The Cosmic Triangle: Revealing the State of the Universe

Abstract

The "cosmic triangle" is introduced as a way of representing the past, present, and future status of the universe. Our current location within the cosmic triangle is determined by the answers to three questions: How much matter is in the universe? Is the expansion rate slowing down or speeding up? And, is the universe flat? A review of recent observations suggests a universe that is lightweight (matter density about one-third the critical value), is accelerating, and is flat. The acceleration implies the existence of cosmic dark energy that overcomes the gravitational self-attraction of matter and causes the expansion to speed up.

arXiv comment36 pages, 8 eps figures, use epsfig.sty, final draft of paper to appear in Science 284, 1481-1488, (1999) Change to CMB plot, Fig. 6 (third MSAM data point corrected) Addition of second CMB plot with more recent data added Minor typo in figs. 1 and 2 corrected

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• Constraints on Intracluster Gas Bulk Motions in Clusters of Galaxies with ASCA
• Vector field mediated models of dynamical light velocity
• Interpreting the New Brookhaven g_mu - 2 Result
• How dominant is the vacuum?
• Constraints on Cosmological Parameters from the Lyman-alpha Forest Power Spectrum and COBE-DMR
• Observational constraints on decaying vacuum dark energy model
• Is a Simple Collisionless Relic Dark Matter Particle Ruled Out?
• Imprint of Scalar Dark Energy on Cosmic Microwave Background Polarization
• Cosmological dynamics of $f(R)$ gravity scalar degree of freedom in Einstein frame
• Binary Black Hole Mergers within the LIGO Horizon: Statistical Properties and prospects for detecting Electromagnetic Counterparts
• Vector field and rotational curves in dark galactic halos
• Questioning the $H_0$ tension via the look-back time
• Gravitational wave echoes from compact stars in $f(\mathcal{R},T)$ gravity
• Measuring the viscosity of dark matter with strongly lensed gravitational waves
• A Dynamical Study of the Friedmann Equations
• The Shape, Multiplicity, and Evolution of Superclusters in LambdaCDM Cosmology
• Observational constraints on the spectral index of the cosmological curvature perturbation
• Testing the Relationship Between Bursty Star Formation and Size Fluctuations of Local Dwarf Galaxies
• MSLED, Neutrino Oscillations and the Cosmological Constant
• Brans-Dicke Scalar Field as a Unique k-essence
• Fitting BOOMERANG and MAXIMA-1 data with a Einstein-Yang-Mills Cosmological Model
• Nonquantum Gravity
• A small universe after all?
• Accelerated expansion from cosmological holography
• Turning noise into signal: learning from the scatter in the Hubble diagram
• CMB Constraints on a Baryonic Dark Matter-Dominated Universe
• Remarks on the Generalized Chaplygin Gas
• Cosmological Consequences of New Dark Energy Models in Einstein-Aether Gravity
• FRW Cosmology From Five Dimensional Vacuum Brans-Dicke Theory
• Gauge Quintessence
• Mass of Galactic Lenses in Modified Newtonian Dynamics
• Dark Radiation Dynamics on the Brane
• First-order formalism for dark energy and dust
• Cosmology with the largest galaxy cluster surveys: Going beyond Fisher matrix forecasts
• Constraining the Dark Universe
• A Brane World Perspective on the Cosmological Constant and the Hierarchy Problems
• Matter fields from a decaying background Lambda vacuum
• Instability of Chaplygin gas trajectories in unified dark matter models
• Open static Chaplygin universe
• Lorentz Symmetry breaking studies with photons from astrophysical observations
• Bianchi type VI1 cosmological model with wet dark fluid in scale invariant theory of gravitation
• Observing the First Stars and Black Holes
• A Small Cosmological Constant, Grand Unification and Warped Geometry
• Are Simulations of CDM Consistent with Galactic-Scale Observations at High Redshift?
• Global fits for the spectral index of the cosmological curvature perturbation
• Geodesic Model of HF QPOs Tested for Black Holes in Spacetimes Reflecting the Effect of Surrounding Dark Matter
• Constraining Self-Interacting Dark Matter with Dwarf Spheroidal Galaxies and High-resolution Cosmological $N$-body Simulations
• Spinodal Instabilities and the Dark Energy Problem
• Einstein energy-momentum complex for a phantom black hole metric
• Cosmological Constraints from a Combined Analysis of the Cluster Mass Function and Microwave Background Anisotropies
• Geodesic structure, shadow and optical appearance of black hole immersed in Chaplygin-like dark fluid
• Dilaton Coupled Quintessence Model in the $\omega -{\omega }^{\prime }$ Plane
• Dynamics of an Anisotropic Universe in $f(R,T)$ Theory
• Born-Infeld Type Phantom Model in the $\omega -{\omega }^{\prime }$ Plane
• Brans-Dicke Theory and Thermodynamical Laws on Apparent and Event Horizons
• Gamma-rays as probes of the Universe
• Interacting $F(R,T)$ gravity with modified Chaplygin gas
• Micrometer Gravitinos and the Cosmological Constant
• Can Cosmic Parallax Distinguish Between Anisotropic Cosmologies?
• Unifying Inflation with early and late Dark Energy in Multi-Fields: Spontaneously broken scale invariant TMT
• Smooth Particle Lensing
• Finding Clusters in SZ Surveys
• Scalar Field Dark Matter, Cross Section and Planck-Scale Physics
• A New Variable Modified Chaplygin Gas Model Interacting with Scalar Field
• Quintessence and the Underlying Particle Physics Theory
• Can Supermassive Black Holes alter Cold Dark Matter cusps through accretion?
• Lyman$\alpha$ Emitters beyond Redshift 5:The Dawn of Galaxy Formation
• Raychaudhuri equation in $k$-essence geometry: conditional singular and non-singular cosmological models
• Accretion of Chaplygin gas upon black holes: Formation of faster outflowing winds
• A critical discussion on the $H_0$ tension
• Liouville-like solutions in dilaton gravity with Gauss-Bonnet modifications
• Subaru Spectroscopy of the Gravitational Lens HST 14176+5226: Implications for a Large Cosmological Constan
• Vacuum Structure and Gravitational Bags Produced by Metric-Independent Spacetime Volume-Form Dynamics
• Transverse Wave Propagation in Relativistic Two-fluid Plasmas around Schwarzschild-de Sitter Black Hole
• Mass Models and Sunyaev-Zeldovich Effect Predictions for a Flux Limited Sample of 22 Nearby X-Ray Clusters
• Giant Arc Statistics and Cosmological Parameters
• Quasinormal modes, temperatures and greybody factors of black holes in a generalized Rastall gravity theory
• Probing Dark Energy with Supernovae : Bias from the time evolution of the equation of state
• Formation of caustics in Dirac-Born-Infeld type scalar field systems
• Cosmology from Moduli Dynamics
• Cosmology models with Ω_M-dependent cosmological constant
• Clustering of SZ clusters on a past light-cone: acoustic oscillations and constraints on dark energy
• Constraining the Cosmological Constant from Large-Scale Redshift-Space Clustering
• Thermodynamic and Optical Behaviors of Quintessential Hayward-AdS Black Holes
• The Central Mass and Phase-Space Densities of Dark Matter Halos: Cosmological Implications
• The Angular Clustering of Galaxy Pairs
• Braneworld effective action and origin of inflation
• Thermodynamic phase transition for Quintessence Dyonic Anti de Sitter Black Holes
• Ultralight Scalars and Spiral Galaxies
• dS/CFT Duality on the Brane with a Topological Twist
• Does black hole continuum spectrum signal f(R) gravity in higher dimensions?
• Brane World Dynamics and Conformal Bulk Fields
• Curvature Dependence of Peaks in the Cosmic Microwave Background Distribution
• Interacting Holographic Dark Energy, the Present Accelerated Expansion and Black Holes
• Evaporation of dynamical horizon with the Hawking temparature in the {\bf K-}essence emergent Vaidya spacetime
• A Holographic Interpretation of Asymptotically de Sitter Spacetimes
• Role of Chameleon Field in Accelerating Universe
• Exact cosmological solutions of models with an interacting dark sector
• Generalizations of normal ordering and applications to quantization in classical backgrounds
• Observational Tests of FRW World Models
• Dark Energy From Fifth Dimensional Brans-Dicke Theory
• Unconventional cosmology on the (thick) brane
• Investigating dark energy by electromagnetic frequency shifts
• Concerning Parameter Estimation Using the Cosmic Microwave Background
• Resource Letter: The Standard Model and Beyond
• Logarithmic entropy corrected holographic dark energy with $F(R,T)$ gravity
• Statefinder parameters for quantum effective Yang-Mills condensate dark energy model
• Bumpy Power Spectra and Galaxy Clusters
• Observations of the High Redshift Universe
• Galileons, phantom fields, and the fate of the Universe
• Testing f(R)-gravity models with DESI DR2 2025-BAO and other cosmological data
• Can Strong Gravitational Lensing Constrain Dark Energy?
• Evolution of the Cluster Correlation Function
• Cosmology from String Theory
• Unification of cosmological scalar fields
• Brane Supersymmetry Breaking and the Cosmological Constant: Open Problems
• Correlation function: biasing and fractal properties of the cosmic web
• Quantum driven Bounce of the future Universe
• From Little Bangs to the Big Bang
• Curvaton reheating in a Scale Invariant Two Measures Theory
• A Quintessence Problem in Brans-Dicke Theory with Varying Speed of Light
• $Om$ Diagnostic for Dilaton Dark Energy
• Sparticle spectrum and dark matter in type I string theory with an intermediate scale
• Boltzmann hierarchies for self-interacting warm dark matter scenarios
• Challenging the Cosmological Constant
• Triple-horizon spherically symmetric spacetime and holographic principle
• Mass Generation for an Ultralight Axion
• Cosmology with the Planck cluster sample
• Secular Evolution of Spiral Galaxies
• CMB Polarization at Large Angular Scales: Data Analysis of the POLAR Experiment
• Satellite Alignment: III. Satellite Galaxies Spatial Distribution and their Dependence on Redshift with A Novel Galaxy Finder
• Cosmological Models and Renormalization Group Flow
• Cosmic Voids in Evolving Dark Sector Cosmologies: the High Redshift Universe
• Dynamical quintessence fields Press-Schechter mass function: detectability and effect on dark haloes
• Varying c and Particle Horizons
• Search for Higgs shifts in white dwarfs
• Simple model of big-crunch/big-bang transition
• Interaction between phantom field and modified Chaplygin gas
• Holographic Dark Energy Interacting with Two Fluids and Validity of Generalized Second Law of Thermodynamics
• Where are the missing baryons in clusters?
• A Dark Energy Model with Generalized Uncertainty Principle in the Emergent, Intermediate and Logamediate Scenarios of the Universe
• Hamiltonian formalism in Friedmann cosmology and its quantization
• Gauge-noninvariance of quantum cosmology and vacuum dark energy
• Bianchi Type V Viscous Fluid Cosmological Models in Presence of Decaying Vacuum Energy
• The current status of observational cosmology
• Evolution of superclusters and supercluster cocoons in various cosmologies
• Cosmographic analysis of sign-switching dark energy
• Investigating dark energy by electromagnetic frequency shifts II: the Pantheon+ sample
• Cosmic Mach Number as a Function of Overdensity and Galaxy Age
• Influences of modified Chaplygin dark fluid around a black hole
• Constraints on the Transition Redshift using Hubble Phase Space Portrait
• Gravitational Origin of Phantom Dark Energy and Late Cosmic Acceleration
• $f(\bar{R},L(X))$-gravity in the context of dark energy with power law expansion and energy conditions
• A Phantom does not Result from a Backreaction
• Joint Analysis of Constraints on f(R) Parametrization from Recent Cosmological Observations
• Foreground contamination of the WMAP CMB maps from the perspective of the matched circle test
• Particle creation in the framework of f(G) gravity
• Questions of Identity
• Probing the dark energy with quasar clustering
• A Comparison of Quintessence and Nonlinear Born-Infeld Scalar Field Using Gold Supernova data
• The observational legacy of preon stars - probing new physics beyond the LHC
• Hunting long-lived gluinos at the Pierre Auger Observatory
• Transverse Wave Propagation in Relativistic Two-fluid Plasmas in de Sitter Space
• Cosmological effects on $f(\bar{R},\bar{T})$ gravity through a non-standard theory
• Probing the cosmological singularity with a particle
• EGUP corrected thermodynamics of RN-AdS black hole with quintessence matter
• Quintessentially Flat Scalar Potentials
• Exact solution to perturbative conformal cosmology in the recombination era
• The 2dF Galaxy Redshift Survey as a Cosmological Laboratory
• Probing the H0 Tension with Holographic Dark Energy in Unimodular Gravity: Insights from DESI DR2
• Rapid onset of the 21-cm signal suggests a preferred mass range for dark matter particle
• Correlation functions in 2D and 3D as descriptors of the cosmic web
• LRS Bianchi I model with constant deceleration parameter
• Physical vacuum and cosmic coincidence problem
• The cluster-galaxy cross-spectrum: an additional probe of cosmological and halo parameters
• On Brane Stabilization and the Cosmological Constant
• Cosmological Higgs fields
• Cosmological Implications and Physical Properties of an X-Ray Flux-Limited Sample of Galaxy Clusters
• Observational Constraints of Homogeneous Higher Dimensional Cosmology with Modified Chaplygin Gas
• Cosmology In Terms Of The Deceleration Parameter. Part II
• Scalar fields in the nonsymmetric Kaluza-Klein (Jordan-Thiry) theory
• Primordial Feature at the Scale of Superclusters of Galaxies
• Quintessence dissipative superattractor cosmology
• Fitting inverse power-law quintessence models using the SNAP satellite
• Phantom shell around black hole and global geometry
• Particle-like solutions in the generalized SU(2) Proca theory
• Tracing Tau-Neutrinos from WIMP-Annihilation
• CDM models with a steplike initial power spectrum
• Modified Teleparallel $f(T)$ Gravity, DESI BAO and the $H_0$ Tension
• Constraining Parameters of Generalized Cosmic Chaplygin Gas in Loop Quantum Cosmology
• Constraints on non-thermal Dark Matter from Planck lensing extraction
• Quintessence and Inflation from Symmetry Breaking Transition of the Internal Manifold
• Closed Universes With Black Holes But No Event Horizons As a Solution to the Black Hole Information Problem
• Anthropic constraints on the cosmological constant from Sun's motion through the Milky Way
• Dynamics of Logamediate and Intermediate Scenarios in the Dark Energy Filled Universe
• Anisotropic Dark Energy and the Generalized Second Law of Thermodynamics
• Tachyon field inspired dark energy and supernovae constraints
• A small non-vanishing cosmological constant from the Krein-Gupta-Bleuler vacuum
• Thermal Relic of Self-Interacting Dark Matter with Retarded Decay of Mediator
• Quintessential Inflation with Dissipative fluid
• The Realistic Scattering of Puffy Dark Matter
• `Hyper Parameters' Approach to Joint Estimation: Applications to Cepheid-Calibrated Distances and X-Ray Clusters
• Chandra discovery of the intracluster medium around UM425 at redshift 1.47
• Evolution of density perturbations in a realistic universe
• Reconstruction of the interaction term between dark matter and dark energy using SNe Ia
• Cosmological observations in non-local $F(R)$ cosmology
• Measuring the cosmological density perturbation
• Evolution of FRW universe in variable modified Chaplygin gas model
• Observational Constraints of Modified Chaplygin Gas in RS II Brane
• Relaxation versus collision times in the cosmological radiative era
• Study of Thermodynamics in Generalized Holographic and Ricci Dark Energy Models
• Self-Interacting Dark Matter in Cosmology: accurate numerical implementation and observational constraints
• Summary of ICHEP 2004
• An Alternative Interpretation for the Moduli Fields of the Cosmology Associated to Type IIB Supergravity with Fluxes
• Dynamical Cosmological Constant from A Very Recent Phase Transition
• Linear perturbations in a universe with a cosmological constant
• Variable Chaplygin Gas: Constraints from Supernovae, GRB and Gravitational Wave Merger Events
• Astroparticle Aspects of Supersymmetry
• Large-Scale Structure Topology in Non-Standard Cosmologies: Impact of Dark Sector Physics
• Interacting Chaplygin gas revisited
• Cosmological Attractors and Anisotropies in Two Measure Theories, Effective EYMH systems, and Off--Diagonal Inflation Models
• Revisiting regularization with Kaluza-Klein states and Casimir vacuum energy from extra dimensional spaces
• Black Hole Dynamics in Power-law based Metric $f(R)$ Gravity
• Matter Growth in Imperfect Fluid Cosmology
• Validity of Thermodynamical Laws in Dark Energy Filled Universe
• Cosmic Evolution with Early and Late Acceleration Inspired by Dual Nature of the Ricci Scalar Curvature
• Intermediate Scale Supersymmetric Inflation, Matter and Dark Energy
• Bayesian analysis of running holographic Ricci dark energy
• Accretion discs onto supermassive compact objects: a portal to dark matter physics in active galaxies
• The Maxwell--Boltzmann gas with non-standard self--interactions: a novel approach to galactic dark matter
• Interacting Induced Dark Energy Model
• How Not to Construct an Asymptotically de Sitter Universe
• Effect of Dynamical Cosmological Constant in presence of Modified Chaplygin Gas for Accelerating Universe
• Varying Speed of Light, Modified Chaplygin Gas and Accelerating Universe
• Entanglement production in Einstein-Cartan theory
• Role of Tachyonic Field in Accelerating Universe in Presence of Perfect Fluid
• Gravitational Forces on a Codimension-2 Brane
• Dynamical Instability of Self-Tuning Solution with Antisymmetric Tensor Field
• Inflationary Constraints on the Van der Waals Equation of State
• New X-ray Clusters in the EMSS II: Optical Properties
• A simple Hubble-like law in lieu of dark energy
• Solar system tests and neutron stars in $f(R)$ gravity revisited
• Inflation is the generic feature of phantom field-not the big-rip
• Thermodynamics of the most generalized form of Holographic Dark Energy and some particular cases with Corrected Entropies
• Maple+GrTensorII libraries for cosmology
• The Energy Density of the Quaternionic Field as Dark Energy in the Universe
• Cosmological Fluctuations on the Light Cone
• Cosmic Shells
• Strong Lensing Effect and Quasinormal Modes of Oscillations of Black Holes in $\mathbf{f}(\mathbf{R},\mathbf{T})$ Gravity Theory
• Observational Study of Higher Dimensional Magnetic Universe in Non-linear Electrodynamics
• Global Black Branes (Extended Global Defects Surrounded by Horizons), Brane Worlds and the Cosmological Constant
• Scaling attractors for quintessence in flat universe with cosmological term
• Observational constraints on a Yang-Mills condensate dark energy model
• Mirage resolution of cosmological singularities
• Exact solution to perturbative conformal cosmology from recombination until the current era
• Cosmological models in the nonsymmetric Kaluza-Klein Theory
• Can Massive Gravity Explain the Mass Discrepancy - Acceleration Relation of Disk Galaxies?
• Small cosmological constant in seesaw mechanism with breaking down SUSY
• Cracking Open the Window for Strongly Interacting Massive Particles as the Halo Dark Matter
• A theoretically-explained new-variant of Modified-Newtonian-Dynamics (MOND)
• Time dependent dark energy and the thermodynamics of many-body systems
• Dark matter halos modeled by polytropic spheres influenced by the relict cosmological constant and trapping polytropes forming supermassive black holes
• In Support of Inflation
• Classical and quantum quintessence cosmology
• Quasinormal Modes and Shadows of Black Holes in Infinite Derivative Theory of Gravity
• Revisiting Puffy Dark Matter with Novel Insights: Partial Wave Analysis
• FLRW Cosmology of Induced Dark Energy Model and Open Universe
• Inhomogeneous Dark Radiation Dynamics on a de Sitter Brane
• Potentials of Coupled Quintessence Based on a Dilaton
• From Large Telescopes to the MUltiplexed Survey Telescope (MUST)
• Study of Some Cosmological Parameters for Interacting New Holographic Dark Energy Model in f(T) Gravity
• Gauguin's questions in particle physics: Where are we coming from? What are we? Where are we going?
• Accelerated Expansion: Theory and Observations
• Isothermal Plasma Wave Properties of the Schwarzschild de-Sitter Black Hole in a Veselago Medium
• Imprint of galactic rotation curves and metric fluctuations on the recombination era anisotropy
• 3-3-1 Self Interacting Dark Matter and the Galaxy Core-Cusp problem
• How does Inflation Depend Upon the Nature of Fluids Filling Up the Universe in Brane World Scenario
• Supergravity models of Quintessence and Supersymmetry breaking
• Variable Modified Chaplygin Gas in Anisotropic Universe with Kaluza-Klein Metric
• Vacuum Polarization in an Anti-de Sitter Space as an Origin for a Cosmological Constant in a Brane World
• Spherical "Top-Hat" Collapse in a Modified Chaplygin Gas Dominated Universe
• Beyond the Standard Model of Cosmology
• Hubble Diagrams in the Jordan and Einstein Frames
• Black Hole Quasi-Periodic Oscillations in the Presence of Gauss-Bonnet Trace Anomaly
• Dispersion Modes of Hot Plasma for Schwarzschild de-Sitter Horizon in a Veselago Medium
• Interaction between Tachyon and Hessence (or Hantom) dark energies
• Cosmography of Cardassian model
• A Direct Detection Search for Hidden Sector New Particles in the 3-60 MeV Mass Range
• Homogeneous cosmologies in scalar tensor theory
• High-Energy Astrophysics and Cosmology
• Constraining super-critical string/brane cosmologies with astrophysical data
• Statefinder Description in Generalized Holographic and Ricci Dark Energy Models
• Expanding Universe: Thermodynamical Aspects From Different Models
• Dynamics of Higgs" Fields and a Quintessence in the Nonsymmetric Kaluza-Klein (Jordan-Thiry) Theory
• Accretion of Dark Energy Candidates Following Redshift Parametrization Type Equation of State : Horava-Lifshitz Gravity
• Searching for Particle Physics Beyond the Standard Model at the LHC and Elsewhere
• Primordial Gravitational Waves and Rescattered Electromagnetic Radiation in the Cosmic Microwave Background
• Perfect fluid cosmologies with varying light speed
• DLAs and Galaxy Formation
• Milgrom's Law and Lambda's Shadow: How Massive Gravity Connects Galactic and Cosmic Dynamics
• Perturbative Renormalisation Group Improved Black Hole Solution and its Quasinormal Modes
• Shadow of a Noncommutative Thin-Shell Gravastar
• Hot Plasma Modes Across Reissner-Nordstrom de Sitter Horizon in a Veselago Medium
• Viaggiu holographic dark energy in light of DESI DR2
• How Dark is Dark Energy? A Lightcones Comparison Approach
• CMB Anisotropies and the Determination of Cosmological Parameters
• Dark Matter Experimental Overview
• Numerical studies of galaxy formation using special purpose hardware
• Modelling cosmological singularity with compactified Milne space
• Nonlinear Effects in the Cosmic Microwave Background
• Manifestations of String Theory in Astrophysical Data and at the LHC
• Supermassive black holes surrounded by dark matter modeled as anisotropic fluid: epicyclic oscillations and their fitting to observed QPOs
• Observed Smooth Energy Fitted by Parametrized Quintessence
• Decaying vacuum and evolution from early inflation to late acceleration
• Maps of the Cosmos: The Cosmic Microwave Background