Recently it has been noted by Di Valentino, Melchiorri and Silk (2019) that the enhanced lensing signal relative to that expected in the spatially flat $Λ$CDM model poses a possible crisis for the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) class of models usually used to interpret cosmological data. The 'crisis' amounts to inconsistencies between cosmological datasets arising when the FLRW curvature parameter $Ω_{k0}$ is determined from the data rather than constrained to be zero a priori. Moreover, the already substantial discrepancy between the Hubble parameter as determined by Planck and local observations increases to the level of $5σ$. While such inconsistencies might arise from systematic effects of astrophysical origin affecting the Planck Cosmic Microwave Background (CMB) power spectra at small angular scales, it is an option that the inconsistencies are due to the failure of the FLRW assumption. In this paper we recall how the FLRW curvature ansatz is expected to be violated for generic relativistic spacetimes. We explain how the FLRW conservation equation for volume-averaged spatial curvature is modified through structure formation, and we illustrate in a simple framework how the curvature tension in a FLRW spacetime can be resolved -- and is even expected to occur -- from the point of view of general relativity. Requiring early-time convergence towards a Friedmannian model with a spatial curvature parameter $Ω_{k0}$ equal to that preferred from the Planck power spectra resolves the Hubble tension within our dark energy-free model.
We compile a complete collection of reliable Hubble parameter $H(z)$ data to redshift $z \leq 2.36$ and use them with the Gaussian Process method to determine continuous $H(z)$ functions for various data subsets. From these continuous $H(z)$'s, summarizing across the data subsets considered, we find $H_0\sim 67 \pm 4\,\rm km/s/Mpc$, more consistent with the recent lower values determined using a variety of techniques. In most data subsets, we see a cosmological deceleration-acceleration transition at 2$σ$ significance, with the data subsets transition redshifts varying over $0.33<z_{\rm da}<1.…
The measurements of the Hubble constant reveal a tension between high-redshift (CMB) and low-redshift (distance ladder) constraints. So far neither observational systematics nor new physics has been successfully implemented to explain this tension away. This paper present a new solution to the Hubble constant problem. The solution is based on the Simsilun simulation (relativistic simulation of the large scale structure of the Universe) with the ray-tracing algorithm implemented. The initial conditions for the Simsilun simulation were set up as perturbations around the $Λ$CDM model. However, un…
Although the Hubble constant $H_0$ and spatial curvature $Ω_{K}$ have been measured with very high precision, they still suffer from some tensions. In this paper, we propose an improved method to combine the observations of ultra-compact structure in radio quasars and strong gravitational lensing with quasars acting as background sources to determine $H_0$ and $Ω_{K}$ simultaneously. By applying the distance sum rule to the time-delay measurements of 7 strong lensing systems and 120 intermediate-luminosity quasars calibrated as standard rulers, we obtain stringent constraints on the Hubble con…
Cosmic microwave background (CMB) anisotropy (spatial inhomogeneity) data provide the tightest constraints on the Hubble constant, matter density, spatial curvature, and dark energy dynamics. Other data, sensitive to the evolution of only the spatially homogeneous part of the cosmological model, such as Type Ia supernova apparent magnitude, baryon acoustic oscillation distance, and Hubble parameter measurements, can be used in conjunction with the CMB data to more tightly constrain parameters. Recent joint analyses of CMB and such non-CMB data indicate that slightly closed spatial hypersurface…
There exist two kinds of stochastic gravitational-wave backgrounds associated with the primordial curvature perturbations. One is called induced gravitational wave due to the nonlinear coupling of curvature perturbations to tensor perturbations, while the other is produced by coalescences of binary primordial black holes formed when the large amplitude curvature perturbations reenter the horizon in the radiation dominant era. In this paper we find a quite useful relation for the peak frequencies of these two stochastic gravitational-wave backgrounds. This relation can not only offer a smoking-…
We use Pantheon Type Ia supernova (SN Ia) apparent magnitude, DES-3yr binned SN Ia apparent magnitude, Hubble parameter, and baryon acoustic oscillation measurements to constrain six spatially flat and non-flat cosmological models. These sets of data provide mutually consistent cosmological constraints in the six cosmological models we study. A joint analysis of these data sets provides model-independent estimates of the Hubble constant, $H_0=68.8\pm1.8\ \rm{km \ s^{-1} \ Mpc^{-1}}$, and the non-relativistic matter density parameter, $Ω_{\rm m_0}=0.294\pm0.020$. Although the joint constraints …
In this paper we use all available baryon acoustic oscillation, Hubble parameter, and quasar angular size data to constrain six dark energy cosmological models, both spatially flat and non-flat. Depending on the model and data combination considered, these data mildly favor closed spatial hypersurfaces (by as much as $1.7σ$) and dark energy dynamics (up to a little over $2σ$) over a cosmological constant $Λ$. The data also favor, at $1.8σ$ to $3.4σ$, depending on the model and data combination, a lower Hubble constant than what is measured from the local expansion rate.
We propose an analytical parametrization of the comoving distance and Hubble parameter to study the cosmic expansion history beyond the vanilla $Λ$CDM model. The parametrization is generalized enough to include the contribution of spatial curvature and to capture the higher redshift behaviors. With this parameterization, we study the late time cosmic behavior and put constraints on the cosmological parameters like present values of Hubble parameter ($H_{0}$), matter energy density parameter ($Ω_{m0}$), spatial curvature energy density parameter ($Ω_{k0}$) and baryonic matter energy density par…
We consider general, non-linear curvature perturbations on scales greater than the Hubble horizon scale by invoking an expansion in spatial gradients, the so-called gradient expansion. After reviewing the basic properties of the gradient expansion, we derive the conservation law for non-linear curvature perturbations for an isentropic fluid. We also define the gauge-invariant curvature perturbation under a finite shift of time-slicing, and derive the non-linear genralization of the $δN$ formalism. The results obtained are straight-forward generalisations of those already proven in linear pertu…
We use all available baryon acoustic oscillation distance measurements and Hubble parameter data to constrain the cosmological constant $Λ$, dynamical dark energy, and spatial curvature in simple cosmological models. We find that the consensus spatially flat $Λ$CDM model provides a reasonable fit to the data, but depending on the Hubble constant prior and cosmological model, it can be a little more than 1$σ$ away from the best-fit model, which can favor mild dark energy dynamics or non-flat spatial hypersurfaces.
We use the age measurements of 114 old astrophysical objects (OAO) in the redshift range $0\lesssim z\lesssim 8$ 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 $Λ$CDM and setting a Gaussian prior on the matter density parameter $Ω_{\rm m}=0.315\pm0.007$ informed by {\it Planck}, we obtain a 95\% confidence-level upper limit of $H_0<70.6 \rm{~km} \rm{~s}^{-1} \rm{~Mpc}^{-1}$, representing a $2σ$ …
We compile an updated list of 38 measurements of the Hubble parameter $H(z)$ between redshifts $0.07 \leq z \leq 2.36$ and use them to place constraints on model parameters of constant and time-varying dark energy cosmological models, both spatially flat and curved. We use five models to measure the redshift of the cosmological deceleration-acceleration transition, $z_{\rm da}$, from these $H(z)$ data. Within the error bars, the measured $z_{\rm da}$ are insensitive to the model used, depending only on the value assumed for the Hubble constant $H_0$. The weighted mean of our measurements is $z…
In this paper we consider an holographic model of dark energy, where the length scale is the Hubble radius, in a non flat geometry. The model contains the possibility to alleviate the cosmic coincidence problem, and also incorporate a mechanism to obtain the transition from decelerated to an accelerated expansion regime. We derive an analytic form for the Hubble parameter in a non flat universe, and using it, we perform a Bayesian analysis of this model using SNIa, BAO and CMB data. We find from this analysis that the data favored a small value for $Ω_k$, however high enough to still produce c…
We examine systematically the (in)consistency between cosmological constraints as obtained from various current data sets of the expansion history, Large Scale Structure (LSS), and Cosmic Microwave Background (CMB) from Planck. We run (dis)concordance tests within each set and across the sets using a recently introduced index of inconsistency (IOI) capable of dissecting inconsistencies between two or more data sets. First, we compare the constraints on $H_0$ from five different methods and find that the IOI drops from 2.85 to 0.88 (on Jeffreys' scales) when the local $H_0$ measurements is remo…
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…
We study cosmological perturbations in two-field inflation, allowing for non-standard kinetic terms. We calculate analytically the spectra of curvature and isocurvature modes at Hubble crossing, up to first order in the slow-roll parameters. We also compute numerically the evolution of the curvature and isocurvature modes from well within the Hubble radius until the end of inflation. We show explicitly for a few examples, including the recently proposed model of `roulette' inflation, how isocurvature perturbations affect significantly the curvature perturbation between Hubble crossing and the …
In this work, we achieve the determination of the cosmic curvature $Ω_K$ in a cosmological model-independent way, by using the Hubble parameter measurements $H(z)$ and type Ia supernovae (SNe Ia). In our analysis, two nonlinear interpolating tools are used to reconstruct the Hubble parameter, one is the Artificial Neural Network (ANN) method, and the other is the Gaussian process (GP) method. We find that $Ω_K$ based on the GP method can be greatly influenced by the prior of $H_0$, while the ANN method can overcome this. Therefore, the ANN method may have more advantages than GP in the measure…
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…
We obtain the reduced CMB data $\{l_A, R, z_*\}$ from WMAP9, WMAP9+BICEP2, Planck+WP and Planck+WP+BICEP2 for the $Λ$CDM and $w$CDM models with or without spatial curvature. We then use these reduced CMB data in combination with low-redshift observations to put constraints on cosmological parameters. We find that including BICEP2 results in a higher value of the Hubble constant especially when the equation of state of dark energy and curvature are allowed to vary. For the $Λ$CDM model with curvature, the estimate of the Hubble constant with Planck+WP+Lensing is inconsistent with the one derive…
Nowadays, according to the observational evidences the curvature parameter of the universe is neglected and spatially flat FLRW model is on the top of interest for cosmologists. However, due to some discrepancies between $Λ$-CDM model anticipations and observations, one may think out the curvature parameter as the solution even though it may be very small. So, in this article we investigate the eras in which the curvature influence was or is more significant. In addition, a geometrical interpretation of Hubble parameter is dedicated. We find that the Hubble parameter is more appropriate to be …
Strongly lensed type Ia supernovae (SNe Ia) are expected to have some advantages in measuring time delays of multiple images, and so they have a great potential to be developed into a powerful late-universe cosmological probe. In this paper, we simulate a sample of lensed SNe Ia with time-delay measurements in the era of the Legacy Survey of Space and Time (LSST). Based on the distance sum rule, we use lensed SNe Ia to implement model-independent constraints on the Hubble constant $H_0$ and cosmic curvature parameter $Ω_K$ in the late universe. We find that if 20 lensed SNe Ia could be observe…
Using the reconstruction technique with an auxiliary field, we investigate which $F(R)$ gravities can produce the matter bounce cosmological solutions. Owing to the specific functional form of the matter bounce Hubble parameter, the reconstruction technique leads, after some simplifications, to the same Hubble parameter as in the matter bounce scenario. Focusing the study to the large and small cosmic time $t$ limits, we were able to find which $F(R)$ gravities can generate the matter bounce Hubble parameter. In the case of small cosmic time limit, which corresponds to large curvature values, …
We generalize the effective potential to scalar field configurations which are proportional to the Hubble parameter of a homogeneous and isotropic background geometry. This may be useful in situations for which curvature effects are significant. We evaluate the one loop contribution to the Hubble Effective Potential for a massless scalar with arbitrary conformal and quartic couplings, on a background for which the deceleration parameter is constant. Among other things, we find that inflationary particle production leads to symmetry restoration at late times.
A $Λ$CDM Extension Explaining the Hubble Tension and the Spatial Curvature $Ω_{k,0} = -0.012 \pm 0.010$ Measured by the Final PR4 of the Planck Mission
In this paper, we propose an improved model-independent method to constrain the cosmic curvature by combining the most recent Hubble parameter $H(z)$ and supernovae Ia (SNe Ia) data. Based on the $H(z)$ data, we first use the model-independent smoothing technique, Gaussian processes, to construct distance modulus $μ_{H}(z)$, which is susceptible to the cosmic curvature parameter $Ω_{k}$. In contrary to previous studies, the light-curve fitting parameters, which account for distance estimation of SN ($μ_{SN}(z)$), are set free to investigate whether $Ω_{k}$ has a dependence on them. By comparin…
We present the luminosity distance series expansion to third order in redshift for a general space-time with no assumption on the metric tensor or the field equations prescribing it. It turns out that the coefficients of this general 'Hubble law' can be expressed in terms of a finite number of physically interpretable multipole coefficients. The multipole terms can be combined into effective direction dependent parameters replacing the Hubble constant, deceleration parameter, curvature parameter, and 'jerk' parameter of the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) class of metrics. Due to …
We consider a DGP inspired brane scenario where the action on the brane is augmented by a function of the Ricci scalar, ${\cal L}(R)$. The cosmological implications that such a scenario entails are examined for $R^{n}$ and shown to be consistent with a universe expanding with power-law acceleration. It is shown that two classes of solutions exist for the usual FRW metric and small Hubble radii. When the Hubble radius becomes larger, we either have a transition to a fully 5D regime or to a self-inflationary solution which produces a late accelerated expansion such that the radius becomes a func…
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 introduce a weighed scalar average formalism ("q-average") for the study of the theoretical properties and the dynamics of spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models models. The "q-scalars" that emerge by applying the q-averages to the density, Hubble expansion and spatial curvature (which are common to FLRW models) are directly expressible in terms of curvature and kinematic invariants and identically satisfy FLRW evolution laws without the back-reaction terms that characterize Buchert's average. The local and non-local fluctuations and perturbations with respect to the …
Lensing amplitude anomaly and varying electron mass alleviate the Hubble and $S_8$ tensions
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台暗物质与空间天文重点实验室）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）
We present an holographic model of the Dvali-Gabadadze-Porrati scenario with a Gauss-Bonnet term in the bulk. We concentrate on the solution that generalises the normal Dvali-Gabadadze-Porrati branch. It is well known that this branch cannot describe the late-time acceleration of the universe even with the inclusion of a Gauss-Bonnet term. Here, we show that this branch in the presence of a Gauss-Bonnet curvature effect and an holographic dark energy with the Hubble scale as the infra-red cutoff can describe the late-time acceleration of the universe. It is worthwhile to stress that such an en…
Consistency between cosmological data sets is essential for ongoing and future cosmological analyses. We first investigate the questions of stability and applicability of some moment-based inconsistency measures to multiple data sets. We show that the recently introduced index of inconsistency (IOI) is numerically stable while it can be applied to multiple data sets. We use an illustrative construction of constraints as well as an example with real data sets (i.e. WMAP versus Planck) to show some limitations of the application of the Karhunen-Loeve decomposition to discordance measures. Second…
In this paper we extend a new method to measure possible variation of the speed of light by using Baryon Acoustic Oscillations and the Hubble function presented in our earlier paper [V. Salzano, M. P. Dcabrowski, and R. Lazkoz, Phys. Rev. D93, 063521 (2016)] onto an inhomogeneous model of the universe. The method relies on the fact that there is a simple relation between the angular diameter distance $(D_{A})$ maximum and the Hubble function $(H)$ evaluated at the same maximum-condition redshift, which includes speed of light $c$. One limit of such method was the assumption of null spatial cur…
In this work, we apply the smooth deformation concept in order to obtain a modification of Friedmann equations. It is shown that the cosmic coincidence can be at least alleviated using the dynamical properties of the extrinsic curvature. We investigate the transition from nucleosynthesis to the coincidence era obtaining a very small variation of the ratio $r=\frac{ρ_{m}}{ρ_{ext}}$, that compares the matter energy density to extrinsic energy density, compatible with the known behavior of the deceleration parameter. We also show that the calculated "equivalence" redshift matches the transition r…
We review the dynamics of spectator scalar fields non-minimally coupled to gravity in the post-inflationary Universe, with particular emphasis on scenarios where the end of inflation is followed by a period of kination. In this context, the evolution of the Ricci scalar can lead to the spontaneous breaking of discrete or continuous symmetries through tachyonic instabilities. These Hubble-induced phase transitions may cause the amplification of field fluctuations, the formation of transient topological defects, and an efficient energy transfer into relativistic degrees of freedom. We analyze th…
The recent observations of gravitational-wave and electromagnetic emission produced by the merger of the binary neutron-star system GW170817 have opened the possibility of using standard sirens to constrain the value of the Hubble constant. While the reported bound of $H_0=70_{-8}^{+12}$ at $68 \%$ C.L. is significantly weaker than those recently derived by observations of Cepheid variables, it does not require any form of cosmic distance ladder and can be considered as complementary and, in principle, more conservative. Here we combine, for the first time, the new measurement with the Planck …
We use updated Hubble parameter and baryon acoustic oscillation data, as well as other lower-redshift Type Ia supernova, Mg II reverberation-measured quasar, quasar angular size, H II starburst galaxy, and Amati-correlated gamma-ray burst data, to jointly constrain cosmological parameters in six cosmological models. The joint analysis provides model-independent determinations of the Hubble constant, $H_0=69.7\pm1.2$ $\rm{km \ s^{-1} \ Mpc^{-1}}$, and the current non-relativistic matter density parameter, $Ω_{m0}=0.295\pm0.017$. These error bars are factors of 2.2 and 2.3 larger than the corres…
A second-order expansion for the quantum fluctuations of the matter field was considered in the framemork of the warm inflation scenario. The friction and Hubble parameters were expanded by means of a semiclassical approach. The fluctuations of the Hubble parameter generates fluctuations of the metric. These metric fluctuations produce an effective term of curvature. The power spectrum for the metric fluctuations can be calculated on the infrared sector.
A second-order expansion for the quantum fluctuations of the matter field was considered in the framework of the warm inflation scenario. The friction and Hubble parameters were expended by means of a semiclassical approach. The fluctuations of the Hubble parameter generates fluctuations of the metric. These metric fluctuations produce an effective term of curvature. The power spectrum for the metric fluctuations can be calculated on the infrared sector.
The last decade has seen increasing efforts to circumscribe and bound the cosmological Hubble flow in terms of model-independent constraints on the cosmological fluid - such as, for instance, the classical energy conditions of general relativity. Quite a bit can certainly be said in this regard, but much more refined bounds can be obtained by placing more precise constraints (either theoretical or observational) on the cosmological fluid. In particular, the use of the w-parameter (w=p/rho) has become increasingly common as a surrogate for trying to say something about the cosmological equation…
We study the dynamics and perturbations during inflation and reheating in a multi-field model where a second scalar field $χ$ is nonminimally coupled to the scalar curvature $(\frac12 ξRχ^2$). When $ξ$ is positive, the usual inflationary prediction for large-scale anisotropies is hardly altered while the $χ$ fluctuation in sub-Hubble modes can be amplified during preheating for large $ξ$. For negative values of $ξ$, however, long-wave modes of the $χ$ fluctuation exhibit exponential increase during inflation, leading to the strong enhancement of super-Hubble metric perturbations even when $|ξ|…
We analyze how predictions of cosmological models depend on a choice of described observational data, restrictions on flatness, and how this choice can alleviate the $H_0$ tension. These effects are demonstrated in the $w$CDM model in comparison with the standard $Λ$CDM model. We describe the Pantheon sample observations of Type Ia supernovae, 31 Hubble parameter data points $H(z)$ from cosmic chronometers, the extended sample with 57 $H(z)$ data points and observational manifestations of cosmic microwave background radiation (CMB). For the $w$CDM and $Λ$CDM models in the flat case and with sp…
In this paper we derive a generic expression, which is valid for scales larger than Hubble radius and contains only the local terms, for the second order curvature perturbations for more than one field, provided the expansion is sourced by the energy density of a single field. As an application, motivated by our previous paper [1], we apply our formalism to two fields during preheating, where the inflaton oscillations are sourced by $λϕ^4$ potential which is governing the expansion of the Universe. A second field $σ$, coupled to the inflaton through $g^2ϕ^2σ^2$, is excited from the vacuum fluc…
