Spatial Flatness Research Articles

On direct estimation of density parameters and Hubble constant for ΛCDM universe using Hubble measurements

The set of cosmological density parameters ( Ω0mh02 , Ω0kh02 , Ω0Λh02 ) and Hubble constant ( hˆ0 ) are useful for fundamental understanding of the Universe from many perspectives. In this article, we propose a new procedure to estimate these parameters for Λ cold dark matter (ΛCDM) universe in the Friedmann-Robertson-Walker (FRW) background. We generalize the two-point statistics first proposed by Sahni et al (2008) to the three point case and estimate the parameters using currently available Hubble parameter (H(z)) values in the redshift range 0.07 ≤ z ≤ 2.36 measured by differential age (DA) and baryon acoustic oscillation (BAO) techniques. All the parameters are estimated assuming the general case of non-flat universe. Using both DA and BAO data we obtain Ω0mh02=0.1485±0.0065 , Ω0kh02=−0.0137±0.017 , Ω0Λh02=0.3126±0.0145 and hˆ0=0.6689±0.0021 . These results are in satisfactory agreement with the Planck results. An important advantage of our method is that to estimate the value of any one of the independent cosmological parameters one does not need to use the values for the rest of them. Each parameter is obtained solely from the measured values of Hubble parameters at different redshifts without any need to use values of other parameters. Such a method is expected to be less susceptible to the undesired effects of degeneracy issues between cosmological parameters during their estimations. Moreover, there is no requirement of assuming spatial flatness in our method.

Why is zero spatial curvature special?

Evidence for almost spatial flatness of the Universe has been provided from several observational probes, including the Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO) from galaxy clustering data. However, other than inflation, and in this case only in the limit of infinite time, there is no strong a priori motivation for a spatially flat Universe. Using the renormalization group (RG) technique in curved spacetime, we present in this work a theoretical motivation for spatial flatness. Starting from a general spacetime, the first step of the RG, coarse-graining, gives a Friedmann-Lemaître-Robertson-Walker (FLRW) metric with a set of parameters. Then, we study the rescaling properties of the curvature parameter, and find that zero spatial curvature of the FLRW metric is singled out as the unique scale-free, non-singular background for cosmological perturbations.

On the uniqueness of ΛCDM-like evolution for homogeneous and isotropic cosmology in General Relativity

We address the question of the uniqueness of spatially flat ΛCDM-like evolution for FLRW cosmologies in General Relativity, i.e. whether any model other than the spatially flat ΛCDM can give rise to the same type of scale factor evolution. Firstly, we elaborate on what we exactly imply by a ΛCDM-like evolution or kinematic/cosmographic degeneracy with the ΛCDM model, using the lessons from the statefinder diagnostic. Then, we consider two models with interaction in the dark sector: coupled fluid-fluid model and coupled quintessence model. We enforce the kinematic degeneracy with the spatially flat ΛCDM model via the cosmographic condition j=1 (j being the jerk parameter), which in turn fixes the function of the interaction term that is a priori unspecified. We argue that in General Relativity this cosmographic condition is consistent only with spatial flatness. Employing a dynamical system approach, we show that the spatially flat coupled fluid-fluid interacting models kinematically degenerate with ΛCDM must necessarily be based on a phantom fluid, whereas the set of physically viable spatially flat coupled quintessence models with power law or exponential potential kinematically degenerate to ΛCDM is of measure zero. Our analysis establishes that coupled fluid-fluid models with non-phantom fluids or coupled quintessence models with power law and exponential potential can never reproduce a cosmological evolution similar to that of the ΛCDM. The astrophysical consequences of our findings are qualitatively discussed in light of observational cosmological tensions.

Prediction of tandem cold-rolled strip flatness based on Attention-LSTM model

Flatness is a key quality indicator of tandem cold-rolled strip. Tandem cold-rolled production is a multi-stand simultaneous rolling process. The prediction of flatness is a typical spatial sequence data prediction problem by considering not only the complex generation mechanism but also the spatial dimension dependence. However, the currently available mechanistic and machine learning models for flatness prediction only focus on its highly nonlinear characteristics and ignore its complex spatial correlation. In addition, the over-parameterized “black box” nature of machine learning models has often been questioned. Based on this, a long-short-term memory model with an attention mechanism (Attention-LSTM) is proposed in this paper. The model is structured as a two-layer LSTM network to fully learn the highly nonlinear and complex spatial data correlation of tandem cold-rolled strip flatness. Furthermore, attention mechanisms are also added to the spatial dimension and flatness feature vector dimension, respectively, to enhance the interpretability of the model. The superiority of the proposed model is verified by comparing the error back propagation neural network model (BPNN), the extreme gradient boosting algorithm model (XGBoost), the deep neural network model (DNN), the LSTM model without the attention mechanism, and the Attention-LSTM model with the same dataset and the same optimum training method. The interpretation of the attention mechanism weights is consistent with the mechanistic model, which enhances the credibility of the model. The results of the ablative experiments also validate the effectiveness of incorporating the attention mechanism in the model.

Dark Energy as a Natural Property of Cosmic Polytropes—A Tutorial

A conventional approach to the dark energy (DE) concept is reviewed and discussed. According to it, there is absolutely no need for a novel DE component in the universe, provided that its matter–energy content is represented by a perfect fluid whose volume elements perform polytropic flows. When the (thermodynamic) energy of the associated internal motions is taken into account as an additional source of the universal gravitational field, it compensates the DE needed to compromise spatial flatness in an accelerating universe. The unified model which is driven by a polytropic fluid not only interprets the observations associated with universe expansion but successfully confronts all the current issues of cosmological significance, thus arising as a viable alternative to the ΛCDM model.

Testing spatial curvature and anisotropic expansion on top of the ΛCDM model

We explore the possible advantages of extending the $\Lambda$CDM model by more realistic backgrounds compared to its spatially flat RW spacetime assumption, while preserving the underpinning physics; in particular, by simultaneously allowing non-zero spatial curvature and anisotropic expansion on top of it, viz., the An-$o\Lambda$CDM model. This is to test whether the latest data support spatial flatness and/or isotropic expansion, and, if not, to explore the roles of spatial curvature and expansion anisotropy (due to its stiff fluid-like behavior) in addressing some of the cosmological tensions. We first present the theoretical background and explicit mathematical construction of An-$o\Lambda$CDM; combining the simplest anisotropic generalizations of the RW spacetime, viz., the Bianchi type I, V, and IX spacetimes. Then we constrain this model and its particular cases, viz., An-$\Lambda$CDM, $o\Lambda$CDM, and $\Lambda$CDM, by using the data sets from different probes, viz., Planck CMB(+Lens), BAO, SnIa Pantheon, and CC data, and discuss the results. Ultimately, we conclude that, within the setup under consideration, (i) the data confirm the spatial flatness and isotropic expansion, though a very small amount of present-day expansion anisotropy cannot be excluded, e.g., $\Omega_{\sigma0}\lesssim10^{-18}$ (95\% C.L.) for An-$\Lambda$CDM from CMB+Lens, (ii) the introduction of spatial curvature or anisotropic expansion, or both, on top $\Lambda$CDM does not offer a possible relaxation to the $H_0$ tension, and (iii) the introduction of anisotropic expansion neither affects the closed space prediction from CMB(+Lens) nor does it improve the drastically reduced value of $H_0$ led by the closed space. We discuss why it is important and indispensable to maintain the geometric generalization work program, especially in models that offer solutions to cosmological tensions. [abridged]

Revisiting the Hubble Constant, Spatial Curvature, and Cosmography with Strongly Lensed Quasar and Hubble Parameter Observations

It is well known that time delays due to strong lensing offer the opportunity of a one-step measurement of the Hubble constant H 0 that is independent of the cosmic distance ladder. In this paper, we go further and propose a cosmological model-independent approach to simultaneously determine the Hubble constant and cosmic curvature with measurements of the time delay due to strong lensing, without any prior assumptions regarding the content of the universe. The data we use comprise the recent compilation of six well studied strongly lensed quasars, while the cosmic chronometer data are utilized to reconstruct distances via cosmographic parameters. In the framework of third-order Taylor expansion and (2, 1) order Padé approximation for cosmographic analysis, our results provide model-independent estimations of the Hubble constant and , which are well consistent with that derived from the local distance ladder by the SH0ES collaboration. The measured cosmic curvature and shows that zero spatial curvature is supported by the current observations of time delays due to strong lensing and cosmic chronometers. Imposing the prior of spatial flatness leads to more precise (at 1.6% level) determinations of the Hubble constant and , values located between the results from Planck and the SH0ES collaboration. If a prior of local (SH0ES) H 0 measurement is adopted, the constraint on curvature parameter can be further improved to and , supporting no significant deviation from a flat universe. Finally, we also discuss the effectiveness of the Padé approximation in reconstructing the cosmic expansion history for redshifts up to z ∼ 2.3, considering its better performance in the Bayes information criterion.

Probing cosmological singularities with quantum fields: Open and closed FLRW universes

It was recently pointed out that linear quantum fields $\hat \phi(x)$ can be meaningfully propagated across the big bang (and the big crunch) singularities of spatially flat Friedmann, Lema\^itre, Robertson, Walker (FLRW) universes \cite{ADLS2021}. Recall that $\hat \phi(x)$, as well as renormalized observables $\langle\hat \phi(x)^2 \rangle_{ren}$ and $\langle \hat T_{ab}(x)\rangle_{ren}$, are distribution-valued already in Minkowskian quantum field theories. It was shown that they can be extended as well-defined distributions even when these space-times are enlarged to include the big-bang (or the big crunch). We generalize these results to spatially closed and open FLRW models, showing that this `tameness' of cosmological singularities is not an artifact of the technical simplifications due to spatial flatness. Our analysis also provides explicit expressions of $\langle\hat \phi(x) \hat \phi(x') \rangle_{ren}$, $\langle\hat \phi(x)^2 \rangle_{ren}$ and $\langle \hat T_{ab}(x)\rangle_{ren}$ in closed and open universes for minimally coupled massless scalar fields and discuss the ambiguities in the definition of $\langle \hat T_{ab}(x)\rangle_{ren}$ at the big-bang. While the technical expressions are more complicated than in the spatially flat case, there is also an unexpected conceptual simplification: the infrared divergence \cite{fp} is now absent because, in effect, the spatial curvature provides a natural cutoff. Finally, we further clarify the sense in which quantum field theory can continue to be well defined even though the extended space-time is not globally hyperbolic because of the singularity, and suggest directions for further work.

Exploring the Hubble Tension and Spatial Curvature from the Ages of Old Astrophysical Objects

Abstract We use the age measurements of 114 old astrophysical objects (OAO) in the redshift range 0 ≲ z ≲ 8 to explore the Hubble tension. The age of the universe at any z is inversely proportional to the Hubble constant, H 0, so requiring the universe to be older than the OAO it contains at any z will lead to an upper limit on H 0. Assuming flat ΛCDM and setting a Gaussian prior on the matter density parameter Ωm = 0.315 ± 0.007 informed by Planck, we obtain a 95% confidence level upper limit of H 0 < 70.6 km s−1 Mpc−1, representing a 2σ tension with the measurement using the local distance ladder. We find, however, that the inferred upper limit on H 0 depends quite sensitively on the prior for Ωm, and the Hubble tension between early-time and local measurements of H 0 may be due in part to the inference of both Ωm and H 0 in Planck, while the local measurement uses only H 0. The age-redshift data may also be used for cosmological model comparisons. We find that the R h = ct universe accounts well for the data, with a reasonable upper limit on H 0, while Einstein–de Sitter fails to pass the cosmic-age test. Finally, we present a model-independent estimate of the spatial curvature using the ages of 61 galaxies and the luminosity distances of 1048 Pantheon Type Ia supernovae. This analysis suggests that the geometry of the universe is marginally consistent with spatial flatness at a confidence level of 1.6σ, characterized as Ω k = 0.43 − 0.27 + 0.27 .

Constraining the curvature density parameter in cosmology

The cosmic curvature density parameter has been constrained in the present work independent of any background cosmological model. The reconstruction is performed adopting the non-parametric Gaussian Processes (GP). The constraints on $\Omega_{k0}$ are obtained via a Markov Chain Monte Carlo (MCMC) analysis. Late-time cosmological probes viz., the Supernova (SN) distance modulus data, the Cosmic Chronometer (CC) and the radial Baryon Acoustic Oscillations ($r$BAO) measurements of the Hubble data have been utilized for this purpose. The results are further combined with the data from redshift space distortions (RSD) which studies the growth of large scale structure in the universe. The only \textit{a priori} assumption is that the universe is homogeneous and isotropic, described by the FLRW metric. Results indicate that a spatially flat universe is well consistent in 2$\sigma$ within the domain of reconstruction $0<z<2$ for the background data. On combining the RSD data we find that the results obtained are consistent with spatial flatness mostly within 2$\sigma$ and always within 3$\sigma$ in the domain of reconstruction $0<z<2$.

Direct Estimate of the Post-Newtonian Parameter and Cosmic Curvature from Galaxy-scale Strong Gravitational Lensing

Abstract Einstein’s theory of general relativity (GR) has been precisely tested on solar system scales, but extragalactic tests are still poorly performed. In this work, we use a newly compiled sample of galaxy-scale strong gravitational lenses to test the validity of GR on kiloparsec scales. In order to solve the circularity problem caused by the presumption of a specific cosmological model based on GR, we employ the distance sum rule in the Friedmann–Lemaître–Robertson–Walker metric to directly estimate the parameterized post-Newtonian (PPN) parameter γ PPN and the cosmic curvature Ω k by combining observations of strong lensing and Type Ia supernovae. This is the first simultaneous measurement of γ PPN and Ω k without any assumptions about the contents of the universe or the theory of gravity. Our results show that γ PPN = 1.11 − 0.09 + 0.11 and Ω k = 0.48 − 0.71 + 1.09 , indicating a strong degeneracy between the two quantities. The measured γ PPN, which is consistent with the prediction of 1 from GR, provides a precise extragalactic test of GR with a fractional accuracy better than 9.0%. If a prior of the spatial flatness (i.e., Ω k = 0) is adopted, the PPN parameter constraint can be further improved to γ PPN = 1.07 − 0.07 + 0.07 , representing a precision of 6.5%. On the other hand, in the framework of GR (i.e., γ PPN = 1), our results are still marginally compatible with zero curvature ( Ω k = − 0.12 − 0.36 + 0.48 ), supporting no significant deviation from a flat universe.

Crustal strain-rate fields estimated from GNSS data with a Bayesian approach and its correlation to seismic activity in Mainland China

We propose a new Bayesian approach to estimate continuous crustal strain-rate fields from spatially discrete displacement-rate data, based on Global Navigation Satellite System (GNSS) observations, under the prior constraint on spatial flatness of the strain-rate fields. The optimal values of the hyperparameters in the model of strain-rate fields are determined by using Akaike's Bayesian Information Criterion. A methodological merit of this approach is that, by introducing a two-layer Delaunay tessellation technique, the time-consuming computation of strain rates can be omitted through the model estimation process. We apply the Bayesian approach to GNSS displacement-rate data in Mainland China to obtain a unique GNSS velocity field for sub-regions with different tectonic backgrounds. We also examine the correlation between the estimated strain-rate fields and seismic activity by using the Molchan Error Diagram. The results show that the rate of maximum shear strain is positively correlated with the occurrence of earthquakes, indicating the strain rate can be used to augment probabilistic earthquake models for background seismicity forecasting.

Simple-graduated dark energy and spatial curvature

In this work, we first discuss the possibility that dark energy models with negative energy density values in the past can alleviate the $H_0$ tension, as well as the discrepancy with the baryon acoustic oscillation (BAO) Lyman-$\alpha$ data, both which prevail within the $\Lambda$CDM model. We then investigate whether two minimal extensions of the $\Lambda$CDM model, together or separately, can successfully realize such a scenario: (i) the spatial curvature, which, in the case of spatially closed universe, mimics a negative density source and (ii) simple-graduated dark energy (gDE), which promotes the null inertial mass density of the usual vacuum energy to an arbitrary constant--if negative, the corresponding energy density decreases with redshift similar to the phantom models, but unlike them crosses below zero at a certain redshift. We find that, when the Planck data are not included in the observational analysis, the models with simple-gDE predict interesting and some significant deviations from the $\Lambda$CDM model. In particular, a spatially closed universe along with a simple-gDE of positive inertial mass density, which work in contrast to each other, results in minor improvement to the $H_0$ tension. The joint dataset, including the Planck data, presents no evidence for a deviation from spatial flatness but almost the same evidence for a cosmological constant and the simple-gDE with an inertial mass density of order $\mathcal{O}(10^{-12})\,\rm eV^4$. The latter case predicts almost no deviation from the $\Lambda$CDM model up until today--so that it results in no improvement regarding the BAO Ly-$\alpha$ data--except that it slightly aggravates the $H_0$ tension. We also study via dynamical analysis the history of the Universe in the models, as the simple-gDE results in futures different than the de Sitter future of the $\Lambda$CDM model.

Non-parametric spatial curvature inference using late-Universe cosmological probes

ABSTRACT Inferring high-fidelity constraints on the spatial curvature parameter, ΩK, under as few assumptions as possible, is of fundamental importance in cosmology. We propose a method to non-parametrically infer ΩK from late-Universe probes alone. Using Gaussian processes (GPs) to reconstruct the expansion history, we combine cosmic chronometers (CCs) 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 ΩK are free from parametric model assumptions for the expansion history and are insensitive to the overall calibration of both the CC and SNe Ia data (being sensitive only to relative distances and expansion rates). Applying this method to Pantheon SNe Ia and the latest compilation of CCs, we find ΩK = −0.03 ± 0.26, consistent with spatial flatness at the $\mathcal {O}(10^{-1})$ level, and independent of any early-Universe probes. Applying our methodology to future baryon acoustic oscillations and SNe Ia data from upcoming Stage IV surveys, we forecast the ability to constrain ΩK at the $\mathcal {O}(10^{-2})$ level.

Test of the cosmic distance duality relation for arbitrary spatial curvature

ABSTRACT The cosmic distance duality relation (CDDR), η(z) = (1 + z)2dA(z)/dL(z) = 1, is one of the most fundamental and crucial formulae in cosmology. This relation couples the luminosity and angular diameter distances, two of the most often used measures of structure in the Universe. We here propose a new model-independent method to test this relation, using strong gravitational lensing (SGL) and the high-redshift quasar Hubble diagram reconstructed with a Bézier parametric fit. We carry out this test without pre-assuming a zero spatial curvature, adopting instead the value ΩK = 0.001 ± 0.002 optimized by Planck in order to improve the reliability of our result. We parametrize the CDDR using η(z) = 1 + η0z, 1 + η1z + η2z2, and 1 + η3z/(1 + z), and consider both the SIS and non-SIS lens models for the strong lensing. Our best-fitting results are: $\eta _0=-0.021^{+0.068}_{-0.048}$, $\eta _1=-0.404^{+0.123}_{-0.090}$, $\eta _2=0.106^{+0.028}_{-0.034}$, and $\eta _3=-0.507^{+0.193}_{-0.133}$ for the SIS model, and $\eta _0=-0.109^{+0.044}_{-0.031}$ for the non-SIS model. The measured η(z), based on the Planck parameter ΩK, is essentially consistent with the value (=1) expected if the CDDR were fully respected. For the sake of comparison, we also carry out the test for other values of ΩK, but find that deviations of spatial flatness beyond the Planck optimization are in even greater tension with the CDDR. Future measurements of SGL may improve the statistics and alter this result but, as of now, we conclude that the CDDR favours a flat Universe.

Planck2018 results

We report on the implications for cosmic inflation of the 2018 release of thePlanckcosmic microwave background (CMB) anisotropy measurements. The results are fully consistent with those reported using the data from the two previousPlanckcosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles.Plancktemperature, polarization, and lensing data determine the spectral index of scalar perturbations to bens = 0.9649 ± 0.0042 at 68% CL. We find no evidence for a scale dependence ofns, either as a running or as a running of the running. The Universe is found to be consistent with spatial flatness with a precision of 0.4% at 95% CL by combiningPlanckwith a compilation of baryon acoustic oscillation data. ThePlanck95% CL upper limit on the tensor-to-scalar ratio,r0.002 &lt; 0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtainr0.002 &lt; 0.056. In the framework of standard single-field inflationary models with Einstein gravity, these results imply that: (a) the predictions of slow-roll models with a concave potential,V″(ϕ) &lt; 0, are increasingly favoured by the data; and (b) based on two different methods for reconstructing the inflaton potential, we find no evidence for dynamics beyond slow roll. Three different methods for the non-parametric reconstruction of the primordial power spectrum consistently confirm a pure power law in the range of comoving scales 0.005 Mpc−1 ≲ k ≲ 0.2 Mpc−1. A complementary analysis also finds no evidence for theoretically motivated parameterized features in thePlanckpower spectra. For the case of oscillatory features that are logarithmic or linear ink, this result is further strengthened by a new combined analysis including thePlanckbispectrum data. The newPlanckpolarization data provide a stringent test of the adiabaticity of the initial conditions for the cosmological fluctuations. In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3%, 1.7%, and 1.7% at 95% CL for cold dark matter, neutrino density, and neutrino velocity, respectively.Planckpower spectra plus lensing set constraints on the amplitude of compensated cold dark matter-baryon isocurvature perturbations that are consistent with current complementary measurements. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadupolar modulation of the primordial fluctuations. However, the polarization data do not support physical models for a scale-dependent dipolar modulation. All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.

The Mira-Titan Universe. III. Emulation of the Halo Mass Function

Abstract We construct an emulator for the halo mass function over group and cluster mass scales for a range of cosmologies, including the effects of dynamical dark energy and massive neutrinos. The emulator is based on the recently completed Mira-Titan Universe suite of cosmological N-body simulations. The main set of simulations spans 111 cosmological models with 2.1 Gpc boxes. We extract halo catalogs in the redshift range z = [0.0, 2.0] and for masses . The emulator covers an eight-dimensional hypercube spanned by { , , , σ 8, h, n s , w 0, w a }; spatial flatness is assumed. We obtain smooth halo mass functions by fitting piecewise second-order polynomials to the halo catalogs and employ Gaussian process regression to construct the emulator while keeping track of the statistical noise in the input halo catalogs and uncertainties in the regression process. For redshifts z ≲ 1, the typical emulator precision is better than 2% for and &lt;10% for . For comparison, fitting functions using the traditional universal form for the halo mass function can be biased at up to 30% at for z = 0. Our emulator is publicly available at https://github.com/SebastianBocquet/MiraTitanHMFemulator.

Creating spatial flatness by combining string gas cosmology and power law inflation

We show that it is possible to combine an early phase of String Gas Cosmology which can explain the origin of the observed structures on cosmological scales with a short later period of power law inflation which creates spatial flatness. The resulting model is consistent with the ``swampland criteria'' and the constraints coming from the {\it Trans-Planckian Censorship Conjecture}. Such a construction is not possible using only canonical slow-roll inflation, but it can emerge in the warm inflation scenario or in cold inflation with an exponential potential. The resulting cosmology is non-singular. We discuss the spectrum of cosmological perturbations resulting in our scenario. On large scales (scales which remain larger than the Hubble radius after the initial string gas phase) the spectrum is determined by the thermal string gas fluctuations set up in the primordial phase, and it is almost scale-invariant with a slight red tilt. On small scales, the perturbations produced during the inflationary phase dominate. On these scales, the spectrum is once again nearly scale-invariant. There is an intermediate range (scales which enter the Hubble radius during the period of inflation) where the string gas fluctuations are damped but continue to dominate over those produced during the period of inflation. On these scales the spectrum has a sharp red spectral index of $n_s - 1 \sim -2$.

Gravitational decoupling in cosmology

Abstract Whereas the nature of dark components in the Universe remains unknown, alternative models of gravity have been developed to offer a geometric explanation to the origin of such components. In this work we use the Minimal Geometric Deformation approach to study extensions of the theory of General Relativity in a cosmological context. This is possible since such approach allows the decoupling of gravitational sources, and the Einstein field equations can be analytically solved with the presence of a new gravitational sector once a known GR solution is considered. In particular, we implement such approach in Friedmann–Robertson–Walker and Kantowski–Sachs universes. We demonstrate that the gravitational decoupling leads to modifications of well known cosmological solutions. For instance, we show that an effective spatial curvature in the Friedmann–Robertson–Walker metric, as well as several kind of matter components in the Kantowski–Sachs case, are obtained. Thus, we found that it is possible to obtain spatial curvature and new matter terms from geometry, which in cosmology they could be useful in addressing problems such as the spatial flatness of the Universe, dark matter and dark energy.

Gaussian process estimation of transition redshift

This paper aims to put constraints on the transition redshift zt, which determines the onset of cosmic acceleration, in cosmological-model independent frameworks. In order to do that, we use the non-parametric Gaussian Process method with H(z) and SNe Ia data. The deceleration parameter reconstruction from H(z) data yields zt=0.59+0.12−0.11. The reconstruction from SNe Ia data assumes spatial flatness and yields zt=0.683+0.11−0.082. These results were found with a Gaussian kernel and we show that they are consistent with two other kernel choices.