We consider perturbations of closed Friedmann universes. Perturbation modes of two lowest wavenumbers ($L=0$ and $1$) are generally known to be fictitious, but here we show that both are physical. The issue is more subtle in Einstein static universes where closed background space has a time-like Killing vector with the consequent occurrence of linearization instability. Proper solutions of the linearized equation need to satisfy the Taub constraint on a quadratic combination of first-order variables. We evaluate the Taub constraint in the two available fundamental gauge conditions, and show that in both gauges the $L\geq 1$ modes should accompany the $L=0$ (homogeneous) mode for vanishing sound speed, $c_{s}$. For $c_{s}^{2}>1/5$ (a scalar field supported Einstein static model belongs to this case with $c_s^2 = 1$), the $L\geq 2$ modes are known to be stable. In order to have a stable Einstein static evolutionary stage in the early universe, before inflation and without singularity, although the Taub constraint does not forbid it, we need to find a mechanism to suppress the unstable $L=0$ and $L=1$ modes.
Cosmological magnetic fields in open Friedmann universes can experience superadiabatic amplification within the realm of conventional electromagnetism. This is possible mathematically, despite the conformal invariance of Maxwell's equations, because Friedmann spacetimes with non-Euclidean spatial geometry are not globally conformal to Minkowski space. Physically, this means that even universes that are marginally open today can sustain large-scale magnetic fields that are substantially stronger than previously anticipated. In the present article, we investigate this purely geometric amplificat…
In this paper we study the origin of inertia in a curved spacetime, particularly the spatially flat, open and closed Friedmann universes. This is done using Sciama's law of inertial induction, which is based on Mach's principle, and expresses the analogy between the retarded far fields of electrodynamics and those of gravitation. After obtaining covariant expressions for electromagnetic fields due to an accelerating point charge in Friedmann models, we adopt Sciama's law to obtain the inertial force on an accelerating mass $m$ by integrating over the contributions from all the matter in the un…
We consider Friedmann-like universes with torsion and take a step towards studying their stability. In so doing, we apply dynamical-system techniques to an autonomous system of differential equations, which monitors the evolution of these models via the associated density parameters. Assuming relatively weak torsion, we identify the system's equilibrium points. These are found to represent homogeneous and isotropic spacetimes with nonzero torsion that undergo accelerated expansion. We then examine the linear stability of the aforementioned fixed points. Our results indicate that Friedmann-like…
We have already shown how a modified Friedmann equation, originating from a model of the Universe built from a certain $W_3$ algebra, is able to explainthe difference between the Hubble constants extracted from CMB data and from local measurements. In this article we show that the same model also describes aspects of the large scale structure of the Universe well.
We study the distance-redshift relation in a universe filled with point particles, and discuss what the universe looks like when we make the number of particles N very large, while fixing the averaged mass density. Using the Raychaudhuri equation and a simple analysis of the probability of strong lensing effects, we show that the statistical nature of the amplification is independent of N, and clarify the appearance of the point particle universe.
We consider radiation-dominated Friedmann universe and evaluate its force four-vector and momentum. We analyse and compare the results with the already evaluated for the matter-dominated Friedmann model. It turns out that the results are physically acceptable.
We report a symmetry property of the Einstein-Friedmann equations for spatially flat Friedmann-Lemaître-Robertson-Walker universes filled with a perfect fluid with any constant equation of state. The symmetry transformations form a one-parameter Abelian group.
We build a simple cosmological model by means of a parabolic Lemaître-Tolman-Bondi (LTB) metric up to a redshift $z\simeq 0.4$, an hyperbolic Friedmann metric for $z\sim 0.4$ up to the scale where dimming galaxies are observed ($z\sim 1.4$) and a bulk spatially flat metric up to the last scattering surface. Following Wiltshire, by taking into account the different rate of clocks for an observer at the centre of a parabolic LTB spacetime with respect to a one in the hyperbolic Friedmann metric, an "apparent" negative deceleration parameter is perceived by the observer at the centre of LTB, prov…
In the present paper we study equations of state of Casimir vacuum of massive scalar field and massive bispinor field in compact Friedmann Universe. With use of the Abel-Plana formula the renormalization of divergent series for calculation of the quantum means of operators is implemented.
In the Friedmann equations, an infinite initial density is avoided only when the universe is spatially flat. With such equations being then valid when the scale factor $a=0$, the universe must also be in the state of vacuum when $a$ is infinitesimal. Matter creation thus largely comes from nonlinearity of the Friedmann equations at a finite $a$. For the correspondence between such an initial vacuum and the Friedmann universe, therefore, a vacuum density is suggested to be gravitationally significant only when it could also have a matter phase. The effective cosmological term is then due to suc…
We study the modified Friedmann equation in the Friedmann-Robertson-Walker universe with quantum effect. Our modified results mainly stem from the new entropy-area relation and the novel idea of T. Padmanabhan, who considers the cosmic space to be emerged from the cosmic time progresses, so that the expansion rate of the universe is determined by the difference of degrees of freedom between the holographic surface and the bulk inside. We also discuss the possibility of having bounce cosmological solution from the modified Friedmann equation in spatially flat geometry.
Despite all fundamental objections against Newtonian concepts in cosmology, the Friedmann equation derives from these in an astoundingly simple way through application of the shell theorem and conservation of Newtonian energy in an infinite universe. However, Friedmann universes in general posses a finite gravitational horizon, as a result of which the application of the shell theorem fails and the Newtonian derivation collapses. We show that in the presence of a gravitational horizon the Friedmann equation can be derived from a Machian definition of kinetic energy, without invoking the shell …
Using as an illustrative example the p=1 operator-ordered Wheeler-DeWitt equation for a closed, radiation-filled Friedmann-Robertson-Walker universe, we introduce and discuss the supersymmetric double Darboux method in quantum cosmology. A one-parameter family of ``quantum'' universes and the corresponding ``wavefunctions of the universe" for this case are presented
The quantum Casimir condensate of a conformal massive scalar field in a compact Friedmann universe is considered in the static approximation. The Abel-Plana formula is used for renormalization of divergent series in the condensate calculation. A differential relation between the static Casimir energy density and static Casimir condensate is derived.
We use a general relativistic approach to investigate the effects of weak cosmological magnetic fields on linear rotational perturbations during the radiation and dust epochs of the universe. This includes ordinary kinematic vorticity, as well as vortex-like inhomogeneities in the density distribution of the cosmic medium. Our study confirms that magnetic fields can source both types of perturbations and shows that their presence also helps cosmic rotation to survive longer. In agreement with previous Newtonian studies, we find that during the dust era vorticity decays slower than in non-magne…
Large-scale bulk peculiar motions introduce a characteristic length scale, inside which the local kinematics are dominated by peculiar-velocity perturbations rather than by the background Hubble expansion. Regions smaller than the aforementioned critical length, which typically varies between few hundred and several hundred Mpc, can be heavily "contaminated" by the observers' relative motion. For example, at the critical length -- hereafter referred to as the "transition scale", the sign of the locally measured deceleration parameter can change from positive to negative, while the surrounding …
In this note, we discuss how possible expansion histories of the universe can be inferred in a simple way, for arbitrary energy contents. No new physical results are obtained, but the goal is rather to discuss an alternative way of writing the Friedmann equation in order to facilitate an intuitive understanding of the possible solutions; for students and researchers alike. As has been noted in passing by others, this specific form of the Friedmann equation allows us to view the universal expansion as a particle rolling along a frictionless track. Specific examples depicted include the current …
We show that the cosmological constant favours significantly the growth of voids in the universe. This dynamical effect is investigated within a newtonian approach with an extension to Friedmann-Lema\^ıtre model.
In the scope of the nonlinear massive gravity, we study fixed points of evolution equations for a Bianchi type--I universe. We find a new attractor solution with non-vanishing anisotropy, on which the physical metric is isotropic but the Stuckelberg configuration is anisotropic. As a result, at the background level, the solution describes a homogeneous and isotropic universe, while a statistical anisotropy is expected from perturbations, suppressed by smallness of the graviton mass.
In a recent article we have introduced Friedmann thermodynamics, where certain geometric parameters in Friedmann models are treated like their thermodynamic counterparts (temperature, entropy, Gibbs potential etc.). This model has the advantage of allowing us to determine the geometry of the universe by thermodynamic stability arguments. In this article we review connections between thermodynamics, geometry and cosmology.
In this paper, we calculate the one-loop quantum cosmological corrections to the kink energy in the closed Friedmann-Robertson-Walker universe in which the fluctuation potential $V^{\prime\prime}$ has a shape invariance property. We use the generalized zeta function regularization method to implement our setup for describing quantum kink-like states. It is conjectured that the corrections lead to the renormalized gravitational constant.
We explore the signatures of quintessence and modified gravity theories in the relativistic description of galaxy clustering within a parametrized post-Friedmann framework. For this purpose, we develop a calibration method to consistently account for horizon-scale effects in the linear parametrized Post-Friedmann perturbations of minimally and nonminimally coupled scalar-tensor theories and test it against the full model-specific fluctuations. We further study the relativistic effects in galaxy clustering for the normal and self-accelerating branches of the Dvali-Gabadadze-Porrati braneworld m…
A global intrinsic time in Friedmann - Robertson - Walker models is proportional to a scaling factor of the spatial metric. The aim of the paper is to study an applicability of the intrinsic global time chosen to nearest non-symmetric cases by taking into account linear metric perturbations. Scalar linear perturbations add some corrections to the effective energy density in the Hubble law. The metric vector and tensor perturbations in linear approximation do not influence the intrinsic time.
The novel idea that spatial expansion of our universe can be regarded as the consequence of the emergence of space was proposed by Padmanabhan. By using of the basic law governing the emergence, which Padmanabhan called holographic equipartition, he also arrives at the Friedmann equation in a flat universe. When generalized to other gravity theories, the holographic equipartition need to be generalized with an expression of $f(ΔN,N_{sur})$. In this paper, we give general expressions of $f(ΔN,N_{sur})$ for generalized holographic equipartition which can be used to derive the Friedmann equations…
Relations between the Friedmann observables of the expanding Universe and the Dirac observables in the generalized Hamiltonian approach are established for the Friedmann cosmological model of the Universe with the field excitations imitating radiation. A full separation of the physical sector from the gauge one is fulfilled by the method of the gaugeless reduction in which the gravitational part of the energy constraint is considered as a new momentum. We show that this reduction removes an infinite factor from the Hartle -- Hawking functional integral, provides the normalizability of the Whee…
We report a new symmetry of the Einstein-Friedmann equations for spatially flat Friedmann- Lemaître-Robertson-Walker universes. We discuss its application to barotropic perfect fluids and its use as a solution-generating technique for scalar field universes.
We illustrate the recently proposed generalized unimodular gravity using simple examples of the Friedmann, Kantowski-Sachs and Schwarzschild geometries and show that it can be further generalized and reveal some unexpected and interesting effects.
The investigation of quantum gravity effects in order to avoid the big bang singularity is a requisite, so that the idea of oscillating universes is introduced as an alternative for standard cosmological model. Therefore, the Friedmann equations arising from the quantum corrections of entropy-area relation provide the possibility of studying the oscillating universes. Addition to necessity of surveying the bouncing solutions, however, the values of unknown constant parameters are still a matter of open debate. In this paper, we consider modified Friedmann equations with logarithmic entropy cor…
The problem of particle creation in cosmology concerning whether the results for the number of particles are infinite or finite is discussed for scalar and spinor particles in Friedmann expanding Universe. It is shown that the results are always finite if one puts in case of scalar particles creation a special term into the Lagrangian. Numerical estimates of the effect of particle creation are made. The role of creation of superheavy particles in cosmology is discussed.
Starting from the generalized Raychaudhuri equation with torsion and non-metricity, and considering an FLRW spacetime we derive the most general form of acceleration equation in the presence of torsion and non-metricity. That is we derive the cosmic acceleration equation when the nonRiemannian degrees of freedom are also taken into account. We then discuss some conditions under which torsion and non-metricity accelerate/decelerate the expansion rate of the Universe.
Recently, we have generalized the Bekenstein-Hawking entropy formula for black holes embedded in expanding Friedmann universes. In this letter, we begin the study of this new formula to obtain the first law of thermodynamics for dynamical apparent horizons. In this regard we obtain a generalized expression for the internal energy $U$ together with a distinction between the dynamical temperature $T_D$ of apparent horizons and the related one due to thermodynamics formulas. Remarkable, when the expression for $U$ is applied to the apparent horizon of the universe, we found that this internal ene…
Oscillating or cyclic models of the universe were inspired by Friedmann's seminal paper of 1922. The model supposes a closed universe. In this work, we study Friedmann closed universe using the adiabatic invariant approach. We start revisiting the cosmological force proposed by N. Rosen and derive the Lagrangian density from Rosen's concepts of cosmological force. Importantly, we introduce the Noether gauge symmetry followed by the Rund-Traumann identity (RTI) and adiabatic invariant approach to examine the cyclic models. We consider a single component form of relativistic matter (stiff matter…
A novel idea that the cosmic acceleration can be understood from the perspective that spacetime dynamics is an emergent phenomena was proposed by T. Padmanabhan. The Friedmann equations of FRW universe can be derived from different gravity theories with different modifications of Padmanabhan's proposal. In this paper, a unified formula is proposed, in which those modifications can be treated as special cases when the formula is applied to different universe radii. Furthermore, the dynamic equations of FRW universe in the $ f(R) $ theory and deformed Ho{ř}ava-Lifshitz theory are investigated. T…
The solution of the problem of describing the Friedmann observables (the Hubble law, the red shift, etc.) in quantum cosmology is proposed on the basis of the method of gaugeless Hamiltonian reduction in which the gravitational part of the energy constraint is considered as a new momentum. We show that the conjugate variable corresponding to the new momentum plays a role of the invariant time parameter of evolution of dynamical variables in the sector of the Dirac observables of the general Hamiltonian approach. Relations between these Dirac observables and the Friedmann observables of the exp…
We consider gravity theories in $4+N$ dimensions which are governed by the Lagrangian written as an extended Gauss-Bonnet density. We can find a naturally generalized Einstein gravity where the maximal symmetric compactification leads to vanishing four-dimensional cosmological constant in the static limit. A later stage in the generalized Kaluza-Klein cosmology is also examined.
We show that the solutions of the Wheeler-DeWitt equation in a homogeneous and isotropic universe are given by triconfluent Heun functions for the spatially closed, flat, and open geometries of the Friedmann-Robertson-Walker universe filled with different forms of energy. In a matter-dominated universe, we find the polynomial solution and the energy density spectrum. In the cases of radiation-dominated and vacuum universes, there are no polynomial solutions as shown.
The Friedmann paradigm for a dynamical universe emanating from a spacetime singularity is critically reviwed. Quantum effects, playing the essential role at the very early stages, suggests that the universe may follow different course to that presented by the standard Friedmann solutions. The investigation of the back-reaction effect of the vacuum energy of quantized massless matter fields at finite temperatures shows that the original spatial singularity is avoided and that the universe is maintained all times at a critical density. Instead of having a universe that was created at once we hav…
Asymptotic properties of electromagnetic waves are studied within the context of Friedmann-Robertson-Walker (FRW) cosmology. Electromagnetic fields are considered as small perturbations on the background spacetime and Maxwell's equations are solved for all three cases of flat, closed and open FRW universes. The asymptotic character of these solutions are investigated and their relevance to the problem of cosmological tails of electromagnetic waves is discussed.
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This leads to a quantisation scheme that yields a Schrodinger-type equation which is in general nonlinear in evolution. Nevertheless it is compatible with a probabilistic interpretation of quantum mechanics and in particular the construction of a Hilbert space with a Euclidean norm is possible. The new scheme is applied to the quantisation of a Friedmann Universe wi…
In a recent paper [arXiv:1206.4916] by T. Padmanabhan, it was argued that our universe provides an ideal setup to stress the issue that cosmic space is emergent as cosmic time progresses and that the expansion of the universe is due to the difference between the number of degrees of freedom on a holographic surface and the one in the emerged bulk. In this note following this proposal we obtain the Friedmann equation of a higher dimensional Friedmann-Robertson-Walker universe. By properly modifying the volume increase and the number of degrees of freedom on the holographic surface from the entr…
This paper is devoted to study the gravitational charged perfect fluid collapse in the Friedmann universe models with cosmological constant. For this purpose, we assume that the electromagnetic field is so weak that it does not introduce any distortion into the geometry of the spacetime. The results obtained from the junction conditions between the Friedmann and the Reissner-Nordstr$\ddot{o}$m de-Sitter spacetimes are used to solve the field equations. Further, the singularity structure and mass effects of the collapsing system on time difference between the formation of apparent horizons and …
We analyse the evolution of primordial magnetic fields in spatially flat Friedmann universes and reconsider the belief that, after inflation, these fields decay adiabatically on all scales. Without~abandoning classical electromagnetism or standard cosmology, we demonstrate that this is not necessarily the case for superhorizon-sized magnetic fields. The underlying reason for this is causality, which confines the post-inflationary process of electric-current formation, electric-field elimination and magnetic-flux freezing within the horizon. As a result, the adiabatic magnetic decay is not a~pr…
In this paper, evolution of the high energy area of universe, through the scenario of 5 dimensional (5D) universe, has been studied. For this purpose, we solve Einstein equations for 5D metric and 5D perfect fuid to derive Friedmann-like equations. Then we obtain the evolution of scale factor and energy density with respect to both space-like and time-like extra dimensions. We obtain the novel equations for the space-like extra dimension and show that the matter with zero pressure cannot exist in the bulk. Also, for dark energy fuid and vacuum fluid, we have both accelerated expansion and cont…
Homogeneous, nearly-isotropic Bianchi cosmological models are considered. Their time evolution is expressed as a complete set of non-interacting linear modes on top of a Friedmann-Robertson-Walker background model. This connects the extensive literature on Bianchi models with the more commonly-adopted perturbation approach to general relativistic cosmological evolution. Expressions for the relevant metric perturbations in familiar coordinate systems can be extracted straightforwardly. Amongst other possibilities, this allows for future analysis of anisotropic matter sources in a more general g…
We present our development of Zeldovich's ideas for the measurement of the cosmological angular diameter distance (ADD) in the Friedmann Universe. We derive the general differential equation for the ADD measurement which is valid for an open, spatially-flat and closed universe, and for any stress energy tensor. We solve the mentioned equations in terms of quadratures in a form suitable for further numerical investigations for the present universe filled by radiation, (baryonic and dark) matter and dark energy. We perform the numerical investigation in the absence of radiation, and show the str…
We recently formulated a model of the universe based on an underlying W3-symmetry. It allows the creation of the universe from nothing and the creation of baby universes and wormholes for spacetimes of dimension 2, 3, 4, 6 and 10. Here we show that the classical large time and large space limit of these universes is one of exponential fast expansion without the need of a cosmological constant. Under a number of simplifying assumptions our model predicts that w=-1.2 in the case of four-dimensional spacetime. The possibility of obtaining a w-value less than -1 is linked to the ability of our mod…
Exact linear retarding spherically symmetric solutions of Einstein equations linearized around Friedmann background for the ultrarelativistic equation of state are obtained and investigated. Uniqueness of the solutions in the $C^{1} $ class is proved.
A highly excited Friedmann universe filled with a scalar field and radiation has been considered. On the basis of a direct solution to the quantum-mechanical problem with a well-defined time variable, it has been shown that such a universe can have features (energy density, scale factor, Hubble constant, density parameter, matter mass, equivalent number of baryons, age, dimensions of large-scale fluctuations, amplitude of fluctuations of cosmic microwave background radiation temperature) identical to those of the currently observed Universe.
Although bulk peculiar motions are commonplace in the universe, most theoretical studies either bypass them, or take the viewpoint of the idealised Hubble-flow observers. As a result, the role of these peculiar flows remains largely unaccounted for, despite the fact that relative-motion effects have led to the misinterpretation of the observations in a number of occasions. Here, we examine the implications of large-scale peculiar flows for the interpretation of the deceleration parameter. We compare, in particular, the deceleration parameters measured by the Hubble-flow observers and by their …
We investigate the derivation of Friedmann equations in Rainbow gravity following Jacobson thermodynamic approach. We do not restrict the rainbow functions to be constant as is customarily used, and show that the first law of thermodynamics with a corresponding `classical' proportionality between entropy and surface area, supplemented eventually by a `quantum' logarithmic correction, are not in general sufficient to obtain the equations in flat FRW metrics.
We show that homogeneous and isotropic cosmological models with radiation and scalar field have, in general, two possible chaotic exits to inflation. These models may describe the early stages of inflation. The central point of our analysis is based on the possible existence of one or two saddle-centers points in the phase space of the models.
We consider space-times with two isometries which represent gravitational waves with distinct wavefronts which propagate into exact Friedmann-Robertson-Walker (FRW) universes. The geometry of possible wavefronts is analysed in detail in all three types of FRW models. In the spatially flat and open universes, the wavefronts can be planar or cylindrical; in the closed case they are toroidal. Exact solutions are given which describe gravitational waves propagating into the FRW universes with a fluid with a stiff equation of state. It is shown that the plane-fronted waves may include impulsive or …
Recently some authors concluded that the energy and momentum of the Fiedman universes, flat and closed, are equal to zero locally and globally (flat universes) or only globally (closed universes). The similar conclusion was also done for more general only homogeneous universes (Kasner and Bianchi type I). Such conclusions originated from coordinate dependent calculations performed only in comoving Cartesian coordinates by using the so-called {\it energy-momentum complexes}. But it is known that the energy-momentum complexes can be reasonably use only in precisely defined asymptotically flat sp…
In this paper we continue the study of the physical consequences of our modified black hole entropy formula in expanding spacetimes. In particular, we apply the new formula to apparent horizons of Friedmann expanding universes with zero, negative and positive spatial curvature. As a first result, we found that, apart from the static Einstein solution, the only Friedmann spacetimes with constant (zero) internal energy are the ones with zero spatial curvature. This happens because, in the computation of the internal energy $U$, the contribution due to the non-vanishing Hubble flow must been adde…
