Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second- and higher-order because perturbative modes are sourced by products of lower-oder modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second-order. We perform much of our analysis using an index-free `vector-calculus' approach which makes manipulating tensor equations considerably simpler.
We discuss how to extract information about the cosmological constant from the Wheeler-DeWitt equation, considered as an eigenvalue of a Sturm-Liouville problem. A generalization to a f(R)theory is taken under examination. The equation is approximated to one loop with the help of a variational approach with Gaussian trial wave functionals. We use a zeta function regularization to handle with divergences. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.
We show that the evolution of interacting massive particles in the de Sitter bulk can be understood at leading order as a series of resonant decay and production events. From this perspective, we classify the cosmological collider signals into local and nonlocal categories with drastically different physical origins. This further allows us to derive a cutting rule for efficiently extracting these cosmological collider signals in an analytical fashion. Our cutting rule is a practical way for extracting cosmological collider signals in model building, and can be readily implemented as symbolic c…
We employ a theorem due to Campbell to build some simple 4-dimensional cosmological models which originate from solutions describing waves propagating along the extra-dimension of a 5-dimensional Ricci-flat space. The dimensional reduction is performed in the Jordan frame according to the induced-matter theory of Wesson.
We study the locally rotational symmetry Bianchi type-I dark energy model in the framework of $f(T)$ theory of gravity, where $T$ denotes the torsion scalar. A viable cosmological model is undertaken and the isotropization of this latter is checked, yielding a result that reflects the real evolution of our universe. Moreover, still in the anisotropic optic, a more complicated $f(T)$ model is obtained from the cosmological reconstruction scheme and the analysis shows that the universe is more anisotropic at the beginning if the terms of higher order in $T$ are not considered. This means that th…
The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is empty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of matter models treated includes perfect fluids, mixtures of non-interacting perfect fluids and collisionless matt…
We consider the problem of extracting physical predictions from the wave function of the universe in quantum cosmological models. We state the features of quantum cosmology an interpretational scheme should confront. We discuss the Everett interpretation, and extensions of it, and their application to quantum cosmology. We review the steps that are normally taken in the process of extracting predictions from solutions to the Wheeler-DeWitt equation for quantum cosmological models. Some difficulties and their possible resolution are discussed. We conclude that the usual wave function-based appr…
It has been recently shown that magnetic reconnection can provide us a novel mechanism to extract black hole rotational energy from a Kerr black holes. In this paper, we study the energy extraction from the Kerr-de Sitter black hole via this magnetic reconnection process. The result shows that, with the increase of the cosmological constant, a slowly spinning Kerr-de Sitter black hole can implement the energy extraction better than its Kerr counterpart. Interestingly, although the numerical results show that the maximum values of the power and efficiency slightly decrease with the cosmological…
We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially {\it closed} inhomogeneous cosmological models. The models, called the {\it locally U(1)$\times$U(1) symmetric models} (or the {\it generalized Gowdy models}), are characterized by the existence of two commuting spatial {\it local} Killing vectors. For systematic investigations we first present a classification of possible spatial topologies in this class. We stress the significance of the locally homogeneous limits (i.e., the Bianchi types or the `geometric structures') of the models. In par…
A cosmic string wake produces a distinct non-Gaussian signal in 21-cm intensity maps at redshifts above that of reionization. While the string signal is (locally) larger in amplitude than the signal of the Gaussian fluctuations of the $Λ$CDM model, they are overwhelmed (even locally in position space) by astrophysical and instrumental foregrounds. Here, we study to what extent the signal can be extracted from noisy interferometric data. The narrowness of the string-induced feature in redshift direction allows for a subtraction of astrophysical and instrumental foregrounds. Based on the specifi…
Modern cosmology relies on the assumption of large-scale isotropy and homogeneity of the Universe. However, locally the Universe is inhomogeneous and anisotropic. So, how can local measurements (at the 100 Mpc scale) be used to determine global cosmological parameters (defined at the 10 Gpc scale)? We use Buchert's averaging formalism and determine a set of locally averaged cosmological parameters in the context of the flat Lambda cold dark matter model. We calculate their ensemble means (i.e. their global values) and variances (i.e. their cosmic variances). We apply our results to typical sur…
This work is a follow-up to the paper, "Numerical Relativity as a Tool for Studying the Early Universe". In this article, we determine if cosmological gravitational waves can be accurately extracted from a dynamical spacetime using an averaging process as opposed to conventional methods of gravitational wave extraction using a complex Weyl scalar. We calculate the normalized energy density, strain and degree of polarization of gravitational waves produced by a simulated turbulent plasma similar to what was believed to have existed shortly after the electroweak scale. This calculation is comple…
Asymptotically locally AdS and asymptotically flat black hole solutions are found for a particular case of the Horndeski action. The action contains the Einstein-Hilbert term with a cosmological constant, a real scalar field with a non minimal kinetic coupling given by the Einstein tensor, the minimal kinetic coupling and the Maxwell term. There is no scalar potential. The solution has two integration constants related with the mass and the electric charge. The solution is given for all dimensions. A new class of asymptotically locally flat spherically symmetric black holes is found when the m…
A `bouncing' cosmological model is proposed in the context of a Weyl-invariant scalar-tensor (WIST) theory of gravity. In addition to being Weyl-invariant the theory is U(1)-symmetric and has a conserved global charge. The entire cosmic background evolution is accounted for by a complex scalar field that evolves in the static `comoving' frame. Its (dimensional) modulus $χ$ regulates the dynamics of masses and the apparent space expansion. Cosmological redshift is essentially due to the cosmic evolution of the Rydberg constant in the comoving frame. The temporal evolution of $χ$ is analogous to…
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the `gauge-fixing' issues and extend the analysis to scalar field models and show that our approach can be applied to any order of perturbation for any first order derivative fields. In the case of Galilean scalar fields, our procedure can extract constrained relations at all orders in perturbations leading to the fact that there is no extra degrees of freedom due to the presence of higher time derivatives of the field…
In this paper we have investigated the cosmological dynamics of non-locally corrected gravity involving a function of the inverse d'Alembertian of the Ricci scalar, $f(\Box^{-1} R))$. Casting the dynamical equations into local form, we derive the fixed points of the dynamics and demonstrate the existence and stability of a one parameter family of dark energy solutions for a simple choice, $f(\Box^{-1} R)\sim \exp(α\Box^{-1} R)$. The effective EoS parameter is given by, $w_{\rm eff}=({α-1})/({3α-1})$ and the stability of the solutions is guaranteed provided that $1/3<α<2/3$. For $1/3<α<1/2$ and…
Weyl's conformal theory of gravity is an extension of Einstein's theory of general relativity which associates metrics with 1-forms . In the case of locally integrable (closed non-exact) 1-forms the spacetime manifolds are no more simply connected. The Weil connections yield curvature tensors which satisfy the basic properties of Riemann curvature tensors. The Ricci tensors are symmetric, conformally invariant, and the Einstein tensors computed with the Weyl connections implicate a cosmological term replacing the cosmological constant by a function of spacetime, and a shear stress tensor. A to…
We analyze local anisotropies induced by anholonomic frames and associated nonlinear connections in general relativity and extensions to affine Poincare and de Sitter gauge gravity and different types of Kaluza-Klein theories. We construct some new classes of cosmological solutions of gravitational field equations describing Friedmann-Robertson-Walker like universes with rotation (ellongated and flattened) ellipsoidal or torus symmetry.
A local void in the globally Friedmann-Robertson-Walker cosmological model with the critical density ($Ω_{0}=1$) is studied. The inhomogeneity is described using a Lema\^ıtre-Tolman-Bondi solution for a spherically symmetric distribution of matter. The scale of the central underdense region is $\sim 150$ Mpc. We investigate the effects this has on the cosmological time scale, the measurement of the Hubble constant and the redshift--luminosity distance for moderately and very distant objects ($z \sim 0.1$ and more). The results indicate that if we happened to live in such a void, but insisted o…
Chameleon mechanism appearing in massive tensor-scalar theory of gravity can effectively reduce locally the non-minimal coupling between the scalar field and matter. This mechanism is invoked to reconcile large-scale departures from general relativity (GR), supposedly accounting for cosmic acceleration, to small scales stringent constraints on GR. In this paper, we carefully investigate this framework on cosmological and solar system scales to derive combined constraints on model parameters, notably by performing a non-ambiguous derivation of observables like luminosity distance and local post…
The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following: (i) There exis…
We apply the method of matched asymptotic expansions to analyse whether cosmological variations in physical `constants' and scalar fields are detectable, locally, on the surface of local gravitationally bound systems such as planets and stars, or inside virialised systems like galaxies and clusters. We assume spherical symmetry and derive a sufficient condition for the local time variation of the scalar fields that drive varying constants to track the cosmological one. We calculate a number of specific examples in detail by matching the Schwarzschild spacetime to spherically symmetric inhomoge…
We study locally spatially homogeneous solutions of the Einstein-Vlasov system with a positive cosmological constant. First the global existence of solutions of this system and the casual geodesic completeness are shown. Then the asymptotic behaviour of solutions in the future time is investigated in various aspects.
The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states of the spacetimes near the singularity or in a phase of unlimited expansion. Bianchi type II models show oscillatory behaviour near the initial singularity which is, however, simpler than that of the mixmaster model.
We show that the energy-momentum tensor of homogeneous fields of arbitrary spin in an expanding universe is always isotropic in average provided the fields remain bounded and evolve rapidly compared to the rate of expansion. An analytic expression for the average equation of state is obtained for Lagrangians with generic power-law kinetic and potential terms. As an example we consider the behavior of a spin-two field in the standard Fierz-Pauli theory of massive gravity. The results can be extended to general space-time geometries for locally inertial observers.
Following renewed interest, the problem of whether the cosmological expansion affects the dynamics of local systems is reconsidered. The cosmological correction to the equations of motion in the locally inertial Fermi normal frame (the relevant frame for astronomical observations) is computed. The evolution equations for the cosmological perturbation of the two--body problem are solved in this frame. The effect on the orbit is insignificant as are the effects on the galactic and galactic--cluster scales.
The path integral, which generates in-in correlation functions of a scalar field in a cosmological spacetime, is shown to admit nontrivial classical solutions as stationary phases. Although the solutions exist for Lorentzian signature, their contribution to the path integral is reminiscent that of the instantons in Euclidean field theories. When the scalar potential has more than one locally stable vacua, the correlation functions receive contributions from all of them via these instanton-like configurations, which is similar to tunneling. We present some explicit solutions for toy models and …
A family of exact solutions is presented which represents a rigidly rotating cylinder of dust in a background with a negative cosmological constant. The interior of the infinite cylinder is described by the Godel solution. An exact solution for the exterior solution is found which depends both on the rotation of the interior and on its radius. For values of these parameters less than a certain limit, the exterior solution is shown to be locally isomorphic to the Linet-Tian solution. For values larger than another limit, it is shown that the exterior solution extends into a region which contain…
In this paper we construct asymptotically locally AdS and flat black holes in the presence of a scalar field whose kinetic term is constructed out from a linear combination of the metric and the Einstein tensor. The field equations as well as the energy-momentum tensor are second order in the metric and the field, therefore the theory belongs to the ones defined by Horndeski. We show that in the presence of a cosmological term in the action, it is possible to have a real scalar field in the region outside the event horizon. The solutions are characterized by a single integration constant, the …
We discuss the effect of super-Hubble cosmological fluctuations on the locally measured Hubble expansion rate. We consider a large bare cosmological constant in the early universe in the presence of scalar field matter (the dominant matter component), which would lead to a scale-invariant primordial spectrum of cosmological fluctuations. Using the leading order gradient expansion we show that the expansion rate measured by a (secondary) clock field which is not comoving with the dominant matter component obtains a negative contribution from infrared fluctuations, a contribution whose absolute …
Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To this end we characterize the topological space whose points are the 3-dimensional oriented homogeneous Riemannian manifolds; locally isometric manifolds are considered as same.
We provide a simple, unified proof of Birkhoff's theorem for the vacuum and cosmological constant case, emphasizing its local nature. We discuss its implications for the maximal analytic extensions of Schwarzschild, Schwarzschild(-anti)-de Sitter and Nariai spacetimes. In particular, we note that the maximal analytic extensions of extremal and over-extremal Schwarzschild-de Sitter spacetimes exhibit no static region. Hence the common belief that Birkhoff's theorem implies staticity is false for the case of positive cosmological constant. Instead, the correct point of view is that generalized B…
This paper presents an exact solution to the long wavelength perturbations for the scalar modes and for a scalar field theory with arbitrary potential. Locally these modes are coordinate transformations of the homogeneous background solutions (although non-locally they are not). These solutions are then used to discuss a couple of recent papers in which such perturbations play a role. Abramo, Brandenberger, and Mukhanov have recently argued that long wavelength perturbations have the effect of driving the cosmological constant to zero if the higher order perturbation equation are examined. I a…
The complete theory of cosmological evolution's macroscopic description is constructed with a help of self-consistent field. The theory includes a subsystem of linear equations of perturbations' evolution and nonlinear macroscopic Einstein equations and equations of a scalar field. We provide examples of system's solution which show the principal difference of the cosmological models of the early Universe built on homogenous and locally fluctuating scalar fields. {\bf Keywords}: macroscopic gravitation, self-consistent field, cosmological model, scalar fields, averaging of local fluctuations, …
The Hubble tension cast a blight on the standard cosmology. As a possible attitude to the problem, the local variation of the expansion rate in an inhomogeneous cosmology has been proposed where the spatial averaging over a finite domain was introduced in order to construct local Friedmann spacetime. However, it is not clear that the concept of the spatial averaging itself is gauge invariant or not. Namely the conclusion obtained by the averaging in a particular gauge is physically meaningful or not. In this paper we address this question, namely the gauge invariance of the spatial averaging i…
We investigate the cosmological behavior in a universe governed by time asymmetric extensions of general relativity, which is a novel modified gravity based on the addition of new, time-asymmetric, terms on the Hamiltonian framework, in a way that the algebra of constraints and local physics remain unchanged. Nevertheless, at cosmological scales these new terms can have significant effects that can alter the universe evolution, both at early and late times, and the freedom in the choice of the involved modification function makes the scenario able to produce a huge class of cosmological behavi…
We study the effect of cosmological expansion on orbits--galactic, planetary, or atomic--subject to an inverse-square force law. We obtain the laws of motion for gravitational or electrical interactions from general relativity--in particular, we find the gravitational field of a mass distribution in an expanding universe by applying perturbation theory to the Robertson-Walker metric. Cosmological expansion induces an ($\ddot a/a) \vec r$ force where $a(t)$ is the cosmological scale factor. In a locally Newtonian framework, we show that the $(\ddot a/a) \vec r$ term represents the effect of a c…
Short distance structure of spacetime may show up in the form of high freqency dispersion. Although such dispersion is not locally Lorentz invariant, we show in a scalar field model how it can nevertheless be incorporated into a generally covariant metric theory of gravity provided the locally preferred frame is dynamical. We evaluate the resulting energy-momentum tensor and compute its expectation value for a quantum field in a thermal state. The equation of state differs at high temperatures from the usual one, but not by enough to impact the problems of a hot big bang cosmology. We show tha…
We show that there are no new consistent cosmological perfect fluid solutions when in an open neighbourhood ${\cal U}$ of an event the fluid kinematical variables and the electric and magnetic Weyl curvature are all assumed rotationally symmetric about a common spatial axis, specialising the Weyl curvature tensor to algebraic Petrov type D. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres dust models. Parts of our results require the assumption of a barotropic equation of state. Additionally we demonstrate that local rotational sy…
In this paper we derive a general solution for the most general rotating and twisting locally rotationally symmetric spacetimes. This is achieved in three steps. First we decompose the manifold via 1+1+2 semi-tetrad formalism that yields a set of geometrical and thermodynamic scalars for the spacetime. We then recast the Einstein field equations in terms of evolution and propagation of these scalars. It is then shown that this class of spacetimes must possess self similarity and we use this property to solve for these scalars, thus obtaining a general solution. This solution has a number of ve…
The present study deals with spatially homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with dominance of dark energy. To get the deterministic model of Universe, we assume that the shear scalar $(σ)$ in the model is proportional to expansion scalar $(θ)$. This condition leads to $A=B^{n}$, where $A$,\;$B$ are metric potential and $n$ is positive constant. It has been found that the anisotropic distribution of dark energy leads to the present accelerated expansion of Universe. The physical behavior of the Universe has been discussed in detail.
A modified form of non-locally corrected theory of gravity is investigated in the context of cosmology and the Newtonian limit. This form of non-local correction to classic Einstein-Hilbert action can be locally represented by a triple-scalar-tensor theory in which one of the scalar degree of freedom is phantom-like and the other two are quintessence-like. We show that there exists a stable de Sitter solution for the cosmological dynamics if a suitable form of potential function $V(ϕ)$ (or equivalently, $f(R)$) is selected. However, no matter what a potential function is selected, there is alw…
The cosmological constant $(1/2)λ_{1}ϕ_{, μ}ϕ^{, μ}/ϕ^{2}$ is introduced to the generalized scalar-tensor theory of gravitation with the coupling function $ω(ϕ)=η/(ξ-2)$ and the Machian cosmological solution satisfying $ϕ=O(ρ/ω)$ is discussed for the homogeneous and isotropic universe with a perfect fluid (with negative pressure). We require the closed model and the negative coupling function for the attractive gravitational force. The constraint $% ω(ϕ)<-3/2$ for $0\leqq ξ<2$ leads to $η>3$. If $λ_{1}<0$ and $0\leqq -η/λ_{1}<2$, the universe shows the slowly accelerating expansion. The coupli…
First order perturbations of homogeneous and hypersurface orthogonal LRS (Locally Rotationally Symmetric) class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime. The perturbations, which are for a general energy-momentum tensor, include scalar, vector and tensor modes and extend some previous works where matter was assumed to be a perfect fluid. Through a harmonic decomposition, the system of equations is then transformed to evolution equations in time and algebraic constraints. This result is then applied to dissipat…
The quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion in the synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized to the case of a two-fluid cosmological model. This solution describes non-decreasing modes of adiabatic and isocurvature scalar perturbations and gravitational waves in the regime when deviations of a space-time metric from the homogeneous isotropic Friedmann-Robertson-Walker (FRW) background are large while locally measurable quantities like Riemann tensor …
Locally rotationally symmetric (L.R.S.) Bianchi type II stiff fluid cosmological model is investigated. To get the deterministic model of the universe, we have assumed a condition $A=B^{m}$ between metric potentials $A,~B$ where $n$ is the constant. It is shown that the vacuum energy density $Λ$ is positive and proportional to $\frac{1}{t^{2}}$. The values of deceleration parameter $q$, matter-energy density $Ω_{m}$ and dark-energy density $Ω_Λ$ are found to be in good agreement with the values obtain from 5-years WMAP observations. the predicted value of the jerk parameter agrees with the SNL…
A Chern--Simons system in $2+1$ dimensions invariant under local Lorentz rotations, $SU(2)$ gauge transformations, and local $\mathcal{N}=2$ supersymmetry transformations is proposed. The field content is that of $(2+1)$-gravity plus an $SU(2)$ gauge field, a spin-1/2 fermion charged with respect to $SU(2)$ and a trivial free abelian gauge field. A peculiarity of the model is the absence of gravitini, although it includes gravity and supersymmetry. Likewise, no gauginos are present. All the parameters involved in the system are either protected by gauge invariance or emerge as integration cons…
In this paper we analyze the local localization of gravity in $AdS_4$ thick brane embedded in $AdS_5$ space. The 3-brane is modelled by domain wall solution of a theory with a bulk scalar field coupled to five-dimensional gravity. In addition to small four-dimensional cosmological constant, the vacuum expectation value (vev) of the scalar field controls the emergence of a localized four-dimensional quasi-zero mode. We introduce high temperature effects, and we show that gravity localization on a thick 3-brane is favored below a critical temperature $T_c$. These investigations suggest the appea…
We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space and the massless scalar field depends only on the radial coordinate. The field equations are decoupled in the general case, and can be solved exactly for the cases when either the cosmological constant vanishes or the base manifold is Ricci flat. We focus on the case of a negative cosmological constant and a Ricci-flat base manifold. The solution has a curva…
