We revisit the observational constraints on spatial curvature following recent claims that the Planck data favour a closed Universe. We use a new and statistically powerful Planck likelihood to show that the Planck temperature and polarization spectra are consistent with a spatially flat Universe, though because of a geometrical degeneracy cosmic microwave background spectra on their own do not lead to tight constraints on the curvature density parameter Omega_K. When combined with other astrophysical data, particularly geometrical measurements of baryon acoustic oscillations, the Universe is constrained to be spatially flat to extremely high precision, with Omega_ K = 0.0004 +/-0.0018 in agreement with the 2018 results of the Planck team. In the context of inflationary cosmology, the observations offer strong support for models of inflation with a large number of e-foldings and disfavour models of incomplete inflation.
The dynamics of a tachyon field plus a barotropic fluid is investigated in spatially curved FRW universe. We perform a phase-plane analysis and obtain scaling solutions accompanying with a discussion on their stability. Furthermore, we construct the form of scalar potential which may give rise to stable solutions for spatially open and closed universe separately.
A string-inspired duality symmetry of the spatially flat Friedmann equations of general-relativistic cosmology is discussed and generalized, providing a map between exact solutions corresponding to different values of the barotropic index.
We introduce the Generalised Lensing and Shear Spectra GLaSS code which is available for download from https://github.com/astro-informatics/GLaSS It is a fast and flexible public code, written in Python, that computes generalized spherical cosmic shear spectra. The commonly used tomographic and spherical Bessel lensing spectra come as built-in run-mode options. GLaSS is integrated into the Cosmosis modular cosmological pipeline package. We outline several computational choices that accelerate the computation of cosmic shear power spectra. Using GLaSS, we test whether the assumption that using …
We investigate the effect of peculiar velocities of inhomogeneities and the spatial curvature of the universe on the shape of the gravitational potential. To this end, we consider scalar perturbations of the FLRW metric. The gravitational potential satisfies a Helmholtz-type equation which follows from the system of linearized Einstein equations. We obtain analytical solutions of this equation in the cases of open and closed universes, filled with cold dark matter in presence of the cosmological constant. We demonstrate that, first, peculiar velocities significantly affect the screening length…
Recent analysis of the Planck measurements opened a possibility that we live in a non-flat universe. Given the renewed interest in non-zero spatial curvature, here we re-visit the light propagation in a non-flat universe and provide the gauge-invariant expressions for the cosmological probes: the luminosity distance, galaxy clustering, weak gravitational lensing, and cosmic microwave background anisotropies. With the positional dependence of the spatial metric, the light propagation in a non-flat universe is much more complicated than in a flat universe. Accounting for all the relativistic eff…
We construct non-linear inflaton potential energy densities that describe not-necessarily very-slowly-rolling closed and open inflation models, and compute tilted primordial spatial inhomogeneity power spectra that follow from quantum mechanical fluctuations during inflation in these models. Earlier non-flat inflation model power spectra computations assumed an inflaton potential energy density with a linear slope that resulted in very-slow-roll during inflation and untilted power spectra. These new tilted power spectra differ from those that have previously been used to study cosmological dat…
The recently proposed theory of "Asymptotically Free Mimetic Gravity" is extended to the general non-homogeneous, spatially non-flat case. We present a modified theory of gravity which is free of higher derivatives of the metric. In this theory asymptotic freedom of gravity implies the existence of a minimal black hole with vanishing Hawking temperature. Introducing a spatial curvature dependent potential, we moreover obtain non-singular, bouncing modifications of spatially non-flat Friedmann and Bianchi universes.
We use six tilted spatially-flat and untilted non-flat dark energy cosmological models in analyses of South Pole Telescope polarization (SPTpol) cosmic microwave background (CMB) data, alone and in combination with Planck 2015 CMB data and non-CMB data, namely, the Pantheon Type Ia supernovae apparent magnitudes, a collection of baryon acoustic oscillation data points, Hubble parameter measurements, and growth rates. Although the cosmological models that best-fit the Planck CMB and non-CMB data do not provide good fits to the SPTpol data, with the $χ^2$'s exceeding the expected value, given th…
A cosmic no-hair theorem for all initially contracting, spatially homogeneous, orthogonal Bianchi Cosmologies is derived - which shows that all such Universes asymptote to a spatially flat, isotropic Universe with the inclusion of a shear viscous stress. This establishes a new mechanism of isotropisation in a contracting Universe, which does not take recourse to an ekpyrosis-like mechanism using an effective ultra-stiff equation of state fluid, that is, one in which the pressure is much greater than the energy density.
An important, and potentially detectable, signature of a non-trivial topology for the universe is the presence of so called circles-in-the-sky in the cosmic microwave background (CMB). Recent searches, confined to antipodal and nearly antipodal circles, have however failed to detect any. This outcome, coupled with recent theoretical results concerning the detectability of very nearly flat universes, is sufficient to exclude a detectable non-trivial cosmic topology for most observers in the inflationary limit ($0< |Ω_{tot}-1| \lesssim 10^{-5}$). In a recent paper we have studied the consequence…
We extend our previous analysis and consider the interacting holographic Ricci dark energy (IRDE) model in non-flat universe. We study astrophysical constraints on this model using the recent observations including the type Ia supernovae (SNIa), the baryon acoustic oscillation (BAO), the cosmic microwave background (CMB) anisotropy, and the Hubble parameter. It is shown that the allowed parameter range for the fractional energy density of the curvature is $-0.005$ $\lesssim$ $Ω_{k0}$ $\lesssim$ $0.015$ in the presence of the interactions between dark energy and matter. Without the interaction,…
One important global topological property of a spacetime manifold is orientability. It is widely believed that spatial orientability can only be tested by global journeys around the Universe to check for orientation-reversing closed paths. Since such global journeys are not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are usually offered to support the choosing of time- and space-orientable spacetime manifolds. The nonexistence of globally defined spinor fields on a non-orientable spacetime is anothe…
Recent cosmological observations indicate that the present universe is flat and dark energy dominated. In such a universe, the calculation of the luminosity distance, d_L, involve repeated numerical calculations. In this paper, it is shown that a quite efficient approximate analytical expression, having very small uncertainties, can be obtained for d_L. The analytical calculation is shown to be exceedingly efficient, as compared to the traditional numerical methods and is potentially useful for Monte-Carlo simulations involving luminosity distances.
We study the evolution of the dark energy parameter within the scope of a spatially non-flat and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and bulk viscous stresses. We have obtained cosmological solutions which exhibit without a big rip singularity. It is concluded that in both non-interacting and interacting cases non-flat open universe crosses the phantom region. We find that during the evolution of the universe, the equation of state (EoS) for dark energy $ω_{D}$ changes from $ω^{eff}_{D} < -1$ to $ω^{eff}_{D} > -1$, which is consistent with recent obser…
Model-independent constraints on the spatial curvature are not only closely related to important problems such as the evolution of the Universe and properties of dark energy, but also provide a test of the validity of the fundamental Copernican principle. In this paper, with the distance sum rule in the Friedmann-Lemaître-Robertson-Walker metric, we achieve model-independent measurements of the spatial curvature from the latest type Ia supernovae and strong gravitational lensing (SGL) observations. We find that a spatially closed Universe is preferred. Moreover, by considering different kinds …
[Abridged] In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations - the so-called circles-in-the-sky. Searches for nearly antipodal circles in maps of cosmic microwave background have so far been unsuccessful. This negative outcome along with recent theoretical results concerning the detectability of nearly flat compact topologies is sufficient to exclude a detectable nontrivial topology for most observers in very nearly flat positively and negatively curved Universes ($0<…
Adiabatic modes are cosmological perturbations that are locally indistinguishable from a (large) change of coordinates. At the classical level, they provide model independent solutions. At the quantum level, they lead to soft theorems for cosmological correlators. We present a systematic derivation of adiabatic modes in spatially-flat cosmological backgrounds with asymptotically-perfect fluids. We find several new adiabatic modes including vector, time-dependent tensor and time-dependent scalar modes. The new vector and tensor modes decay with time in standard cosmologies but are the leading m…
The spatial curvature ($Ω_K$) of the Universe is one of the most fundamental quantities that could give a link to the early universe physics. In this paper we develop an approximate method to compute the nonlinear matter power spectrum, $P(k)$, for "non-flat" $Λ$CDM models using the separate universe (SU) ansatz which states that the effect of the curvature on structure formation is equivalent to that of long-wavelength density fluctuation ($δ_{\rm b}$) in a local volume in the "flat" $Λ$CDM model, via the specific mapping between the background cosmological parameters and redshifts in the non…
The anisotropies of the cosmic microwave background (CMB) are computed for the half-turn space E_2 which represents a compact flat model of the Universe, i.e. one with finite volume. This model is inhomogeneous in the sense that the statistical properties of the CMB depend on the position of the observer within the fundamental cell. It is shown that the half-turn space describes the observed CMB anisotropies on large scales better than the concordance model with infinite volume. For most observer positions it matches the temperature correlation function even slightly better than the well studi…
We determine constraints on spatially-flat tilted dynamical dark energy XCDM and $ϕ$CDM inflation models by analyzing Planck 2015 cosmic microwave background (CMB) anisotropy data and baryon acoustic oscillation (BAO) distance measurements. XCDM is a simple and widely used but physically inconsistent parameterization of dynamical dark energy, while the $ϕ$CDM model is a physically consistent one in which a scalar field $ϕ$ with an inverse power-law potential energy density powers the currently accelerating cosmological expansion. Both these models have one additional parameter compared to stan…
We constrain spatially-flat tilted and nonflat untilted scalar field ($ϕ$) dynamical dark energy inflation ($ϕ$CDM) models by using Planck 2015 cosmic microwave background (CMB) anisotropy measurements and recent baryonic acoustic oscillation distance observations, Type Ia supernovae apparent magnitude data, Hubble parameter measurements, and growth rate data. We assume an inverse power-law scalar field potential energy density $V(ϕ)=V_0 ϕ^{-α}$. We find that the combination of the CMB data with the four non-CMB data sets significantly improves parameter constraints and strengthens the evidenc…
We calculate the average numbers of closed, flat, and open universes spontaneously created from nothing in third quantization. The creation of universes is exponentially suppressed for large values of the kinetic energy of the inflaton, while for small kinetic energies it is exponentially favoured for closed universes over flat and open ones: For a scale of inflation less than about $2 \times 10^{16}$GeV, the ratio of the number of closed universes to either the number of flat or open universes is \begin{equation} \frac{n_{closed}}{n_{flat,open}} \gtrsim 10^{10^{10}} . \nonumber \end{equation}
Process of formation of the universe with its further expansion in the first evolution stage is investigated in the framework of Friedmann-Robertson-Walker metrics on the basis of quantum model, where a new type of matter is introduced, which energy density is dependent on velocity of the expansion. It is shown that such an improvement of the model forms potential barrier for the flat universe at $k=0$ (in contrast with generalized Chaplygin gas model). Peculiarities of wave function are analyzed in details, which is calculated by fully quantum (non-semiclassic) approach, for the different bar…
We discuss the generalized second law (GSL) and the constraints imposed by it for two types of Friedmann universes. The first one is the Friedmann universe with radiation and a positive cosmological constant, and the second one consists of non-relativistic matter and a positive cosmological constant. The time evolution of the event horizon entropy and the entropy of the contents within the horizon are analyses in an analytical way by obtaining the Hubble parameter. It is shown that the GSL constraint the temperature of both the radiation and matter of the Friedmann universe. It is also shown t…
This paper presents the linearised Boltzmann equation for photons for scalar, vector and tensor perturbations in flat, open and closed FLRW cosmologies. We show that E- and B-mode polarisation for all types can be computed using only a single hierarchy. This was previously shown explicitly for tensor modes in flat cosmologies but not for vectors, and not for non-flat cosmologies.
Cosmological observations indicate that our universe is flat and dark energy (DE) dominated at present. The luminosity distance plays an important role in the investigation of the evolution and structure of the universe. Nevertheless, the evaluation of the luminosity distance d_L is associated computationally heavy numerical quadratures in practice. In this Letter we find a series solution of the luminosity distance in a spatially flat LCDM cosmological model. And it is further shown that the series solution has a relative error of less than 0.36% for any relative parameter β(β= Omega_m / Omeg…
We present a new method for calculating CMB anisotropies in a non-flat Friedmann universe, relying on a very stable algorithm for the calculation of hyperspherical Bessel functions, that can be pushed to arbitrary precision levels. We also introduce a new approximation scheme which gradually takes over in the flat space limit, and significant speeds-up calculations. Our method is implemented in the Boltzmann code CLASS. It can be used to benchmark the accuracy of the CAMB code in curved space, which is found to match expectations. For default precision settings, corresponding to 0.1% for scala…
We construct Barrow holographic dark energy in the case of non-flat universe. In particular, considering closed and open spatial geometry we extract the differential equations that determine the evolution of the dark-energy density parameter, and we provide the analytical expression for the corresponding dark energy equation-of-state parameter. We show that the scenario can describe the thermal history of the universe, with the sequence of matter and dark energy epochs. Comparing to the flat case, where the phantom regime is obtained for relative large Barrow exponents, the incorporation of po…
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…
In this article,we investigate some features of the perturbation theory in spatially closed universe. We will show that the perturbative field equations in a spatially closed universe always have two independent adiabatic solutions provided that the wavelengths of perturbation modes are very longer than the Hubble horizon. It will be revealed that these adiabatic solutions do not depend on the curvature directly. We also propound a new interpretation for the curvature perturbation in terms of the unperturbed geometry.
Contrarily to general believe, a first-order cosmological perturbation theory based on Einstein's General Theory of Relativity explains the formation of massive primeval stars in a flat Friedmann-Lemaitre-Robertson-Walker universe after decoupling of matter and radiation, whether or not Cold Dark Matter is present. The growth rate of a density perturbation depends on the heat loss of a perturbation during the contraction, but is independent of the particle mass. The relativistic Jeans mass does depend on the particle mass. If the Cold Dark Matter particle mass is equal to the proton mass, then…
In a series of recent papers, including arXiv:1210.1183, it was claimed that large-scale magnetic fields generated during inflation in a spatially open universe could remain astrophysically significant at the present time since they experienced superadiabatic amplification specific to an open universe. We reexamine this assertion and show that, on the contrary, large-scale magnetic fields in a realistic open universe decay in much the same manner as they would in a spatially flat universe. Consequently, their amplitude today is extremely small (B0 < 10^{-59} G) and is unlikely to be of astroph…
Inflationary theory predicts that the observable Universe should be very close to flat, with a spatial-curvature parameter |Omega_K| < 10^-4. The WMAP satellite currently constrains |Omega_K| < 0.01, and the Planck satellite will be sensitive to values near 10^-3. Suppose that Planck were to find Omega_K to be non-zero at this level. Would this necessarily be a serious problem for inflation? We argue that an apparent departure from flatness could be due either to a local (wavelength comparable to the observable horizon) inhomogeneity, or a truly superhorizon departure from flatness. If there i…
In this paper, we investigate the agegraphic dark energy (ADE) model by including the sign-changeable interaction between ADE and dark matter in non-flat universe. It is shown that the interaction induces an energy flow of which the direction is first from dark matter to ADE and then from ADE to dark matter. The phase space analysis is made and the critical points are found, one of which is the accelerated scaling attractor solution. So, the coincidence problem can be alleviated. Furthermore, we show the evolution of the density parameter $Ω$, the deceleration parameter $q$ and the equation of…
It is shown that the decomposition theorems of York, Stewart and Walker for symmetric spatial second-rank tensors, such as the perturbed metric tensor and perturbed Ricci tensor, and the spatial fluid velocity vector imply that, for open, flat or closed Friedmann-Lemaitre-Robertson-Walker universes, there are exactly two, unique, independent gauge-invariant quantities which describe the true, physical perturbations to the energy density and particle number density. Using these two new quantities, evolution equations for cosmological density perturbations and for entropy perturbations, adapted …
We study the constraints on the cosmic opacity using the latest BAO and Union2 SNIa data in this paper and find that the best fit values seem to indicate that an opaque universe is preferred in redshift regions $0.20-0.35$, $0.35-0.44$ and $0.60-0.73$, whereas, a transparent universe is favored in redshift regions $0.106-0.20$, $0.44-0.57$and $0.57-0.60$. However, our result is still consistent with a transparent universe at the 1$σ$ confidence level, even though the best-fit cosmic opacity oscillates between zero and some nonzero values as the redshift varies.
We propose a model of the Universe based on Minkowski flat space-time metric. In this model the space-time does not evolve. Instead the matter evolves such that all the mass parameters increase with time. We construct a model based on unimodular gravity to show how this can be accomplished within the framework of flat space-time. We show that the model predicts the Hubble law if the masses increase with time. Furthermore we show that it fits the high z supernova data in a manner almost identical to the standard Big Bang model. Furthermore we show that at early times the Universe is dominated b…
Oscillons are extremely long lived, oscillatory, spatially localized field configurations that arise from generic initial conditions in a large number of non-linear field theories. With an eye towards their cosmological implications, we investigate their properties in an expanding universe. We (1) provide an analytic solution for one dimensional oscillons (for the models under consideration) and discuss their generalization to 3 dimensions, (2) discuss their stability against long wavelength perturbations and (3) estimate the effects of expansion on their shapes and life-times. In particular, …
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.
The standard model of cosmology is based on the hot Big Bang theory and the inflationary paradigm. Recent precise observations of the temperature and polarization anisotropies in the cosmic microwave background and the matter distribution in large scale structures like galaxies and clusters confirm the general paradigm and put severe constrains on variations of this simple idea. In this essay I will discuss the epistemological foundations of such a paradigm and speculate on its possible realization within a more fundamental theory.
