We present an analytical approximation formula for the luminosity distance in spatially flat cosmologies with dust and a cosmological constant.
We also show the approximate formulae for the so-called Dyer-Roeder distance (empty beam case) and the generalised angular diameter distance from redshift $z=z_1$ to $z=z_2$, which are particularly useful in analysing the gravitational lens effects. Our formulae are widely applicable over the range of the density parameter and the redshift with sufficiently small uncertainties. In particular, in the range of density parameter $0.3 \lid Ω_{\rmn m} \lid 1$ and redshift $0.03 \lid z \lid 1000$, the relative error for the luminosity distance by our formula is always smaller than that of the recent work by \cite{wu}.
We present an analytical approximation formula for the luminosity distance in spatially flat cosmologies with dust and a cosmological constant. Apart from the overall factor, the effect of non-zero cosmological constant in our formula is written simply in terms of a rational function. We also show the approximate formulae for the Dyer-Roeder distance (empty beam case) and the generalized angular diameter distance from redshift $z_1$ to $z_2$, which are particularly useful in analyzing the gravitational lens effects. Our formulae are widely applicable over the range of the density parameter and…
This paper presents the linearised Boltzmann equation for photons for scalar, vector and tensor perturbations in flat, open and closed FLRW cosmologies. We show that E- and B-mode polarisation for all types can be computed using only a single hierarchy. This was previously shown explicitly for tensor modes in flat cosmologies but not for vectors, and not for non-flat cosmologies.
We show that bouncing open or flat Friedmann-Robertson-Walker cosmologies are inconsistent with worldsheet string theory to first approximation. Specifically, the Virasoro constraint translates to the null energy condition in spacetime at leading order in the alpha-prime expansion. Thus one must go beyond minimally-coupled Einstein gravity in order to find bounce solutions.
We investigate two dark energy cosmological models (i.e., the $Λ$CDM and $ϕ$CDM models) with massive neutrinos assuming two different neutrino mass hierarchies in both the spatially flat and non-flat scenarios, where in the $ϕ$CDM model the scalar field possesses an inverse power-law potential, $V(ϕ)\propto ϕ^{-α}$ ($α>0$). Cosmic microwave background data from Planck 2015, baryon acoustic oscillations data from 6dFGS, SDSS-MGS, BOSS-LOWZ and BOSS CMASS-DR11, the JLA compilation of Type Ia supernova apparent magnitude observations, and the Hubble Space Telescope $H_0$ prior, are jointly employ…
We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lemaître cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.
We investigate the dependence of the galaxy-halo connection and galaxy density field in modified gravity models using the $N-$body simulations for $f(R)$ and nDGP models at $z=0$. Because of the screening mechanisms employed by these models, chameleon and Vainshtein, halos are clustered differently in the non-linear regime of structure formation. We quantify their deviations in the galaxy density field from the standard $Λ$CDM model under different environments. We populate galaxies in halos via the (Sub)Halo Abundance Matching. Our main results are: 1) The galaxy-halo connection {\it strongly…
The spatial curvature ($Ω_K$) of the Universe is one of the most fundamental quantities that could give a link to the early universe physics. In this paper we develop an approximate method to compute the nonlinear matter power spectrum, $P(k)$, for "non-flat" $Λ$CDM models using the separate universe (SU) ansatz which states that the effect of the curvature on structure formation is equivalent to that of long-wavelength density fluctuation ($δ_{\rm b}$) in a local volume in the "flat" $Λ$CDM model, via the specific mapping between the background cosmological parameters and redshifts in the non…
We use six tilted spatially-flat and untilted non-flat dark energy cosmological models in analyses of South Pole Telescope polarization (SPTpol) cosmic microwave background (CMB) data, alone and in combination with Planck 2015 CMB data and non-CMB data, namely, the Pantheon Type Ia supernovae apparent magnitudes, a collection of baryon acoustic oscillation data points, Hubble parameter measurements, and growth rates. Although the cosmological models that best-fit the Planck CMB and non-CMB data do not provide good fits to the SPTpol data, with the $χ^2$'s exceeding the expected value, given th…
Constraints on AvERA Cosmologies from Cosmic Chronometers and Type Ia Supernovae
ELTE Eötvös Loránd University（布达佩斯厄特沃什·洛兰大学）；HUN-REN–ELTE Extragalactic Astrophysics Research Group（匈牙利研究网络-厄特沃什·洛兰大学河外天体物理学研究组）；University of Helsinki（赫尔辛基大学）；University of Hawaii（夏威夷大学）
In this work, we investigate Newtonian cosmologies with a time-varying gravitational constant, $G(t)$. We examine whether such models can reproduce the low-redshift cosmological observations without a cosmological constant, or any other sort of explicit dark energy fluid. Starting with a modified Newton's second law, where $G$ is taken as a function of time, we derive the first Friedmann--Lema{î}tre equation, where a second parameter, $G^*$, appears as the gravitational constant. This parameter is related to the original $G$ from the second law, which remains in the acceleration equation. We u…
We use phase space method to study possible consequences of fixed points in flat FLRW models. One of these consequences is that a fluid with a finite sound speed, or a differentiable pressure, reaches a fixed point in an infinite time and has no finite-time singularities of types I, II and III described in hep-th/0501025. It is impossible for such a fluid to cross the phantom divide in a finite time. We show that a divergent $dp/dH$, or a speed of sound is necessary but not sufficient condition for phantom crossing. We use pressure properties, such as asymptotic behavior and fixed points, to q…
We analyse the full shape of anisotropic clustering measurements from the extended Baryon Oscillation Spectroscopic survey (eBOSS) quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey (BOSS). We obtain constraints on the cosmological parameters independent of the Hubble parameter $h$ for the extensions of the $Λ$CDM models, focusing on cosmologies with free dark energy equation of state parameter $w$. We combine the clustering constraints with those from the latest CMB data from Planck to obtain joint constraints for these cosmologies for $w$ …
We test the concordance LCDM cosmology by comparing predictions for the mean properties of galaxy clusters to observations. We use high-resolution N-body simulations of cosmic structure formation and semi-analytic models of galaxy formation to compute the abundance, mean density profile, and mass of galaxy clusters as a function of richness and luminosity, and we compare these predictions to observations of clusters in the Sloan Digital Sky Survey (SDSS) maxBCG catalogue. We discuss the scatter in the mass-richness relation, the reconstruction of the cluster mass function from the mass-richnes…
We present a new insight into the interpretation of the primordial spectrum of scalar particles density perturbations. On the assumption of spectrum universality, i.e., that the mean energy density and the typical value of inhomogeneity can be chosen arbitrarily in the framework of the model considered, the form of the spectrum becomes completely defined. It is close to the flat Harrison-Zeldovich spectrum, but with the suppressed low-frequency modes.
Cosmological measurements are affected by the energy density of both active and sterile massive neutrinos. We extend here a recent analysis of current cosmological data to non minimal cosmologies. Several possible scenarios are examined: a constant w \neq -1 dark energy equation of state, a non flat universe, a time varying dark energy component and coupled dark matter dark energy universes or modified gravity scenarios. When considering cosmological data only, (3+2) massive neutrino models with ~0.5 eV sterile species are allowed at 95% CL. This scenario has been shown to reconcile reactor, L…
In this work, we aim to show the possibilities of the variable speed of light (VSL) theory in explaining the type Ia supernovae observations without introducing dark energy. The speed of light is assumed to be scale factor dependent, which is the most popular assumption in VSL theory. We show the modified calculation of the distance modulus, and the validity of the redshift-scale factor relation in VSL theory. Three different models of VSL are tested SNe data-sets with proper constraints on the model parameters. The comparison of the three models and flat $Λ$CDM in distance modulus is showed. …
We consider flat Friedmann-Lema\^ıtre-Robertson-Walker cosmological models in the framework of general scalar-tensor theories of gravity with arbitrary coupling functions, set in the Jordan frame, in the cosmological epoch when the energy density of the ordinary dust matter dominates over the energy density of the scalar potential. Motivated by cosmological observations, we apply an approximation scheme in the regime close to the so-called limit of general relativity. The ensuing nonlinear approximate equations for the scalar field and the Hubble parameter can be solved analytically in cosmolo…
We consider the potential dominated era of Friedmann-Lemaitre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling functions, and focus upon the phase space of the scalar field. To study the regime suggested by the local weak field tests (i.e. close to the so-called limit of general relativity) we propose a nonlinear approximation scheme, solve for the phase trajectories, and provide a complete classification of possible phase portraits. We argue that the topology of trajectories in the nonlinear approximat…
We investigate in detail solutions of supergravity that involve warped products of flat geometries of the type M(p+1) x R x T(D-p-2) depending on a single coordinate. In the absence of fluxes, the solutions include flat space and Kasner-like vacua that break all supersymmetries. In the presence of a symmetric flux, there are three families of solutions that are characterized by a pair of boundaries and have a singularity at one of them, the origin. The first family comprises supersymmetric vacua, which capture a universal limiting behavior at the origin. The first and second families also cont…
The fundamental singularity theorem of FLRW cosmologies assumes that the matter content in the cosmological model obeys the strong energy condition along with a nonpositive cosmological constant which gives rise to an irrotational geodesic singularity. In this paper, we show that the important case of a spatially flat Friedmann-Lemaître-Robertson-Walker universe with barotropic matter obeying only the \emph{weak} energy condition with a nonnegative cosmological constant also contains a past singularity. We accomplish this using topological methods from dynamical systems theory. The methods emp…
We propose a large class of nonsingular cosmologies of arbitrary spatial curvature whose cosmic history is determined by a primeval dynamical $Λ(t)$-term. For all values of the curvature, the models evolve between two extreme de Sitter phases driven by the relic time-varying vacuum energy density. The transition from inflation to the radiation phase is universal and points to a natural solution of the graceful exit problem regardless of the values of the curvature parameter. The flat case recovers the scenario recently discussed in the literature (Perico et al., Phys. Rev. D88, 063531, 2013). …
In the context of Horndeski cosmologies, we consider a dynamical adjustment mechanism able to screen any value of the vacuum energy of the matter fields leading to a fixed de Sitter geometry. Thus, we present the most general scalar-tensor cosmological models without higher than second order derivatives in the field equation that have a fixed spatially flat de Sitter critical point for any kind of material content or vacuum energy. These models allow us to understand the current accelerated expansion of the universe as the result of the evolution towards the critical point when it is an attrac…
We consider Friedmann-Lema\^ıtre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We give the solutions in cosmological time with a particular attention to the class…
We discuss the dynamics of the universe within the framework of Massive Graviton Dark Matter scenario (MGCDM) in which gravitons are geometrically treated as massive particles. In this modified gravity theory, the main effect of the gravitons is to alter the density evolution of the cold dark matter component in such a way that the Universe evolves to an accelerating expanding regime, as presently observed. Tight constraints on the main cosmological parameters of the MGCDM model are derived by performing a joint likelihood analysis involving the recent supernovae type Ia data, the Cosmic Micro…
We investigate the process of reionisation in a model in which the dark matter is a warm elementary particle such as a sterile neutrino. We focus on models that are consistent with the dark matter decay interpretation of the recently detected line at 3.5 keV in the X-ray spectra of galaxies and clusters. In warm dark matter models the primordial spectrum of density perturbations has a cut-off on the scale of dwarf galaxies. Structure formation therefore begins later than in the standard cold dark matter (CDM) model and very few objects form below the cut-off mass scale. To calculate the number…
In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that $arbitrarily$ inhomogeneous and anisotropic cosmologies with "flat" (including toroidal) and "open" (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some regi…
The cosmic distance duality (CDD) relation (based on the Etherington reciprocity theorem) plays a crucial role in a wide assortment of cosmological measurements. Attempts at confirming it observationally have met with mixed results, though the general consensus appears to be that the data do support its existence in nature. A common limitation with past approaches has been their reliance on a specific cosmological model, or on measurements of the luminosity distance to Type Ia SNe, which introduces a dependence on the presumed cosmology in spite of beliefs to the contrary. Confirming that the …
Bouncing cosmologies are often proposed as alternatives to standard inflation for the explanation of the homogeneity and flatness of the universe. In such scenarios, the present cosmological expansion is preceded by a contraction phase. However, during the contraction, in general the anisotropy of the universe grows and eventually leads to a chaotic mixmaster behavior. This would either be hard to reconcile with observations or even lead to a singularity instead of the bounce. In order to preserve a smooth and isotropic bounce, the source for the contraction must have a super-stiff equation of…
The Standard Cosmological Model has experienced tremendous success at reproducing observational data by assuming a universe dominated by a cosmological constant and dark matter in a flat geometry. However, several studies, based on local measurements, indicate that the universe is expanding too fast, in disagreement with the Cosmic Microwave Background. Taking into account combined data from CMB, Baryon Acoustic Oscillation, and type Ia Supernovae, we show that if the mechanism behind the production of dark matter particles has at least a small non-thermal origin, one can induce larger values …
