Abstract: The recent analysis of low-redshift supernovae (SN) has increased the apparent tension between the value of H0 estimated from low and high redshift observations such as the cosmic microwave background (CMB) radiation. At the same time other observations have provided evidence of the existence of local radial inhomogeneities extending in different directions up to a redshift of about 0.07. About 40% of the Cepheids used for SN calibration are directly affected because they are located along the directions of these inhomogeneities. We compute with different methods the effects of these inhomogeneities on the low-redshift luminosity and angular diameter distance using an exact solution of the Einstein’s equations, linear perturbation theory and a low-redshift expansion. We confirm that at low redshift the dominant effect is the nonrelativistic Doppler redshift correction, which is proportional to the volume averaged density contrast and to the comoving distance from the center. We derive a new simple formula...

Abstract: The cosmic distance duality relation (DDR), which connects the angular diameter distance and luminosity distance through a simple formula $D_A(z)(1+z)^2/D_L(z)\equiv1$, is an important relation in cosmology. Therefore, testing the validity of DDR is of great importance. In this paper, we test the possible violation of DDR using the available local data including type Ia supernovae (SNe Ia), galaxy clusters and baryon acoustic oscillations (BAO). We write the modified DDR as $D_A(z)(1+z)^2/D_L(z)=\eta(z)$, and consider two different parameterizations of $\eta(z)$, namely $\eta_1(z)=1+\eta_0 z$ and $\eta_2(z)=1+\eta_0 z/(1+z)$. The luminosity distance from SNe Ia are compared with the angular diameter distance from galaxy clusters and BAO at the same redshift. Two different cluster data are used here, i.e. elliptical clusters and spherical clusters. The parameter $\eta_0$ is obtained using the Markov chain Monte Carlo methods. It is found that $\eta_0$ can be strictly constrained by the elliptical clusters + BAO data, with the best-fitting values $\eta_0=-0.04\pm 0.12$ and $\eta_0=-0.05\pm 0.22$ for the first and second parametrizations, respectively. However, the spherical clusters + BAO data couldn't strictly constrain $\eta_0$ due to the large intrinsic scatter. In any case studied here, no evidence for the violation of DDR is found.

Abstract: Future gravitational wave (GW) observations are capable of detecting millions of compact star binary mergers in extragalactic galaxies, with $1\%$ luminosity-distance ($D_L$) measurement accuracy and better than arcminute positioning accuracy. This will open a new window of the large scale structure (LSS) of the universe, in the 3D {\bf luminosity-distance space (LDS)}, instead of the 3D redshift space of galaxy spectroscopic surveys. The baryon acoustic oscillation and the AP test encoded in the LDS LSS constrain the $D_L$-$D^{\rm co}_A$ (comoving angular diameter distance) relation and therefore the expansion history of the universe. Peculiar velocity induces the LDS distortion, analogous to the redshift space distortion, and allows for a new structure growth measure $f_L\sigma_8$. When the distance duality is enforced ($1+z=D_L/D^{\rm co}_A$), the LDS LSS by itself determines the redshift to $\sim 1\%$ level accuracy, and alleviates the need of spectroscopic follow-up of GW events.But a more valuable application is to test the distance duality to $1\%$ level accuracy, in combination with conventional BAO and supernovae measurements. This will put stringent constraints on modified gravity models in which the gravitational wave $D^{\rm GW}_L$ deviates from the electromagnetic wave $D^{EM}_L$. All these applications require no spectroscopic follow-ups.

Abstract: The ΛCDM model of cosmology assumes the existence of an exotic component, called dark energy, to explain the late-time acceleration of the expansion of the universe at redshift z < 0.7. Alternative scenarios to this cosmological constant suggest to modify the theory of gravitation based on general relativity at cosmological scales. Since fall 2014, the SDSS-IV eBOSS multi-object spectrograph has undertaken a survey of quasars in the almost unexplored redshift range 0.8 ≤ z ≤ 2.2 with the key science goal to complement the constraints on dark energy and extend the test of general relativity at higher redshifts by using quasars as direct tracers of the matter field.In this thesis work, we measure and analyse the two-point correlation function of the two-year data taking of eBOSS quasar sample to constrain the cosmic distances, i.e. the angular diameter distance DA and the expansion rate H, and the growth rate of structure fσ8 at an effective redshift Zeff = 1.52. First, we build large-scale structure catalogues that account for the angular and radial incompleteness of the survey. Then to obtain robust results, we investigate several potential systematics, in particular modeling and observational systematics are studied using dedicated mock catalogs which are fictional realizations of the data sample. These mocks are created with known cosmological parameters such that they are used as a benchmark to test the analysis pipeline. The results on the evolution of distances are consistent with the predictions for ΛCDM with Planck parameters assuming a cosmological constant. The measurement of the growth of structure is consistent with general relativity and hence extends its validity to higher redshift. We also provide updated constraints on extensions of ΛCDM and models of modified gravity. This study is a first use of eBOSS quasars as tracers of the matter field and will be included in the analysis of the final eBOSS sample at the end of 2019 with an expected improvement on the statistical precision of a factor 2. Together with BOSS, eBOSS will pave the way for future programs such as the ground-based Dark Energy Spectroscopic Instrument (DESI) and the space-based mission Euclid. Both programs will extensively probe the intermediate redshift range 1 < z < 2 with millions of spectra, improving the cosmological constraints by an order of magnitude with respect to current measurements.

Abstract: 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 fields generated by Fisher information metric from the probability distributions p and q of the entropies carried by their quanta, respectively. This model of the quantum structure of the spacetime determines a specific form of the dynamical terms of Dark Energy and Dark Matter and predicts the existence of a new "residual" matter term with equation of state w_r=-1/3. This term plays a role of a curvature term in the Hubble function with negative curvature k=-1. Its consistency with the curvature term in the Robertson-Walker metric then predicts a positive present curvature density \Omega_{c,0} which places constraints on the cosmological parameters. In this work we test these predictions in fits to the Hubble data and angular diameter distance data. The fits confirm all predictions and support our model of the quantum structure of the spacetime.

Abstract: The latest Planck results on the power spectrum of the Compton-$y$ parameter are the most accurate probe of the thermal Sunyaev Zeldovich (tSZ) effect caused by resolved and un-resolved clusters of galaxies. On large angular scales, the power spectrum amplitude is mostly due to the statistical distribution of clusters in the sky and therefore is an indirect probe of the clustering of matter, $\sigma_8$, as well as the angular diameter distance that depends on other cosmological parameters such as the Hubble parameter, $h$, and the matter density $\Omega_m$. Here I discuss the constraining power of the tSZ power spectrum, in light of the Planck Compton-$y$ map data, and our current understanding and measurements of the intra-cluster medium.

Abstract: We investigate the propagation of light rays and evolution of optical scalars in gauge theories of gravity where torsion is present. Recently the modified Raychaudhuri equation in the presence of torsion has been derived. We use this result to derive the basic equations of geometric optics for several different interesting solutions of the Poincar{e} gauge theory of gravity. The results show that the focusing effects for neighboring light rays will be different than general relativity. This in turn has practical consequences in the study of gravitational lensing effects and also determining the angular diameter distance for cosmological objects.

Abstract: We explore the cosmological implications of anisotropic clustering measurements of the quasar sample from Data Release 14 (DR14) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) in configuration space. The ~147 000 quasar sample observed by eBOSS offers a direct tracer of the density field and bridges the gap of previous baryon acoustic oscillation measurements between redshift 0.8 < z < 2.2. By analysing the two-point correlation function characterized by clustering wedges ξ (s) and multipoles ξl(s), we measure the angular diameter distance, Hubble parameter, and cosmic structure growth rate. We define a systematic error budget for our measurements based on the analysis of N-body simulations and mock catalogues. Based on the DR14 large-scale structure quasar sample at the effective redshift z = 1.52, we find the growth rate of cosmic structure fσ(z) = 0.396 ± 0.079, and the geometric parameters D(z)/r = 26.47 ± 1.23, and FAP(z) = 2.53 ± 0.22, where the uncertainties include both statistical and systematic errors. These values are in excellent agreement with the best-fitting standard Λ cold dark matter model to the latest cosmic microwave background data from Planck.

Abstract: We test the possible deviation of the cosmic distance duality relation D_A(z)(1 + z)^2/D_L(z) ≡ 1 using the standard candles/rulers in a fully model-independent manner. Type Ia supernovae are used as the standard candles to derive the luminosity distance D_L(z), and ultracompact radio sources are used as the standard rulers to obtain the angular diameter distance D_A(z). We write the deviation of distance duality relation as D_A(z)(1 + z)^2/D_L(z) = η(z). Specifically, we use two parametrizations of η(z), i.e. η_1(z) = 1 + η_0z and η_2(z) = 1 + η_0z/(1 + z). The parameter η_0 is obtained using the Markov chain Monte Carlo methods by comparing D_L(z) and D_A(z) at the same redshift. The best-fitting results are η_0 = −0.06 ± 0.05 and −0.18 ± 0.16 for the first and second parametrizations, respectively. Our results depend on neither the cosmological models nor the matter contents or the curvature of the Universe.

Abstract: Of all the distance and temporal measures in cosmology, the angular-diameter distance, d_A(z), uniquely reaches a maximum value at some finite redshift z_max and then decreases to zero towards the big bang. This effect has been difficult to observe due to a lack of reliable, standard rulers, though refinements to the identification of the compact structure in radio quasars may have overcome this deficiency. In this Letter, we assemble a catalog of 140 such sources with 0 < z < 3 for model selection and the measurement of z_max. In flat LCDM, we find that Omega_m= 0.24^{+0.1}_{-0.09}, fully consistent with Planck, with z_max=1.69. Both of these values are associated with a d_A(z) indistinguishable from that predicted by the zero active mass condition, rho+3p=0, in terms of the total pressure p and total energy density rho of the cosmic fluid. An expansion driven by this constraint, known as the R_h=ct universe, has z_max=1.718, which differs from the measured value by less than ~1.6%. Indeed, the Bayes Information Criterion favours R_h=ct over flat LCDM with a likelihood of ~81% versus 19%, suggesting that the optimized parameters in Planck LCDM mimic the constraint p=-rho/3.

Abstract: We propose an $f(T)$ teleparallel gravity theory including a torsional infrared (IR) correction. We show that the governing Friedmann's equations of a spatially flat universe include a phantom-like effective dark energy term sourced by the torsion IR correction. As has been suggested, this phantom phase does indeed act as to reconcile the tension between local and global measurements of the current Hubble value $H_0$. The resulting cosmological model predicts an electron scattering optical depth $\tau_e\thickapprox 0.058$ at reionization redshift $z_{re} \sim 8.1$, in agreement with observations. The predictions are however in contradiction with baryon acoustic oscillations (BAO) measurements, particularly the distance indicators. We argue that this is the case with any model with a phantom dark energy model that has effects significant enough at redshifts $z \lesssim 2$ as to be currently observable. The reason being that such a scenario introduces systematic differences in terms of distance estimates in relation to the standard model; e.g., if the angular diameter distance to the recombination era is to be kept constant while $H_0$ is increased in the context of a phantom scenario, the distances there are systematically overestimated to all objects at redshifts smaller than recombination. But no such discrepancies exist between $\Lambda$CDM predictions and current data for $z \lesssim 2$.

Abstract: We study observational consequences of the model for dark energy proposed in [1] (Aoki et al., Phys.Rev. D97 (2018) no.4, 043517). We assume our universe has been created by bubble nucleation, and consider quantum fluctuations of an ultralight scalar field. Residual effects of fluctuations generated in an ancestor vacuum (de Sitter space in which the bubble was formed) is interpreted as dark energy. Its equation of state parameter w(z) has a characteristic form, approaching -1 in the future, but -1/3 in the past. A novel feature of our model is that dark energy effectively increases the magnitude of the negative spatial curvature in the evolution of the Hubble parameter, though it does not alter the definition of the angular diameter distance. We perform Fisher analysis and forecast the constraints for our model from future galaxy surveys by Square Kilometre Array and Euclid. Due to degeneracy between dark energy and the spatial curvature, galaxy surveys alone can determine these parameters only for optimistic choices of their values, but combination with other independent observations, such as CMB, will greatly improve the chance of determining them.

Abstract: Unlike other observational signatures in cosmology, the angular-diameter distance d_A(z) uniquely reaches a maximum (at z_max) and then shrinks to zero towards the big bang. The location of this turning point depends sensitively on the model, but has been difficult to measure. In this paper, we estimate and use z_max inferred from quasar cores: (1) by employing a sample of 140 objects yielding a much reduced dispersion due to pre-constrained limits on their spectral index and luminosity, (2) by reconstructing d_A(z) using Gaussian processes, and (3) comparing the predictions of seven different cosmologies and showing that the measured value of z_max can effectively discriminate between them. We find that z_max=1.70 +\- 0.20---an important new probe of the Universe's geometry. The most strongly favoured model is R_h=ct, followed by Planck LCDM. Several others, including Milne, Einstein-de Sitter and Static tired light are strongly rejected. According to these results, the R_h=ct universe, which predicts z_max=1.718, has a ~92.8% probability of being the correct cosmology. For consistency, we also carry out model selection based on d_A(z) itself. This test confirms that R_h=ct and Planck LCDM are among the few models that account for angular-size data better than those that are disfavoured by z_max. The d_A(z) comparison, however, is less discerning than that with z_max, due to the additional free parameter, H_0. We find that H_0=63.4 +\- 1.2 km/s/Mpc for R_h=ct, and 69.9 +\- 1.5 km/s/Mpc for LCDM. Both are consistent with previously measured values in each model, though they differ from each other by over 4 sigma. In contrast, model selection based on z_max is independent of H_0.

Abstract: In this paper, we test the cosmic distance–duality (CDD) relation using the luminosity distances from joint light-curve analysis Type Ia supernovae (SNe Ia) sample and angular diameter distance sample from galaxy clusters. The R_h = ct and Λ cold dark matter (CDM) models are considered. In order to compare the two models, we constrain the CDD relation and the SNe Ia light-curve parameters simultaneously. Considering the effects of Hubble constant, we find that η ≡ D_A(1 + z)^2/D_L = 1 is valid at the 2σ confidence level in both models with H_0= 67.8 ± 0.9 km ^−1s^−1 Mpc. However, the CDD relation is valid at 3σ confidence level with H_0= 73.45 ± 1.66 km ^−1s^−1Mpc. Using the Akaike Information Criterion and the Bayesian Information Criterion, we find that the ΛCDM model is very stongly preferred over the R_h = ct model with these data sets for the CDD relation test.

Abstract: In order to clarify the tension between estimates of the Hubble Constant (H0) from local (z ≪ 1) and global (z ≫ 1) measurements, Lima and Cunha (LC) proposed a new method to measure H0 in intermediate redshifts (z ≈ 1), which were obtained H0 = 74.1 ± 2.2 km s− 1Mpc− 1 (1σ), in full agreement to local measurements via Supernovae/Cepheid dataset. However, Holanda et al. (Month. Not. R. Astronom. Soc. Lett. 443(1) L74–L78 (2014)) affirm that a better understanding of the morphology of galaxy clusters in LC framework is needed to a more robust and accurate determination of H0. Moreover, that kind of sample has been strongly questioned in the literature. In this context, (i) we investigated if the sample of galaxy clusters used by LC has a relevant role in their results, then (ii) we perform a more accurate and competitive determination of H0 in intermediate redshifts, free of unknown systematic uncertainties. First, we found that the exclusion of the sample of galaxy clusters from the determination initially proposed by LC leads to significantly different results. Finally, we performed a new determination in H0, where we obtained H0 = 68.00 ± 2.20 km s− 1 Mpc− 1 (1σ) with statistical and systematic errors and $H_{0} = 68.71^{+ 1.37}_{-1.45}$ km s− 1 Mpc− 1 (1σ) with statistical errors only. Contrary to those obtained by LC, these values are in full harmony with the global measurements via Cosmic Microwave Background (CMB) radiation and to the other recent estimates of H0 in intermediate redshifts.

Abstract: Strongly gravitational lensed quasars can be used to measure the so-called time-delay distance D_Δt, and thus the Hubble constant H_0 and other cosmological parameters. Stellar kinematics of the deflector galaxy play an essential role in this measurement by: (i) helping break the mass-sheet degeneracy; (ii) determining in principle the angular diameter distance D_d to the deflector and thus further improving the cosmological constraints. In this paper we simulate observations of lensed quasars with integral field spectrographs and show that spatially resolved kinematics of the deflector enablesfurther progress by helping break the mass-anisotropy degeneracy. Furthermore, we use our simulations to obtain realistic error estimates with current/upcoming instruments like OSIRIS on Keck and NIRSPEC on the James Webb Space Telescope for both distances (typically ∼6 per cent on D_Δt and ∼10 per cent on D_d). We use the error estimates to compute cosmological forecasts for the sample of nine lenses that currently have well-measured time delays and deep Hubble Space Telescope images and for a sample of 40 lenses that is projected to be available in a few years through follow-up of candidates found in ongoing wide field surveys. We find that H_0 can be measured with 2 per cent (1 per cent) precision from nine (40) lenses in a flat Λcold dark mattercosmology. We study several other cosmological models beyond the flat Λcold dark matter model and find that time-delay lenses with spatially resolved kinematics can greatly improve the precision of the cosmological parameters measured by cosmic microwave background data.