The long-wavelength coherent overdensity and tidal force, which are not direct observables for a finite-volume survey, affect time evolution of cosmic structure formation and therefore clustering observables through the mode coupling. In this paper we develop an "anisotropic" separate universe (SU) simulation technique to simulate large-scale structure formation taking into account the effect of large-scale tidal force into the anisotropic expansion of local background. We modify the TreePM N-body simulation code to implement the anisotropic SU simulations, and then study the "response" function of matter power spectrum that describes how the matter power spectrum responds to the large-scale tidal effect as a function of wavenumber and redshift for a given global cosmology. We test and validate the SU simulation results from the comparison with the perturbation theory predictions and the results from high-resolution PM simulations. We find that the response function displays characteristic scale dependences over the range of scales down to nonlinear scales, up to k ~ 6 h/Mpc.
In this paper, we present the higher order spectra of a scalar field produced through the higher derivative interactions in the initially anisotropic universe. Although we ignore the backreaction of the scalar field on the geometry, our analysis should have much overlap with the quantum fluctuations of the inflaton field in the anisotropic universe. We also include the planar modes whose momenta are along the plane which is perpendicular to the primordial preferred direction, for which effects of the initial anisotropy are not suppressed. The presence of a negative frequency mode produces feat…
We calculate the 4He abundance in a universe of Bianchi type I whose cosmic anisotropy is dynamically generated by a fluid with anisotropic equation of state. Requiring that the relative variation of mass fraction of 4He is less than 4% with respect to the standard isotropic case to be consistent with astrophysical data, we constrain the parameter of cosmic anisotropy, the shear Σ, as |Σ(T_f)| < 0.4, where T_f is the freeze-out temperature of the weak interactions that interconvert neutrons and protons. Anisotropic fluids, whose energy density is subdominant with respect to the energy content …
A cosmological model with anisotropic dark energy is analyzed. The amount of deviation from isotropy of the equation of state of dark energy, the skewness δ, generates an anisotropization of the large-scale geometry of the Universe, quantifiable by means of the actual shear Σ_0. Requiring that the level of cosmic anisotropization at the time of decoupling is such to solve the "quadrupole problem" of cosmic microwave background radiation, we find that |δ| \sim 10^{-4} and |Σ_0| \sim 10^{-5}, compatible with existing limits derived from the magnitude-redshift data on type Ia supernovae.
In this paper we introduce a LTB-Bianchi I (plane symmetric) model of Universe. We study and solve Einstein field equations. We investigate the effects of such model of Universe in particular these results are important in understanding the effect of the combined presence of an inhomogeneous and anisotropic Universe. The observational magnitude-redshift data deviated from UNION 2 catalog has been analyzed in the framework of this LTB-anisotropic Universe and the fit has been achieved without the inclusion of any dark energy.
Type-Ia supernovae (SNe Ia) are often used as the standard candles to probe the anisotropic expansion of the Universe. In this paper, we make a comprehensive comparison between the hemisphere comparison (HC) method and dipole-fitting (DF) method in searching for the cosmological preferred direction using the Union2 dataset, a compilation of 557 well-calibrated SNe Ia. We find that the directions of the faintest SNe Ia derived from these two methods are approximately opposite. Monte Carlo simulations show that the results of the HC method strongly depend on the distribution of the data points i…
We calculate the temperature and polarization patterns generated in anisotropic cosmological models drawn from the Bianchi classification. We show that localized features in the temperature pattern, perhaps similar to the cold spot observed in the Wilkinson Microwave Anisotropy Probe (WMAP) data, can be generated in models with negative spatial curvature, i.e. Bianchi types V and VII$_{h}$. Both these models also generate coherent polarization patterns. In Bianchi VII$_h$, however, rotation of the polarization angle as light propagates along geodesics can convert E modes into B modes but in Bi…
We present anisotropic "separate universe" simulations which modify the N-body code Gadget-4 in order to represent a large-scale tidal field through an anisotropic expansion factor. These simulations are used to measure the linear, quasi-linear and nonlinear response of the matter power spectrum to a spatially uniform trace-free tidal field up to wavenumber $k = 7 h \text{Mpc}^{-1}$. Together with the response to a large-scale overdensity measured in previous work, this completely describes the nonlinear matter bispectrum in the squeezed limit. We find that the response amplitude does not appr…
We propose a simple technique to detect any anisotropic expansion stage in the history of the universe starting from the inflationary stage to the surface of last scattering from the CMBR data. We use the property that any anisotropic expansion in the universe would deform the shapes of the primordial density perturbations and this deformation can be detected in a shape analysis of superhorizon fluctuations in CMBR. Using this analysis we obtain the constraint on any previous anisotropic expansion of the universe to be less than about 35%.
We propose that the early Universe was not Lorentz symmetric and that a gradual transition to the Lorentz symmetric phase occurred. An underlying form of the Dirac equation hints to such a transition for fermions. Fermions were coupled to space-time in a non-trivial manner such that they were massless in the Lorentz violating phase. The partition function is used as a transfer matrix to model this transition on a two level thermodynamics system that describes how such a transition might have occurred. The system that models this transition evolves, with temperature, from a state of large to ne…
In an anisotropic universe, observers not positioned at a point of special symmetry should observe cosmic parallax - the relative angular motion of test galaxies over cosmic time. It was recently argued that the non-observance of this effect in upcoming precision astrometry missions such as Gaia may be used to place strong bounds on the position of off-center observers in a void-model universe described by the Lemaitre-Tolman-Bondi metric. We consider the analogous effect in anisotropic cosmological models described by an axisymmetric homogeneous Bianchi type I metric and discuss whether any o…
We study the possibly existing anisotropy in the accelerating expansion universe with the Union2 Type Ia supernovae data and Gamma-ray burst data. We construct a direction-dependent dark energy model and constrain the anisotropy direction and strength of modulation. We find that the maximum anisotropic deviation direction is $(l,\,b)=(126^{\circ},\,13^{\circ})$ (or equivalently $(l,\,b)=(306^{\circ},\,-13^{\circ})$), and the current anisotropy level is $g_0=0.030_{+0.010}^{-0.030}$ ($1σ$ confidence level with Union2 data). Our results do not show strong evidence for the anisotropic dark energy…
Recent released Planck data and other astronomical observations show that the universe may be anisotropic on large scales. Inspired by this, anisotropic cosmological models have been proposed. We note that the Finsler-Randers spacetime provides an appropriate framework for the anisotropic cosmology. By adding an arbitrary 1-form to the Friedmann-Robertson-Walker (FRW) line element, a privileged axis in the universe is picked out. The distance-redshift relation is modified to be direction-dependent. We wish that the anisotropic cosmological model may be tested crossly by independent observation…
We analyze the state space of a Bianchi-I universe with anisotropic sources. Here we consider an extended state space which includes null geodesics in this background. The evolution equations for all the state observables are derived. Dynamical systems approach is used to study the evolution of these equations. The asymptotic stable fixed points for all the evolution equations are found. We also check our analytic results with numerical analysis of these dynamical equations. The evolution of the state observables are studied both in cosmic time and using a dimensionless time variable. Then we …
We study the singularity of the congruences for both timelike and null geodesic curves using the expansion of the early anisotropic Bianchi type I Universe. In this paper, we concentrate on the influence of the shear of the timelike and null geodesic congruences in the early Universe. Under some natural conditions, we derive the Raychaudhuri type equation for the expansion and the shear-related equations. Recently, scientists working on the LIGO (Laser Interferometer Gravitational-Wave Observatory) have shown many possibilities to observing the anisotropy of the primordial gravitational wave b…
We investigate the cosmological reconstruction in anisotropic universe for both homogeneous and inhomogeneous content of the universe. Special attention is attached to three interesting cases: Bianchi type-I, Bianchi type-III and Kantowski-Sachs models. The de Sitter, power-law and general exponential solutions are assumed for the scale factor in each spatial direction and the corresponding cosmological models are reconstructed. Moreover, for the general exponential solutions, from which the de Sitter and power-law solutions may be obtained, we obtain models which reproduce the early universe,…
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 this paper we have investigated the general form of viscous and non-viscous dark energy equation of state (EoS) parameter in the scope of anisotropic Bianchi type I space-time. We show that the presence of bulk viscosity causes transition of $ω^{de}$ from quintessence to phantom but the phantom state is an unstable state (as expected) and EoS of DE tends to $-1$ at late time. Then we show this phantomic description of the viscous dark energy and reconstruct the potential of the phantom scalar field. It is found that bulk viscosity pushes the universe to a darker region. We have also shown t…
In the presence of anisotropic cosmic expansions at global or local scale the equations of electrodynamics in expanding space-time are modified and presented here. A new effect should arise in regions of local anisotropic expansion in a cosmologically isotropic background. These regions should naturally exist, being connected with scales decoupling from the Hubble flow. Possible observational consequences of this effect are suggested. In particular, I predict the appearance or variation of the polarization of electromagnetic radiation coming from or passing through these regions. This effect i…
We propose that fast radio bursts (FRBs) can be used as the probes to constrain the possible anisotropic distribution of baryon matter in the Universe. Monte Carlo simulations show that, 400 (800) FRBs are enough to detect the anisotropy at 95\% (99\%) confidence level, if the dipole amplitude is at the order of magnitude 0.01. However, much more FRBs are required to tightly constrain the dipole direction. Even 1000 FRBs are far from enough to constrain the dipole direction within angular uncertainty $Δθ<40^{\circ}$ at 95\% confidence level. The uncertainty on the dispersion measure of host ga…
Modern cosmology rests on the working assumption that the Universe is isotropic and homogeneous at large scales. Here, we document a number of anomalous observations pointing to an anisotropic Universe in a direction consistent with the CMB dipole. If physical, this should be confirmed by any cosmological probe with sufficient data quality. To that end, we perform the first hemispherical decomposition of bright and dark standard siren $H_0$ determinations, finding that the maximum of the $H_0$ posterior is larger in the CMB dipole direction for dark sirens, but including the bright siren poste…
A primordial inflationary phase allows one to erase any possible anisotropic expansion thanks to the cosmic no-hair theorem. If there is no global anisotropic stress, then the anisotropic expansion rate tends to decrease. What are the observational consequences of a possible early anisotropic phase? We first review the dynamics of anisotropic universes and report analytic approximations. We then discuss the structure of dynamical equations for perturbations and the statistical properties of observables, as well as the implication of a primordial anisotropy on the quantization of these perturba…
In a landscape of compactifications with different numbers of macroscopic dimensions, it is possible that our universe has nucleated from a vacuum where some of our four large dimensions were compact while other, now compact, directions were macroscopic. From our perspective, this shapeshifting can be perceived as an anisotropic background spacetime. As an example, we present a model where our universe emerged from a tunneling event which involves the decompactification of two dimensions compactified on the two-sphere. In this case, our universe is of the Kantowski-Sachs type and therefore hom…
We study the asymptotic dynamics of $f(T, B)$-theory in an anisotropic Bianchi III background geometry. We show that an attractor always exists for the field equations, which depends on a free parameter provided by the specific $f(T, B)$ functional form. The attractor is an accelerated spatially flat FLRW or non-accelerated LRS Bianchi III geometry. Consequently, the $f(T, B)$-theory provides a spatially flat and isotropic accelerated Universe.
In this work, the linear and gauge-invariant theory of cosmological perturbations in a class of anisotropic and shear-free spacetimes is developed. After constructing an explicit set of complete eigenfunctions in terms of which perturbations can be expanded, we identify the effective degrees of freedom during a generic slow-roll inflationary phase. These correspond to the anisotropic equivalent of the standard Mukhanov-Sasaki variables. The associated equations of motion present a remarkable resemblance to those found in perturbed Friedmann-Robertson-Walker spacetimes with curvature, apart fro…
In the context of the modified teleparallel $f(T, B)$-theory of gravity, we consider a homogeneous and anisotropic background geometry described by the Kantowski-Sachs line element. We derive the field equations and investigate the existence of exact solutions. Furthermore, the evolution of the trajectories for the field equations is studied by deriving the stationary points at the finite and infinite regimes. For the $f(T,B)=T+F\left( B\right) $ theory, we prove that for a specific limit of the function $F\left( B\right) $, the anisotropic Universe has the expanding and isotropic Universe as …
This article proposes a comprehensive analysis of light propagation in an anisotropic and spatially homogeneous Bianchi I universe. After recalling that null geodesics are easily determined in such a spacetime, we derive the expressions of the redshift and direction drifts of light sources; by solving analytically the Sachs equation, we then obtain an explicit expression of the Jacobi matrix describing the propagation of narrow light beams. As a byproduct, we recover the old formula by Saunders for the angular diameter distance in a Bianchi I spacetime, but our derivation goes further since it…
We investigate the electrodynamic in a Bianchi type I cosmological model. This scenario reveals the possibility that photons, during their traveling, can make quantum interference. This effect is only due to the presence of two different axes of expansion in the cosmic evolution. In other word, it is possible to conclude that a purely metrical - or, equivalently, gravitational - phenomenon gives rise up to a quantum effect that manifests itself in the light propagation.
We show that the inclusion of simple anisotropic pressures stops the isotropic Friedmann universe being a stable attractor as an initial or final singularity is approached when pressures can exceed the energy density. This shows that the situation with isotropic pressures, studied earlier in the context of cyclic and ekpyrotic cosmologies, is not generic, and Kasner-like behaviour occurs when simple pressure anisotropies are present. We find all the asymptotic behaviours and determine the dynamics when the anisotropic principal pressures are proportional to the density. We expect distortions a…
We present the analytic forms for the spectra of the cosmological perturbations from an initially anisotropic universe for the high momentum modes in the context of WKB approximations, as the continuation of the work [29]. We consider the Einstein gravity coupled to a light scalar field. We then assume that the scalar field has the zero velocity initially and then slowly rolls down on the potential toward the origin. In the slow-roll approximations, the Kasner-de Sitter universe with a planar symmetry is a good approximation as the background evolution. Quantization of the perturbations in the…
We study the behaviour of Bianchi class A universes containing an ultra-stiff isotropic ghost field and a fluid with anisotropic pressures which is also ultra-stiff on the average. This allows us to investigate whether cyclic universe scenarios, like the ekpyrotic model, do indeed lead to isotropisation on approach to a singularity (or bounce) in the presence of dominant ultra-stiff pressure anisotropies. We specialise to consider the closed Bianchi type IX universe and show that when the anisotropic pressures are stiffer on average than any isotropic ultra-stiff fluid then, if they dominate o…
We study a warm inflationary model for different expansions assuming an anisotropic universe described by Bianchi I metric. The universe is filled with a scalar field or inflaton, radiation, and bulk viscous pressure. We carry out the inflationary analysis for different solutions of such universe in two different cases of the bulk viscosity coefficient $ξ$ and the dissipation coefficient $Γ$ as constant and variable parameters, respectively. We compare the obtained results with the recent observations, in order to find the observational constraints on the parameters space of the models. Moreov…
We consider the precession of a Dirac particle spin in some anisotropic Bianchi universes. This effect is present already in the Bianchi-I universe. We discuss in some detail the geodesics and the spin precession for both the Kasner and the Heckmann-Schucking solutions. In the Bianchi-IX universe the spin precession acquires the chaotic character due to the stochasticity of the oscillatory approach to the cosmological singularity. The related helicity flip of fermions in the very early Universe may produce the sterile particles contributing to dark matter.
In the separate universe approach, an inhomogeneous universe is rephrased as a set of glued numerous homogeneous local patches. This is the essence of the gradient expansion and the $δN$ formalism, which have been widely used in solving a long wavelength evolution of the universe. In this paper, we show that the separate universe approach can be generically used, as long as a theory under consideration is local and preserves the spatial diffeomorphism invariance. Focusing on these two conditions, we also clarify the condition for the existence of the so-called Weinberg's adiabatic mode. Remark…
We study an inflationary scenario with a vector field coupled with an inflaton field and show that the inflationary universe is endowed with anisotropy for a wide range of coupling functions. This anisotropic inflation is a tracking solution where the energy density of the vector field follows that of the inflaton field irrespective of initial conditions. We find a universal relation between the anisotropy and a slow-roll parameter of inflation. Our finding has observational implications and gives a counter example to the cosmic no-hair conjecture.
This article details the computation of the two-point correlators of the convergence, $E$- and $B$-modes of the cosmic shear induced by the weak-lensing by large scale structure assuming that the background spacetime is spatially homogeneous and anisotropic. After detailing the perturbation equations and the general theory of weak-lensing in an anisotropic universe, it develops a weak shear approximation scheme in which one can compute analytically the evolution of the Jacobi matrix. It allows one to compute the angular power spectrum of the $E$- and $B$-modes. In the linear regime, the existe…
We present an effective Eulerian description, in the non-relativistic regime, of the growth of cosmological perturbations around a homogeneous but anisotropic Bianchi I spacetime background. We assume a small deviation from isotropy, sourced at late times for example by dark energy anisotropic stress. We thus derive an analytic solution for the linear dark matter density contrast, and use it in a formal perturbative approach which allows us to derive a second order (non-linear) solution. As an application of the procedure followed here we derive analytic expressions for the power spectrum and …
We study both the background evolution and cosmological perturbations of anisotropic inflationary models supported by coupled scalar and vector fields. The models we study preserve the U(1) gauge symmetry associated with the vector field, and therefore do not possess instabilities associated with longitudinal modes (which instead plague some recently proposed models of vector inflation and curvaton). We first intoduce a model in which the background anisotropy slowly decreases during inflation; we then confirm the stability of the background solution by studying the quadratic action for all th…
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…
A model of a cloud formed by massive strings is used as a source of Bianchi type II. We assumed that the expansion $(θ)$ in the model is proportional to the shear $(σ)$. To get exact solution, we have considered the equation of state of the fluid to be in the stiff form. It is found that the bulk viscosity plays a very important rule in the history of the universe. In presence of bulk viscosity the particles dominate over strings whereas in absence of it, strings dominate over the particles which is not in consistence with the recent observations. Also we observe that the viscosity caused the …
We constrain several models of the early Universe that predict a statistical anisotropy of the cosmic microwave background (CMB) sky. We make use of WMAP9 maps deconvolved with beam asymmetries. As compared to previous releases of WMAP data, they do not exhibit the anomalously large quadrupole of statistical anisotropy. This allows to strengthen the limits on the parameters of models established earlier in the literature. In particular, the amplitude of the special quadrupole is constrained as |g_*|<0.072 at 95% C.L. (-0.046<g_*<0.048 at 68% C.L.) independently of the preferred direction in th…
Anisotropic separate universe : Long-wavelength perturbations and conserved quantities
Ewha Womans University（梨花女子大学）；National Institute of Technology, Fukui College（福井工业技术学院）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Yokohama National University（横滨国立大学）
We present some exact solutions of the Einstein equations with an anisotropic fluid exploiting the Chaplygin equation of state. The solutions describe spacetimes with two identical T regions and an intermediate static spherically symmetric R region containing a wormhole. The metric in the T region represents an anisotropic Kantowski-Sachs cosmological model. Its evolution starts from an event horizon and develops according to different scenarios including eternal expansion, contraction and also a finite universe lifetime.
We discuss the primordial spectrum of a massless and minimally coupled scalar field, produced during the initial anisotropic epoch before the onset of inflation. We consider two models of the anisotropic cosmology, the (planar) Kasner de Sitter solution (Bianchi I) and the Taub-NUT de Sitter solution (Bianchi IX), where the 3-space geometry is initially anisotropic, followed by the de Sitter phase due to the presence of a positive cosmological constant. We discuss the behavior of a quantized, massless and minimally coupled scalar field in the anisotropic stage. We focus on the quantization pro…
We study the evolution of linear density perturbations in a large spherical void universe which accounts for the acceleration of the cosmic volume expansion without introducing dark energy. The density contrast of this void is not large within the light cone of an observer at the center of the void. Therefore, we describe the void structure as a perturbation with a dimensionless small parameter $κ$ in a homogeneous and isotropic universe within the region observable for the observer. We introduce additional anisotropic perturbations with a dimensionless small parameter $ε$, whose evolution is …
