We investigate anisotropic fluid cosmology in a situation where the spacetime metric back-reacts in a local, time-dependent way to the presence of inhomogeneities. We derive exact solutions to the Einstein field equations describing Friedmann-Lemaitre-Robertson-Walker (FLRW) large scale cosmological evolution in the presence of local inhomogeneities and time-dependent back reaction. We use our derivation to tackle the cosmological constant problem. A cosmological constant emerges by averaging the back reaction term on spatial scales of the order of $100 \ \text{Mpc}$, at which our universe begins to appear homogeneous and isotropic. We find that the order of magnitude of the "emerged" cosmological constant agrees with astrophysical observations and is related in a natural way to baryonic matter density. Thus, there is no coincidence problem in our framework.
Anisotropic generalization of Randall and Sundrum brane-world model is considered. A new class of exact solutions for brane and bulk geometry is found; it is related to anisotropic Kasner solution. In view of this, the old question of isotropy of initial conditions in cosmology rises once again in the brane-world context.
The two-loop (order $α'$) $β$-function equations, which are equivalent to the equations of motion of $α'$-corrected string effective action, are considered for anisotropic homogeneous space-times. These equations are solved for all Bianchi-type models in two schemes of effective action, namely $R^2$ and Gauss-Bonnet schemes with zero cosmological constant and then the metric, dilaton and $B$-field are found at $α'$ perturbative corrections.
In the present work we show that the widely believed pathology of the non-unitarity of anisotropic quantum cosmological models cannot be a generic problem. We exhibit a non trivial example, a Bianchi-I model with an ultrarelativistic fluid, that has a well behaved time independent norm. We also show that a suitable operator ordering should produce time independent norms for the wave packets in the case of other more realistic fluids as well.
We investigate the dynamics of a Bianchi I brane Universe in the presence of a nonlocal anisotropic stress ${\cal P}_{μν}$ proportional to a "dark energy" ${\cal U}$. Using this ansatz for the case ${\cal U} > 0$ we prove that if a matter on a brane satisfies the equation of state $p=(γ-1)ρ$ with $γ\le 4/3$ then all such models isotropize. For $γ> 4/3$ anisotropic future asymptotic states are found. We also describe the past asymptotic regimes for this model.
We construct physical semi-classical states annihilated by the Hamiltonian constraint operator in the framework of loop quantum cosmology as a method of systematically determining the regime and validity of the semi-classical limit of the quantum theory. Our results indicate that the evolution can be effectively described using continuous classical equations of motion with non-perturbative corrections down to near the Planck scale below which the universe can only be described by the discrete quantum constraint. These results, for the first time, provide concrete evidence of the emergence of c…
The stability analysis of an anisotropic inflationary universe of the four dimensional Neveu-Schwarz--Neveu-Schwarz string model with a nonvanishing cosmological constant is discussed in this paper. The accelerating expansion solution found earlier is shown to be stable against the perturbations with respect to the dilaton and axion fields once the dilaton field falls close to the local minimum of the symmetry-breaking potential. This indicates that the Bianchi I space tends to evolve to an isotropic flat Friedmann-Robertson-Walker space. This expanding solution is also shown to be stable agai…
We discuss the possibility of a smooth transition from the pre- to the post-big bang regime, in the context of the lowest-order string effective action (without higher-derivative corrections), taking into account with a phenomenological model of source the repulsive gravitational effects due to the back-reaction of the quantum fluctuations outside the horizon. We determine a set of necessary conditions for a successful and realistic transition, and we find that such conditions can be satisfied (by an appropriate model of source), provided the background is higher-dimensional and anisotropic.
The dynamics of the early universe may have been profoundly influenced by spatial anisotropies. A search for such backgrounds in the context of string cosmology has uncovered the existence of an entire class of (spatatially) homogeneous but not necessarily isotropic space-times, analogous to the class of Bianchi-types in general relativity. Configurations with vanishing cosmological constant but non-vanishing dilaton and antisymmetric field are explicitly found for all types. This is a new class of solutions, whose isotropy limits reproduce all known and, further, all possible FRW-type of mode…
We consider a mimetic set up in which the mimetic scalar is coupled to a vector field. It is shown that such a field with a time-like component does not contribute to the background equations and yet produces healthy isocurvature perturbations with respect to ghost and gradient instabilities in spite of the absence of any propagating curvature perturbations at the level of the quadratic action. We then consider a vector field with space-like components which leads to an anisotropic Bianchi universe and show that the ghost and gradient instabilities are absent in the limit of high momenta and t…
We demonstrate that it is possible to produce different isotropic embeddings of anisotropic Loop Quantum Cosmology, resulting to "lattice refinement" in the isotropic system. To introduce the general approach, we first use a simple model with only two anisotropic directions. We then employ the specific case of a Bianchi I model, to show how the method extends to three-dimensional systems. To concisely calculate the step-size of the resulting isotropic state, we define the "symmetric dual" of states and operators, for the two- and three-dimensional systems, respectively.
We construct an anisotropic Weyl invariant theory in the ADM formalism and discuss its cosmological consequences. It extends the original anisotropic Weyl invariance of Hořava-Lifshitz gravity using an extra scalar field. The action is invariant under the anisotropic transformations of the space and time metric components with an arbitrary value of the critical exponent $z$. One of the interesting features is that the cosmological constant term maintains the anisotropic symmetry for $z=-3$. We also include the ordinary matter and show that it can preserve the anisotropic Weylinvariance if the …
We summarize the main ideas behind TGFT condensate cosmology and sketch the technical steps that bring from the fundamental theory to the effective cosmological dynamics. This framework is presented as an explicit illustration of (and possibly a general template for) the emergence of spacetime from non-spatiotemporal quantum entities in quantum gravity, and the many aspects involved in it.
In this article we perform the Wheeler-DeWitt quantization for Bianchi type $I$ anisotropic cosmological model in the presence of a scalar field minimally coupled to the Einstein-Hilbert gravity theory. We also consider the cosmological (perfect) fluid to construct the matter sector of the model whose dynamics plays the role of time. After obtaining the Wheeler-DeWitt equation from the Hamiltonian formalism, we then define the self-adjointness relations properly. Doing that we proceed to get a solution for the Wheeler-DeWitt equation and construct a well behaved wave function for the universe.…
The present work proves that the folk-lore of the pathology of non-conservation of probability in quantum anisotropic models is wrong. It is shown in full generality that all operator ordering can lead to a Hamiltonian with a self-adjoint extension as long as it is constructed to be a symmetric operator, thereby making the problem of non-unitarity in context of anisotropic homogeneous model a ghost. Moreover, it is indicated that the self-adjoint extension is not unique and this non-uniqueness is suspected not to be a feature of Anisotropic model only, in the sense that there exists operator o…
This paper gives an elementary introduction to some of the conceptual problems of quantum cosmology. Contents: 1. Why quantum cosmology? 2. Time in quantum gravity 3.Decoherence and the recovery of the Schrodinger equation 4. The direction of time
In the homogeneous and isotropic Friedmann-Robertson-Walker minisuperspace model, it is known that there are no Euclidean wormhole solutions in the pure gravity system. Here it is demonstrated explicitly that in Taub cosmology, which is one of the simplest anisotropic cosmology models, wormhole solutions do exist in pure general relativity in both classical and quantum contexts.
In this letter we investigate whether the isotropy problem is naturally solved in inflationary cosmologies inspired by string theory, so called pre-big-bang cosmologies. We find that, in contrast to what happens in the more common 'potential inflation' models, initial anisotropies do not decay during pre-big-bang inflation.
We study anisotropic cosmology in Hořava's gravity theory and obtain Kasner type solutions, valid for any number d of spatial dimensions. The corresponding exponents satisfy two relations, one involving the marginal coupling λ. Also, Hořava's (super)renormalisable theory predicts (super)stiff matter whose equation of state is p = w ρwith w \ge 1. We discuss briefly the implications of these results for the nature of cosmological collapse.
We present non-critical Bianchi type $I$ string cosmology solutions in the presence of central charge deficit term $Λ$. The leading order string frame curvature appears to be in the high curvature limit $Rα'\gtrsim1$, which underlines the necessity of including higher order $α'$-corrections. We give new solutions of two-loop (order $α'$) $β$-function equations of $σ$-model with non-zero $Λ$ and dilaton field in both cases of absence and presence of spatially homogeneous $H$-field ($H=dB$). Also, the evolution of solutions is studied in the Einstein frame, where the string effective action can …
In the context of brane cosmology, a scenario where our universe is a 3+1-dimensional surface (the ``brane'') embedded in a five-dimensional spacetime (the ``bulk''), we study geometries for which the brane is anisotropic - more specifically Bianchi I - though still homogeneous. We first obtain explicit vacuum bulk solutions with anisotropic three-dimensional spatial slices. The bulk is assumed to be empty but endowed with a negative cosmological constant. We then embed Z_2-symmetric branes in the anisotropic spacetimes and discuss the constraints on the brane energy-momentum tensor due to the…
Intrinsic time-dependent invariants are constructed for classical, flat, homogeneous, anisotropic cosmology with a massless scalar material source. Invariance under the time reparameterization-induced canonical symmetry group is displayed explicitly.
A multidimensional cosmological model describing the dynamics of n+1 Ricci-flat factor-spaces M_i in the presence of a one-component anisotropic fluid is considered. The pressures in all spaces are proportional to the density: p_i = w_i ρ, i = 0,...,n. Solutions with accelerated expansion of our 3-space M_0 and small enough variation of the gravitational constant G are found. These solutions exist for two branches of the parameter w_0. The first branch describes superstiff matter with w_0 > 1, the second one may contain phantom matter with w_0 < - 1, e.g., when G grows with time.
We use the Sáez-Ballester theory on anisotropic Bianchi I cosmological model, with barotropic fluid and cosmological constant. We obtain the classical solution by using the Hamilton-Jacobi approach. Also the quantum regime is constructed and exact solutions to the Wheeler-DeWitt equation are found.
To derive loop quantum cosmology from loop quantum gravity, I apply the model given in \cite{lin1} to a system with coupled gravitational and matter fields. The matter sector consists of a scalar field $phi$ serving as a cosmological clock, and other fields ${psi}$ providing physical spatial coordinates and frames. The physical Hilbert space of the model is constructed from the kinematical Hilbert space of loop quantum gravity, and the local observables in the physical Hilbert space are constructed using the matter coordinates and frames. A specific coherent physical state is then chosen, whos…
In this paper, we have studied Brans-Dicke Cosmology in anisotropic Kantowski-Sachs space-time model; considering variation of the velocity of light. We have addressed the flatness problem considering both the cases namely, (i) when the Brans-Dicke scale field $ϕ$ is constant (ii) when $ϕ$ varies, specially for radiation dominated era perturbatively and non-perturbatively and asymptotic behaviour have been studied.
In the case of two-scalar field cosmology and, specifically for the Chiral model, we determine an exact solution for the field equations with a anisotropic background space. The exact solution can describe anisotropic inflation with a Kantowski-Sachs geometry and it can be seen as the anisotropic analogue of the hyperbolic inflation. Finally, we investigate the evolution for the homogeneous perturbations around the new asymptotic solution.
In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter $β$ in the modified dispersion relation of the modes. Hence inducing an isotropic deformati…
Solutions to the field equations of the Nonsymmetric Gravitational Theory with $g_[i0] = 0$ are obtained for the homogeneous, plane-symmetric, time-dependent case, both in vacuum and in the presence of a perfect fluid. Cosmological consequences include a dependence of the speed of light on its polarisation, as in a birefringent crystal.
We use anisotropic fluid cosmology to describe the present, dark energy-dominated, universe. Similarly to what has been proposed for galactic dynamics, the anisotropic fluid gives an effective description of baryonic matter, dark energy and their possible interaction, without assuming the presence of dark matter. The resulting anisotropic fluid spacetime naturally generates inhomogeneities at small scales, triggered by an anisotropic stress, and could therefore be responsible for structure formation at these scales. Solving the cosmological equations, we show that the dynamics of the scale fac…
The dynamics of a homogeneous, anisotropic universe are investigated within the context of spinfoam cosmology. Transition amplitudes are calculated for a graph consisting of a single node and three links - the `Daisy graph' - probing the behaviour a classical Bianchi I spacetime. It is shown further how the use of such single node graphs gives rise to a simplification of states such that all orders in the spin expansion can be calculated, indicating that it is the vertex expansion that contains information about quantum dynamics.
We study the effect of the antisymmetric tensor field $B_{μν}$ on the large curvature phase of string cosmology. It is well-known that a non-vanishing value of $H=dB$ leads to an anisotropic expansion of the spatial dimensions. Correspondingly, in the string phase of the model, including $α'$ corrections, we find anisotropic fixed points of the evolution, which act as regularizing attractors of the lowest order solutions. The attraction basin can also include isotropic initial conditions for the scale factors. We present explicit examples at order $α'$ for different values of the number of spa…
There have been recent attempts at justifying, from first principles, and within the standard framework, the emergence of classical behavior in the post-inflationary cosmological context. Accounting for this emergence is an important issue, as it underlies the extraordinary empirical success of our current understanding of cosmology. In this work, we offer a critique of different efforts at explaining the emergence of classical behavior in cosmology within the standard framework. We argue that such endeavors are generically found lacking in conceptual clarity, as they invariably rely, either u…
We examine the behaviour of homogeneous, anisotropic space-times, specifically the locally rotationally symmetric Bianchi types $I$ and $VII_o$ in the presence of anisotropic matter. By finding an appropriate constant of the motion, and transforming the equations of motion we are able to provide exact solutions in the presence perfect fluids with anisotropic pressures. The solution space covers matter consisting of a single perfect fluid which satisfies the weak energy condition and is rich enough to contain solutions which exhibit behaviour which is qualitatively distinct from the isotropic s…
Recently a new no-global-recollapse argument was given for some inhomogeneous and anisotropic cosmologies that utilizes surface deformation by the mean curvature flow. In this paper we discuss important properties of the mean curvature flow of spacelike surfaces in Lorentzian manifolds. We show that singularities may form during cosmic evolution and the theorems forbidding the global recollapse lose their validity. The time evolution of the spatial scalar curvature that may kinematically prevent the recollapse is determined in normal coordinates, which shows the impact of inhomogeneities expli…
In this paper we are looking for the exponential solutions (i.e. the solutions with the scale factors change exponentially over time) in the Einstein-Gauss-Bonnet gravity. We argue that we found all possible non-constant-volume solutions (up to permutations) in lower dimensions ((4+1) and (5+1)) and developed a scheme which allows one to find necessary conditions in arbitrary dimension.
We investigate dynamics of (4+1) and (5+1) dimensional flat anisotropic Universe filled by a perfect fluid in the Gauss-Bonnet gravity. An analytical solutions valid for particular values of the equation of state parameter $w=1/3$ have been found. For other values of $w$ structure of cosmological singularity have been studied numerically. We found that for $w > 1/3$ the singularity is isotropic. Several important differences between (4+1) and (5+1) dimensional cases are discussed.
The dynamics of a (3 + 1) dimensional homogeneous anisotropic universe is modified by Loop Quantum Cosmology and, consequently, it has generically a big bounce in the past instead of a big-bang singularity. This modified dynamics can be well described by effective equations of motion. We generalise these effective equations of motion empirically to (d + 1) dimensions. The generalised equations involve two functions and may be considered as a class of LQC -- inspired models for (d + 1) dimensional early universe cosmology. As a special case, one can now obtain a universe which has neither a big…
We investigate quantum cosmological models in an n-dimensional anisotropic universe in the presence of a massless scalar field. Our basic inspiration comes from Chodos and Detweiler's classical model which predicts an interesting behaviour of the extra dimension, shrinking down as time goes by. We work in the framework of a recent geometrical scalar-tensor theory of gravity. Classically, we obtain two distinct type of solutions. One of them has an initial singularity while the other represents a static universe considered as a whole. By using the canonical approach to quantum cosmology, we inv…
In this paper we investigate the constant volume exponential solutions (i.e. the solutions with the scale factors change exponentially over time so that the comoving volume remains the same) in the Einstein-Gauss-Bonnet gravity. We find conditions for these solutions to exist and show that they are compatible with any perfect fluid with the equation of state parameter $ω<1/3$ if the matter density of the Universe exceeds some critical value. We write down some exact solutions which generalize ones found in our previous paper for models with a cosmological constant.
In this work, the cosmological implications of brane world scenario are investigated when the gravitational coupling $G$ and the cosmological term $Λ$ are not constant but rather there are time variation of them. From observational point of view, these time variations are taken in the form $\frac{\dot{G}}{G}\sim H$ and $Λ\sim H^{2}$. The behavior of scale factors and different kinematical parameters are investigated for different possible scenarios where the bulk cosmological constant $Λ_{5}$ can be zero, positive or negative.
We study stability conditions of the full Hamiltonian constraint equation describing the quantum dynamics of the diagonal Bianchi I model in the context of LQC. Our analysis has shown robust evidence of an instability in the explicit implementation of the difference equation, implying important consequences for the correspondence between the full LQG theory and LQC. As a result, one may question the choice of the quantisation approach, the model of lattice refinement, and/or the role of the ambiguity parameters; all these should in principle be dictated by the full LQG theory.
We present a class of exact solutions for homogeneous, anisotropic cosmologies in four dimensions derived from the low-energy string effective action including a homogeneous dilaton $ϕ$ and antisymmetric tensor potential $B_{μν}$. Making this potential time-dependent produces an anisotropic energy-momentum tensor, and leads us to consider a Bianchi I cosmology. The solution for the axion field must then only be a linear function of one spatial coordinate. This in turn places an upper bound on the product of the two scale factors evolving perpendicular to the gradient of the axion field. The on…
In this paper, we investigate the exact solution of an anisotropic space-time in the context of $f(Q)$ gravity, where $f\left( Q\right) $ is the arbitrary function of the non-metricity scalar $Q$. Here, we consider a specific power-law form as $f\left( Q\right) =αQ^{n+1}+β$, where $α$, $β$, and $n$ are free model parameters. Using power-law cosmology ($a\left( t\right) \propto t^{m}$), we analyze the physical behavior of cosmological parameters such as the energy density, pressure, EoS parameter, skewness parameter. Further, we validated the model with energy conditions and found that our $f\l…
The anisotropic Bianchi type I in multi-scalar field cosmology is studied with a particular potential of the form $\rm V= V_0 e^{-\left[λ_1 ϕ_1 + \cdots + λ_n ϕ_n \right]}\,,$ which emerges as a condition between the time derivatives of their corresponding momenta. Using the Hamiltonian formalism for the inflation epoch with a quintessence framework we find the exact solutions for the Einstein-Klein-Gordon (EKG) system with different scenarios specified by the parameter $\rm λ^2= \sum_{i=1}^n λ_i^2$. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solve…
This article addresses the issue of estimating the duration in inflation in bouncing cosmology when anisotropies, inevitably playing an important role, are taken into account. It is shown that in Bianchi-I loop quantum cosmology, the higher the shear, the shorter the period of inflation. In a range of parameters, the probability distribution function of the duration of inflation is however peaked at values compatible with data, but not much higher. This makes the whole bounce/inflationary scenario consistent and phenomenologically appealing as all the information from the bounce might then not…
D-dimensional cosmological model describing the evolution of a perfect fluid with negative pressure (x-fluid) and a fluid possessing both shear and bulk viscosity in n Ricci-flat spaces is investigated. The second equations of state are chosen in some special form of metric dependence of the shear and bulk viscosity coefficients. The equations of motion are integrated and the dynamical properties of the exact solutions are studied. It is shown the possibility to resolve the cosmic coincidence problem when the x-fluid plays role of quintessence and the viscous fluid is used as cold dark matter.
We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaitre-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion an…
The dynamics of Dvali-Gabadadze-Porrati Cosmology (DGP) braneworld with an anisotropic brane is studied. The Friedmann equations and their solutions are obtained for two branches of anisotropic DGP model. The late time behavior in DGP cosmology is examined in the presence of anisotropy which shows that universe enters a self-accelerating phase much later compared to the isotropic case. The acceleration conditions and slow-roll conditions for inflation are obtained.
We investigate the observational effects of a quintessence model in an anisotropic spacetime. The anisotropic metric is a non-rotating particular case of a generalized Godel's metric and is classified as Bianchi III. This metric is an exact solution of the Einstein-Klein-Gordon field equations with an anisotropic scalar field, which is responsible for the anisotropy of the spacetime geometry. We test the model against observations of type Ia supernovae, analyzing the SDSS dataset calibrated with the MLCS2k2 fitter, and the results are compared to standard quintessence models with Ratra-Peebles…
Evolution of the density parameter in the anisotropic DGP braneworld model is studied. The role of shear and cross-over scale in the evolution of $Ω_ρ$ is examined for both the branches of solution in the DGP model. The evolution is modified significantly compared to the FRW model and further it does not depend on the value of $γ$ alone. Behaviour of the cosmological density parameter $Ω_ρ$ is unaltered in the late universe. The study of decceleration parameter shows that the entry of the universe into self accelerating phase is determined by the value of shear. We also obtain an estimate of t…
