We propose a new model-independent method to test the cosmic curvature by comparing the proper distance and transverse comoving distance. Using the measurements of Hubble parameter $H(z)$ and angular diameter distance $d_A$, the cosmic curvature parameter $Ω_K$ is constrained to be $-0.09\pm0.19$, which is consistent with a flat universe. We also use Monte Carlo simulation to test the validity and efficiency, and find that our method can give a reliable and efficient constraint on cosmic curvature. Compared with other model-independent methods testing the cosmic curvature, our method can avoid some drawbacks and give a better constraint.
Bayesian model averaging is a procedure to obtain parameter constraints that account for the uncertainty about the correct cosmological model. We use recent cosmological observations and Bayesian model averaging to derive tight limits on the curvature parameter, as well as robust lower bounds on the curvature radius of the Universe and its minimum size, while allowing for the possibility of an evolving dark energy component. Because flat models are favoured by Bayesian model selection, we find that model-averaged constraints on the curvature and size of the Universe can be considerably stronge…
The question of determining the spatial geometry of the Universe is of greater relevance than ever, as precision cosmology promises to verify inflationary predictions about the curvature of the Universe. We revisit the question of what can be learnt about the spatial geometry of the Universe from the perspective of a three-way Bayesian model comparison. We show that, given current data, the probability that the Universe is spatially infinite lies between 67% and 98%, depending on the choice of priors. For the strongest prior choice, we find odds of order 50:1 (200:1) in favour of a flat Univer…
Cosmological distances as a function of redshift depend on the effective curvature density via the effect on the geometrical path of photons from large scale spatial curvature and its effect on the expansion history, H(z). Cosmological time, however, depends on the expansion history only. Therefore, by combining distance and lookback time observations (or other estimates of the expansion history), it is possible to isolate the geometrical curvature contribution and measure the curvature in a model independent way, i.e., free from assumptions about the energy content of the universe. We investi…
The curvature parameter tension between Planck 2018, cosmic microwave background lensing, and baryon acoustic oscillation data is measured using the suspiciousness statistic to be 2.5 to 3$σ$. Conclusions regarding the spatial curvature of the universe which stem from the combination of these data should therefore be viewed with suspicion. Without CMB lensing or BAO, Planck 2018 has a moderate preference for closed universes, with Bayesian betting odds of over 50:1 against a flat universe, and over 2000:1 against an open universe.
We use two model-independent methods to constrain the curvature of the universe. In the first method, we study the evolution of the curvature parameter ($Ω_k^0$) with redshift by using the observations of the Hubble parameter and transverse comoving distances obtained from the age of galaxies. Secondly, we also use an indirect method based on the mean image separation statistics of gravitationally lensed quasars. The basis of this methodology is that the average image separation of lensed images will show a positive, negative or zero correlation with the source redshift in a closed, open or fl…
Current cosmological observations indicate a preference for a cosmological constant that is drastically smaller than what can be explained by conventional particle physics. The Causal Entropic Principle (Bousso, {\it et al}.) provides an alternative approach to anthropic attempts to predict our observed value of the cosmological constant by calculating the entropy created within a causal diamond. We have extended this work to use the Causal Entropic Principle to predict the preferred curvature within the "multiverse". We have found that values larger than $ρ_k = 40ρ_m$ are disfavored by more t…
When using distance measurements to probe spatial curvature, the geometric degeneracy between curvature and dark energy in the distance-redshift relation typically requires either making strong assumptions about the dark energy evolution or sacrificing precision in a more model-independent approach. Measurements of the redshift evolution of the linear growth of perturbations can break the geometric degeneracy, providing curvature constraints that are both precise and model-independent. Future supernova, CMB, and cluster data have the potential to measure the curvature with an accuracy of sigma…
A recently published paper by Nielsen, Guffanti and Sarkar argues that the evidence for cosmic acceleration is marginal and that a coasting universe - the Milne Universe - fits the same supernovae data in a Hubble diagram nearly as well. The Milne Universe has negative spatial curvature. Nevertheless, we confirm that the Milne model fits the data just as well as LCDM. We show that this unexpected result points to a weakness in the Hubble diagram rather than to a flaw in LCDM. It seems the Hubble diagram is insensitive to spatial curvature. Here we present the data and both models in a scale fa…
Recently Barrow, and Tsagas [Phys Rev D 77: 107302, (2008)] have shown that slow decay of cosmological magnetic slowly decay in FRW universes on curvature scales as $B\sim{a^{-1}}$ in the context of general relativity (GR). This helps possible amplification of cosmic magnetic fields. In this paper starting from dynamo equations in spacetimes with torsion we obtain also slow decay of magnetic fields naturally on curvature-torsion scales of Riemann-Cartan spacetime on a de Sitter universe. In this case the constant of proportionality between the magnetic field and the curvature scale is the tors…
In a universe with quintessence isocurvature, or perturbations in dark energy that are independent from the usual curvature perturbations, structure formation is changed qualitatively. The existence of two independent fields, curvature and isocurvature, causes the growth rate of matter perturbations to depend on their initial conditions. The quintessence perturbations cause their growth to depend on scale. We perform the first separate universe simulations for this cosmology. We demonstrate that the power spectrum response and the halo bias depend on scale and initial conditions and that the p…
We investigate the observational viability of a class of interacting dark energy (iDE) models in the light of the latest Cosmic Microwave Background (CMB), type Ia supernovae (SNe) and SH0ES Hubble parameter measurements. Our analysis explores the assumption of a non-zero spatial curvature, the correlation between the interaction parameter $α$ and the current expansion rate $H_0$, and updates the results reported in \cite{micol}. Initially, assuming a spatially flat universe, the results show that the best-fit of our joint analysis clearly favours a positive interaction, i.e., an energy flux f…
The curvature of a spacetime, either in a topological sense, or averaged over super-horizon-sized patches, is often equated with the global curvature term that appears in Friedmann's equation. In general, however, the Universe is inhomogeneous, and gravity is a nonlinear theory, thus any curvature perturbations violate the assumptions of the FLRW model; it is not necessarily true that local curvature, averaged over patches of constant-time surfaces, will reproduce the observational effects of global symmetry. Further, the curvature of a constant-time hypersurface is not an observable quantity,…
It is well known that observations of the cosmic microwave background (CMB) are highly sensitive to the spatial curvature of the Universe, k. Here we find that what is in fact being tightly constrained by small angle fluctuations is spatial curvature near the surface of last scattering, and that if we allow k to be a function of position, rather than taking a constant value everywhere, then considerable spatial curvature is permissible within our own locale. This result is of interest for the giant void models that attempt to explain the supernovae observations without Dark Energy. We find voi…
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 …
We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate Friedmann-Robertson-Walker cosmology in their angle average. In order to be able to identify the local volume expansion and curvature in a long-wavelength perturbation with those of the separate universe, we show that the lapse perturbation must be much smaller in amplitude than the curvature potential on a time slicing that comoves with the Einstein tensor. Interpreti…
In this paper, by using the recently compiled set of 120 intermediate-luminosity quasars (ILQSO) observed in a single-frequency VLBI survey, we propose an improved model-independent method to probe cosmic curvature parameter $Ω_k$ and make the first measurement of the cosmic curvature referring to a distant past, with redshifts up to $z\sim 3.0$. Compared with other methods, the proposed one involving the quasar data achieves constraints with higher precision in this redshift range. More importantly, our results indicate that the measured $Ω_k$ is in good agreement with zero cosmic curvature, …
Model-independent measurements for the cosmic spatial curvature, which is related to the nature of cosmic space-time geometry, plays an important role in cosmology. On the basis of the Distance Sum Rule in the Friedmann-Lema{î}tre-Robertson-Walker metric, (distance ratio) measurements of strong gravitational lensing (SGL) systems together with distances from type Ia supernovae observations have been proposed to directly estimate the spatial curvature without any assumptions for the theories of gravity and contents of the universe. However, previous studies indicated that a spatially closed uni…
We discuss the advantages of using metric theories of gravity with curvature-matter couplings in order to construct a relativistic generalisation of the simplest version of Modified Newtonian Dynamics (MOND), where Tully-Fisher scalings are valid for a wide variety of astrophysical objects. We show that these proposals are valid at the weakest perturbation order for trajectories of massive and massless particles (photons). These constructions can be divided into local and non-local metric theories of gravity with curvature-matter couplings. Using the simplest two local constructions in a FLRW …
In this paper we suppose that the cosmological constant will change when the universe expends. For a general consideration, the cosmological constant is assumed to be a function of scale factor and Hubble constant. According to the ADM formulation, to the FRW metric, the extrinsic curvature $I$ equals $-6H^{2}$ and spatial curvature $R$ equals $6k/a^{2}$. Therefore we suppose cosmological constant is a function of extrinsic curvature and spatial curvature. We investigate the cosmological evolution of FRW universe in these models. At last we investigate two particular models which could fit the…
Within the cosmic screening approach, we obtain the exact formulas for the velocity-independent gravitational potentials produced by matter in the form of discrete sources distributed in the open and closed Universes. These formulas demonstrate that spatial curvature of the Universe considerably affect the form of the potentials and forces. While in the open Universe the gravitational force undergoes exponential suppression at cosmological distances, in the closed Universe the force induced by an individual mass is equal to zero at the antipodal point with respect to this mass. The derived for…
The Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological models are based on the assumptions of large-scale homogeneity and isotropy of the distribution of matter and energy. They are usually taken to have spatial sections that are simply connected; they have finite volume in the positive curvature case, and infinite volume in the null and negative curvature ones. I want to call the attention to the existence of an infinite number of models, which are based on these same metrics, but have compact, finite volume, multiply connected spatial sections. Some observational implications are briefly…
The universe can be made flat and smooth by undergoing a phase of ultra-slow (ekpyrotic) contraction, a condition achievable with a single, canonical scalar field and conventional general relativity. It has been argued, though, that generating scale-invariant density perturbations, requires at least two scalar fields and a two-step process that first produces entropy fluctuations and then converts them to curvature perturbations. In this paper, we identify a loophole in the argument and introduce an ekpyrotic model based on a single, canonical scalar field that generates nearly scale-invariant…
We study cosmological solutions for the very early universe beginning at the Planck scale for a universe containing radiation, curvature and, as a simplification of a possible scalar field potential, a cosmological constant term. The solutions are the natural counterpart of the well known results for a post-inflationary universe of non-relativistic matter, curvature and a cosmological constant. Contrary to the common belief that inflation arises independently of the initial curvature we show that in the positive curvature case the universe collapses again into a Big Crunch without allowing the…
We propose a class of theories that can limit scalars constructed from the extrinsic curvature. Applied to cosmology, this framework allows us to control not only the Hubble parameter but also anisotropies without the problem of Ostrogradsky ghost, which is in sharp contrast to the case of limiting spacetime curvature scalars. Our theory can be viewed as a generalization of mimetic and cuscuton theories (thus clarifying their relation), which are known to possess a structure that limits only the Hubble parameter on homogeneous and isotropic backgrounds. As an application of our framework, we c…
In a homogeneous and isotropic universe with non-zero spatial curvature we consider the effects of gravitational particle production in the dynamics of the universe. We show that the dynamics of the universe in such a background is characterized by a single nonlinear differential equation which is significantly dependent on the rate of particle creation and whose solutions can be dominated by the curvature effects at early times. For different particle creation rates we apply the singularity test in order to find the analytic solutions of the background dynamics. We describe the behavior of th…
Inferring high-fidelity constraints on the spatial curvature parameter, $Ω_{\rm K}$, under as few assumptions as possible, is of fundamental importance in cosmology. We propose a method to non-parametrically infer $Ω_{\rm K}$ from late-Universe probes alone. Using Gaussian Processes (GP) to reconstruct the expansion history, we combine Cosmic Chronometers (CC) and Type Ia Supernovae (SNe~Ia) data to infer constraints on curvature, marginalized over the expansion history, calibration of the CC and SNe~Ia data, and the GP hyper-parameters. The obtained constraints on $Ω_{\rm K}$ are free from pa…
The thoughts expressed in this article are based on remarks made by Jürgen Ehlers at the Albert-Einstein-Institut, Golm, Germany in July 2007. The main objective of this article is to demonstrate, in terms of plausible order-of-magnitude estimates for geometrical scalars, the relevance of spatial curvature in realistic models of the Universe that describe the dynamics of structure formation since the epoch of matter-radiation decoupling. We introduce these estimates with a commentary on the use of a quasi-Newtonian metric form in this context.
Chicone et al [Comm Math Phys (1997)] investigated existence of fast dynamos by analyzing the spectrum kinematic magnetic dynamo. In real non-degenerate branch of the spectrum, the kinematic dynamo operator lies on a compact Riemannian 2D space of constant negative curvature. Here, generalization of Marklund and Clarkson [MNRAS (2005)], general relativistic GR-MHD dynamo equation to include mean-field dynamos is obtained. In the absence of kinetic helicity, adiabatic constant $γ={1/2}$ and gravitational colapse of negative Riemann curvature of spatial sections enhance dynamo effect $\frac{δB}{…
We analyze observational signatures arising from an epoch in cosmology corresponding to the simple harmonic universe, which consists of positive curvature, a negative cosmological constant, and one or more exotic matter sources with $-1 < w = p/ρ\leq -1/3$, which may then evolve or tunnel into an inflating and hot Big Bang phase. Particular relics specific to this class of models include spatial curvature with $Ω_k < 0$, modifications to the dark energy sector due to the presence of residual exotic matter, and the possibility that the cosmological constant may ultimately be negative. We review…
This paper discusses the phenomenon of backreaction within the Szekeres model. Cosmological backreaction describes how the mean global evolution of the Universe deviates from the Friedmannian evolution. The analysis is based on models of a single cosmological environment and the global ensemble of the Szekeres models (of the Swiss-Cheese-type and Styrofoam-type). The obtained results show that non-linear growth of cosmic structures is associated with the growth of the spatial curvature $Ω_{\cal R}$ (in the FLRW limit $Ω_{\cal R} \to Ω_k$). If averaged over global scales the result depends on t…
We find a class of solutions for a homogeneous and isotropic universe in which the initially expanding universe stops expanding, experiences contraction, and then expands again (the "bounce"), in the framework of Einstein gravity with a real scalar field without violating the null energy condition nor encountering any singularities. Two essential ingredients for the bouncing universe are the positive spatial curvature and the scalar potential which becomes flatter at large field values. Depending on the initial condition, either the positive curvature or the negative potential stops the cosmic…
In the absence of new physics around $10^{10}$ GeV, the electroweak vacuum is at best metastable. This represents a major challenge for high scale inflationary models as, during the early rapid expansion of the universe, it seems difficult to understand how the Higgs vacuum would not decay to the true lower vacuum of the theory with catastrophic consequences if inflation took place at a scale above $10^{10}$ GeV. In this paper we show that the non-minimal coupling of the Higgs boson to curvature could solve this problem by generating a direct coupling of the Higgs boson to the inflationary pot…
The spatial curvature of the universe is not yet known. Even though at present the Universe is very close to being essentially flat and most signatures of curvature appear to have been diluted by inflation, if the number of e-foldings during inflation is close to the minimum necessary to explain the horizon problem, the curvature of the universe may have left imprints in the cosmic microwave background (CMB) that may be observable, especially at large angles. Motivated by general results on quantum cosmology and using effective field theory techniques, we develop a general approach for analyti…
Mimetic gravity can be described as a formulation capable of mimicking different evolutionary scenarios regarding the universe dynamics. Notwithstanding its initial aim of producing a similar evolution to the one expected from the dark components of the standard cosmology, a recent association with loop quantum cosmology could also provide interesting results. In this work, we reinterpret the physics behind the curvature potential of mimetic gravity description of loop quantum cosmology. Furthermore, we also test the compatibility of our formulation for a Higgs-type field, proving that the mim…
A short inflationary phase may not erase all traces of the primordial universe. Associated observables include both spatial curvature and "anomalies" in the microwave background or large scale structure. The present curvature $Ω_{K,0}$ reflects the initial curvature, $Ω_{K,\mathrm{start}}$, and the angular size of anomalies depends on $k_\mathrm{start}$, the comoving horizon size at the onset of inflation. We estimate posteriors for $Ω_{K,\mathrm{start}}$ and $k_\mathrm{start}$ using current data and simulations, and show that if either quantity is measured to have a non-zero value, both are l…
In this paper we consider the effects of adding curvature in extended cosmologies involving a free-to-vary neutrino sector and different parametrizations of Dark Energy (DE). We make use of the Planck 2018 cosmic microwave background temperature and polarization data, Baryon Acoustic Oscillations and Pantheon type Ia Supernovae data. Our main result is that a non-flat Universe cannot be discarded in light of the current astronomical data, because we find an indication for a closed Universe in most of the DE cosmologies explored in this work. On the other hand, forcing the Universe to be flat c…
We consider cosmic chronometer (CC) data for the Hubble parameter, quasar (QSO) luminosities data of X-rays and ultraviolet rays emission, and the latest measurements of the present value of the Hubble parameter from 2018 Planck mission (PL18), and SH0ES observations (SHOES) to constrain the present value of cosmic curvature density parameter. We consider three kinds of dark energy models: the $Λ$CDM model, the wCDM model, and the CPL parametrization. In all these three models, we find higher values of the matter-energy density parameter, $Ω_{\rm m0}$ compared to the one obtained from the Plan…
We provide evidence that gravitational radiation in a 4D radiation-dominated universe, with equation-of-state $w=1/3$, consists of two components: helicity-2 gravitons and massless scalar acoustic waves. On physical grounds, we would expect the homogeneous solution of the Weyl tensor components to be a good approximation to its inhomogeneous counterparts, whenever the observer is located well in the far zone of an isolated astrophysical source of cosmological gravitational radiation. We show explicitly that these homogeneous and inhomogeneous solutions both receive contributions from the gauge…
A precise measurement of the curvature of the Universe is of primeval importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early Universe scenarios. The recent observations, while broadly consistent with a spatially flat standard $Λ$ Cold Dark Matter ($Λ$CDM) model, are showing tensions that still allow (and, in some cases, even suggest) a few percent deviations from a flat universe. In particular, the Planck Cosmic Microwave Background power spectra, assuming the nominal likelihood, prefer a closed univ…
Distance measurement provide no constraints on curvature independent of assumptions about the dark energy, raising the question, how flat is our Universe if we make no such assumptions? Allowing for general evolution of the dark energy equation of state with 20 free parameters that are allowed to cross the phantom divide, w(z) = -1, we show that while it is indeed possible to match the first peak in the Cosmic Microwave Background with non-flat models and arbitrary Hubble constant, H_0, the full WMAP7 and supernova data alone imply -0.12 < Ω_k < 0.01 (2σ). If we add an H_0 prior, this tightens…
Spacetime curvature plays the primary role in general relativity but Einstein later considered a theory where torsion was the central quantity. Just as the Einstein-Hilbert action in the Ricci curvature scalar R can be generalized to f(R) gravity, we consider extensions of teleparallel, or torsion scalar T, gravity to f(T) theories. The field equations are naturally second order, avoiding pathologies, and can give rise to cosmic acceleration with unique features.
In the Part I of this work we show that Friedmann equations and the thermodynamical Gibbs-Duhem relation determine a general form of the Hubble function called Model E which predicts a dynamical Dark Energy and Dark Matter with equations of state w_0=-1 and w_M=0, respectively. We identify Dark Energy and Dark Matter with Space. General theory of relativity asserts that Space is gravitational fields. We propose the Space has a specific quantum structure: entangled Space quanta form Dark Energy, non-entangled ones form Dark Matter. We identify Dark Matter and Dark Energy as the gravitational fi…
Inflation creates large-scale cosmological density perturbations that are characterized by an isotropic, homogeneous, and Gaussian random distribution about a locally flat background. Even in a flat universe, the spatial curvature measured within one Hubble volume receives contributions from long wavelength perturbations, and will not in general be zero. These same perturbations determine the Cosmic Microwave Background (CMB) temperature fluctuations, which are O(10^-5). Consequently, the low-l multipole moments in the CMB temperature map predict the value of the measured spatial curvature Ω_k…
Theoretical arguments and cosmological observations suggest that Einstein's theory of general relativity needs to be modified at high energies. One of the best motivated higher-curvature extensions of general relativity is Einstein-scalar-Gauss-Bonnet gravity, in which a scalar field is coupled to quadratic curvature invariants. This theory is inspired by an effective string-theory model and its predictions dramatically differ from Einstein's theory in high-curvature regions - such as the interior of black holes and the early universe - where it aims at resolving curvature singularities. In th…
We present limits on the parameters of the o$Λ$CDM, $w_0$CDM, and $w_0 w_a$CDM models obtained from the joint analysis of the full-shape, baryon acoustic oscillations (BAO), big bang nucleosynthesis (BBN) and supernovae data. Our limits are fully independent of the data on the cosmic microwave background (CMB) anisotropies, but rival the CMB constraints in terms of parameter error bars. We find the spatial curvature consistent with a flat universe $Ω_k=-0.043_{-0.036}^{+0.036}$ ($68\%$ C.L.); the dark-energy equation of state parameter $w_0$ is measured to be $w_0=-1.031_{-0.048}^{+0.052}$ ($6…
Observations conducted over the last few decades show that the expansion of the Universe is accelerating. In the standard model of cosmology, this accelerated expansion is attributed to a dark energy in the form of a cosmological constant. It is conceivable, however, for the dark energy to exhibit mild dynamics (so that its energy density changes with time rather than having a constant value), or for the accelerated expansion of the Universe to be caused by some mechanism other than dark energy. In this work I will investigate both of these possibilities by using observational data to place co…
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…
We consider spatially averaged inhomogeneous universe models and argue that, already in the absence of sources, an effective scalar field arises through foliating and spatially averaging inhomogeneous geometrical curvature invariants of the Einstein vacuum. This scalar field (the `morphon') acts as an inflaton, if we prescribe a potential of some generic form. We show that, for any initially negative average spatial curvature, the morphon is driven through an inflationary phase and leads - on average - to a spatially flat, homogeneous and isotropic universe model, providing initial conditions …
