Walker (FLRW) background. The actions of bouncing cosmology are studied under consideration of different viable models in $f(\mathcal{R})$ gravity theory that can resolve the difficulty of singularity in standard Big-Bang cosmology. Under different viable models in $f(\mathcal{R})$ gravity theory, the cosmological constraints are plotted in provisions of cosmic-time, then investigated the bounce circumstance. In addition, the red-shift parameter is used to reconstruct the modified gravit…
We introduce the Brans-Dick de Rham-Gabadadze-Tolley massive gravity theory which is the new extension of nonlinear massive gravity. We demonstrate a detailed study of the cosmological properties of this theory of gravity, and we show the transformation of the Jordan frame to the Einstein frame. We obtain the cosmological background equations and show the analyses of self-accelerating solutions for explaining the accelerated expansion of the Universe. In the following, we analyze the background perturbations, which consist of tensor, vector, and scalar perturbations within the framework of the…
We study the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology in the Weyl-transverse (WTDiff) gravity in a general space-time dimension. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeormorphisms (transverse diffeomorphisms) and is believed to be equivalent to general relativity at least at the classical level (perhaps, even in the quantum regime). It is explicitly shown by solving the equations of motion that the FLRW metric is a classical solution in the WTDiff gravity only when the spatial metric is flat, that is, the …
This talk describes the evolution of studies of chaos in Yang-Mills fields, gravity, and cosmology. The main subject is a BKL regime near the singularity $t=0$ and its survival in higher dimensions and in string theory. We also describe the recent progress in the search for particle-like solutions of the Einstein-Yang-Mills system (monopoles and dyons), colored black holes and the problem of their stability.
In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in solving other problems. The purpose of this work is to give an introduction both to the Hamiltonian formalism and to the cosmology of bigravity. We sketch three roads to the Hamiltonian of bigravity with the dRGT potential: the metric, the tetrad and the minisuperspace approaches.
We explore the cosmological consequences of Modified Gravity (MOG), and find that it provides, using a minimal number of parameters, good fits to data, including CMB temperature anisotropy, galaxy power spectrum, and supernova luminosity-distance observations without exotic dark matter. MOG predicts a bouncing cosmology with a vacuum energy term that yields accelerating expansion and an age of ~13 billion years.
I review some aspects of non-critical strings in connection with Lorentz-Invariance violating approaches to quantum gravity. I also argue how non-critical strings may provide a unifying framework where string Cosmology and quantum gravity may be tackled together.
We construct the gauge invariant potentials of Hermitian Gravity and derive the linearized equations of motion they obey. A comparison reveals a striking similarity to the Bardeen potentials of general relativity. We then consider the response to a point particle source, and discuss in what sense the solutions of Hermitian Gravity reduce to the Newtonian potentials. In a rather intriguing way, the Hermitian Gravity solutions exhibit a generalized reciprocity symmetry originally proposed by Born in the 1930s. Finally, we consider the trajectories of massive and massless particles under the infl…
As massive gravity and its extensions offer physically well-defined gravitational theories with a nonzero graviton mass, we present a new extension of the de Rham-Gabadadze-Tolley (dRGT)massive gravity, which is tachyonic massive gravity theory. We firstly introduce the new extension of the dRGT massive gravity, constructed by adding a tachyonic term. We then find the cosmological background equations, and present the analysis of self-accelerating solutions. We examine the tensor perturbations to calculate the dispersion relation of gravitational waves (GWs). In a special case, we consider a c…
We apply quantum gravitational results to spatially unbounded Friedmann universes and try to answer some questions related to dark energy, dark matter, inflation and the missing antimatter.
We study late-time cosmic accelerating dynamics from Born-Infeld-$f(R)$ gravity in a simplified conformal approach. We find that a variety of cosmic efects such as Little Rip, $Λ$CDM universe and dark energy cosmology with finite-time future singularities may occur. Unlike the convenient Born-Infeld gravity where in the absence of matter only de Sitter expansion may emerge, apparentlly any FRW cosmology maybe reconstructed from this conformal version of the Born-Infeld-$f(R)$ theory. Despite the fact that the explicit form of $f(R)$ is fixed by the conformal ansatz, the relation between the tw…
A global O$(2,2)$ symmetry is found in the Brans-Dicke theory of gravity when the dilaton is coupled to axion and moduli fields. The symmetry is broken if a cosmological constant is introduced. Within the class of spatially homogeneous Bianchi cosmologies, only the type I and V models respect the symmetry. Isotropic cosmological solutions are found for arbitrary spatial curvature. In the region of parameter space relevant to the pre-big bang scenario, the interplay between the scalar fields results in a bouncing cosmology.
We propose a modification of Einstein-Cartan gravity equations. The modified cosmology departs from the standard model of cosmology for small Hubble parameter. A characteristic Hubble scale h0, which is intrinsically related to cosmological constant, marks the boundary between the validity domains of the standard model of cosmology and modified cosmology. For large Hubble parameter, the standard model of cosmology is restored. In the opposite limit of small Hubble parameter, which is the case for present epoch, Lorentz-violating effects would manifest themselves. One of the implications is tha…
In this paper, we study $F(R)$ gravity by Hu-Sawicki model in Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) background. The Friedmann equations are calculated by modified gravity action, and then the obtained Friedmann equations are written in terms of standard Friedmann equations. Next behavior of bouncing cosmology is investigated in the modified gravity model, i.e., this behavior can solve problem of non-singular in standard Big Bang cosmology. We plot the cosmological parameters in terms of cosmic time and then bouncing condition is investigated. In what follows, we reconstruct the modified…
The Averaging problem in general relativity and cosmology is discussed. The approach of macroscopic gravity to resolve the problem is presented. An exact cosmological solution to the equations of macroscopic gravity is given and its properties are discussed. Contents: 1. Introduction to General Relativity 2. General Relativity -> Relativistic Cosmology 3. Introduction to Relativistic Cosmology 4. Relativistic Cosmology -> Mathematical Cosmology 5. Averaging Problem in Relativistic Cosmology 6. History of the Averaging Problem 7. Averaging and FLRW Cosmologies 8. Averaging Problem in General Re…
We present a new cosmological model derived from Loop Quantum Gravity. The formulation is based on a projection of the kinematical Hilbert space of the full theory down to a subspace representing the proper arena for an inhomogeneous Bianchi I model. This procedure gives a direct link between the full theory and its cosmological sector. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could also shed light on Loop Quantum Cosmology and its relation with the full theory.
We review inflationary cosmology in modified gravity such as $R^2$ gravity with its extensions in order to generalize the Starobinsky inflation model. In particular, we explore inflation realized by three kinds of effects: modification of gravity, the quantum anomaly, and the $R^2$ term in loop quantum cosmology. It is explicitly demonstrated that in these inflationary models, the spectral index of scalar modes of the density perturbations and the tensor-to-scalar ratio can be consistent with the Planck results. Bounce cosmology in $F(R)$ gravity is also explained.
We study inflationary cosmology and the late-time accelerated expansion of the universe in non-minimal Yang-Mills (YM) theory, in which the YM field couples to a function of the scalar curvature. It is shown that power-law inflation can be realized due to the non-minimal YM field-gravitational coupling which maybe caused by quantum corrections. Moreover, it is demonstrated that both inflation and the late-time accelerated expansion of the universe can be realized in a modified YM-$F(R)$ gravity which is consistent with solar system tests. Furthermore, it is shown that this result can be realiz…
We apply the Noether Symmetry Approach to point-like teleparallel Lagrangians in view to derive minisuperspaces suitable for Quantum Cosmology. Adopting the Arnowitt-Deser-Misner formalism, we find out related Wave Functions of the Universe. Specifically, by means of appropriate changes of variables suggested by the existence of Noether symmetries, it is possible to obtain the cosmological Hamiltonians whose solutions are classical trajectories interpretable as observable universes.
We develop a Gauss-Bonnet extension of Loop Quantum Cosmology, by introducing holonomy corrections in modified $F(\mathcal{G})$ theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of Loop Quantum Gravity theories, and we result in having leading order corrections to the classical $F(\mathcal{G})$ theories of gravity. After extensively discussing the formalism, we present a reconstruction method that makes possible to find the Loop Quantum Cosmology corrected $F(\mathcal{G})$ theory that can realize va…
Guided by a linearized approximation to Einstein theory, an interim prescription for ``weak source of gravity'' - - in ``particle'' energy-momentum distributed along standpoint light cone - - is formulated for (classical) standpoint cosmology.
We study cosmological evolutions of the generalized model of nonlinear massive gravity in which the graviton mass is given by a rolling scalar field and is varying along time. By performing dynamical analysis, we derive the critical points of this system and study their stabilities. These critical points can be classified into two categories depending on whether they are identical with the traditional ones obtained in General Relativity. We discuss the cosmological implication of relevant critical points.
In this paper, we will study the rainbow deformation of the FRW cosmology in both Einstein gravity and Gauss-Bonnet gravity. We will demonstrate that the singularity in the FRW cosmology can be removed because of the rainbow deformation of the FRW metric. We will obtain the general constraints required for the FRW cosmology to be free from singularities. It will be observed that the inclusion of Gauss-Bonnet gravity can significantly change the constraints required to obtain a nonsingular universes. We will use a rainbow functions motivated from the hard spectra of gamma-ray bursts to deform t…
We study the cosmology of a quadratic metric-compatible torsionful gravity theory in the presence of a perfect hyperfluid. The gravitational action is an extension of the Einstein-Cartan theory given by the usual Einstein-Hilbert contribution plus all the admitted quadratic parity even torsion scalars and the matter action also exhibits a dependence on the connection. The equations of motion are obtained by regarding the metric and the metric-compatible torsionful connection as independent variables. We then consider a Friedmann-Lemaître-Robertson-Walker background, analyze the conservation la…
We consider a DGP brane scenario where a scalar field is present on the brane through the introduction of a scalar potential, itself motivated by the notion of modified gravity. This theory predicts that the mass appearing in the gravitational potential is modified by the addition of the mass of the scalar field. The cosmological implications that such a scenario entails are examined and shown to be consistent with a universe expanding with power-law acceleration.
A quantum cosmology in teleparallel gravity is presented in this article. Teleparallel gravity is used to perform such an analysis once in General Relativity (GR) the concept of gravitational energy is misleading preventing the establishment of a concise quantum cosmology. The Wheeler-DeWitt like equation is obtained using the Weyl quantization and the teleparallel expression of energy.
Despite many nice properties and numerous achievements, general relativity is not a complete theory. One of actual approaches towards more complete theory of gravity is its nonlocal modification. We present here a brief review of nonlocal gravity with its cosmological solutions. In particular, we pay special attention to two nonlocal models and their nonsingular bounce solutions for the cosmic scale factor.
The search for a consistent and empirically established quantum theory of gravity is among the biggest open problems of fundamental physics. The obstacles are of formal and of conceptual nature. Here, I address the main conceptual problems, discuss their present status and outline further directions of research. For this purpose, the main current approaches to quantum gravity are briefly reviewed and compared.
Recently, Kenna-Allison et.al. claimed that bimetric gravity cannot give rise to a viable cosmological expansion history while at the same time being compatible with local gravity tests. In this note we review that claim and combine various results from the literature to provide several simple counter examples. We conclude that the results of Kenna-Allison et.al. cannot hold in general.
Flat Space Cosmology (FSC) spacetimes are exact solutions of 3D gravity theories. In this work, we study phase transition between FSC spacetimes and Hot Flat Spacetimes (HFS) in general minimal massive gravity and exotic general massive gravity. We show that similar to topological massive gravity the tunneling occurs between two spacetimes by comparing their free energies. We also obtain the corrections to the Bekenstein-Hawking entropy, and its effect on the phase transition is studied.
We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to determine the connection coefficients from a geometric Lagrangian that is an arbitrary function of the generalized Ricci curvature tensor and of other fundamental tensors. Such a theory supplements the standard Einstein gravity with dark energy (the cosmological constant, in the first approximation), a neutral massive (or tachyonic) vector field vecton, and mass…
It has been shown that anisotropy of homogeneous spacetime described by the general Kasner metric can be damped by quantum fluctuations coming from perturbative quantum gravity in one-loop approximation. Also, a formal argument, not limited to one-loop approximation, is put forward in favor of stability of isotropy in the exactly isotropic case.
In this review we discuss the connection between two seemingly disparate topics, macroscopic gravity on astrophysical scales and Hamiltonians that are not Hermitian but $PT$ symmetric on microscopic ones. In particular we show that the quantum-mechanical unitarity problem of the fourth-order derivative conformal gravity theory is resolved by recognizing that the scalar product appropriate to the theory is not the Dirac norm associated with a Hermitian Hamiltonian but is instead the norm associated with a non-Hermitian but $PT$-symmetric Hamiltonian. Moreover, the fourth-order theory Hamiltonia…
The exact renormalization group flow equations for gravity lead to quantum corrections of Newton's constant and cosmological constant. Using this we investigate the Bianchi-I cosmological model at late times. In particular, we obtain the scale factors in different directions, and observe that they eventually evolve into Friedmann-Lemaître-Robertson-Walker (FLRW) universe for radiation. However, for stiff matter the universe shows a Kasner like behaviour. The presentation is based on our work published in \cite{Mandal:2019xlg}.
We develop a technique for the reconstruction of the potential for a scalar field in cosmological models based on induced gravity. The potentials reproducing cosmological evolutions driven by barotropic perfect fluids, a cosmological constant, a Chaplygin gas and a modified Chaplygin gas are constructed explicitly.
This work deals with $F(T)$ gravity models driven by real scalar fields with usual and phantom dynamics. We illustrate the results with examples of current interest, and we find some analytical solutions for scale factors and scalar fields. The results indicate that torsion-scalar models also admit the accelerated expansion of the universe.
We study a scalar-tensor cosmological model where the Einstein tensor is non-minimally coupled to the free scalar field dynamics. Using FRW metric, we investigate the behavior of scale factor for vacuum, matter and dark energy dominated eras. Especially, we focus on the inflationary behavior at early universe. Moreover, we study the perturbation analysis of this model in order to confront the inflation under consideration with the observational results.
We discuss the cosmology of recently proposed Horava-Lifshitz f(R) gravity. In particular, we derive the modified Hubble equation that reduces to the standard HL gravity case in appropriate limit. We show how the bounce solutions in this theory are modified due to nonlinear effect of f(R) gravity. We also show that in principle, the Universe in this set-up can show cyclic behavior.
A short review of recent results on exact solutions in multidimensional cosmology and overview of reports at workshop in MG8 (held by the author) are presented.
We propose a new phenomenological model for quantum gravity. This is based on a new interpretation in which quantum gravity is not an interaction, rather it is just responsible for generation of space-time-matter. Then we show this model is capable of solving the important problems of cosmology and particle physics.
The study of cosmological perturbation theory in $f(T)$ gravity is a topic of great interest in teleparallel gravity since this is one of the simplest generalizations of the theory that modifies the teleparallel equivalent of general relativity. In this work, we explore the possibility of a non-flat FLRW background solution and perform perturbations for positively as well as negatively curved spatial geometries, together with a comparison to the flat case. We determine the generalized behaviour of the perturbative modes for this non-flat FLRW setting for arbitrary $f(T)$ models, when the most …
