The Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data provide stringent limits on deviations from the minimal, six-parameter Λ cold dark matter model. We report these limits and use them to constrain the physics of cosmic inflation via Gaussianity, adiabaticity, the power spectrum of primordial fluctuations, gravitational waves, and spatial curvature. We also constrain models of dark energy via its equation of state, parity-violating interaction, and neutrino properties, such as mass and the number of species. We detect no convincing deviations from the minimal model. The six parameters and the corresponding 68% uncertainties, derived from the WMAP data combined with the distance measurements from the Type Ia supernovae (SN) and the Baryon Acoustic Oscillations (BAO) in the distribution of galaxies, are: Ω b h 2 = 0.02267+0.00058 –0.00059, Ω c h 2 = 0.1131 ± 0.0034, ΩΛ = 0.726 ± 0.015, ns = 0.960 ± 0.013, τ = 0.084 ± 0.016, and at k = 0.002 Mpc-1. From these, we derive σ8 = 0.812 ± 0.026, H 0 = 70.5 ± 1.3 km s-1 Mpc–1, Ω b = 0.0456 ± 0.0015, Ω c = 0.228 ± 0.013, Ω m h 2 = 0.1358+0.0037 –0.0036, z reion = 10.9 ± 1.4, and t 0 = 13.72 ± 0.12 Gyr. With the WMAP data combined with BAO and SN, we find the limit on the tensor-to-scalar ratio of r 1 is disfavored even when gravitational waves are included, which constrains the models of inflation that can produce significant gravitational waves, such as chaotic or power-law inflation models, or a blue spectrum, such as hybrid inflation models. We obtain tight, simultaneous limits on the (constant) equation of state of dark energy and the spatial curvature of the universe: –0.14 < 1 + w < 0.12(95%CL) and –0.0179 < Ω k < 0.0081(95%CL). We provide a set of WMAP distance priors, to test a variety of dark energy models with spatial curvature. We test a time-dependent w with a present value constrained as –0.33 < 1 + w 0 < 0.21 (95% CL). Temperature and dark matter fluctuations are found to obey the adiabatic relation to within 8.9% and 2.1% for the axion-type and curvaton-type dark matter, respectively. The power spectra of TB and EB correlations constrain a parity-violating interaction, which rotates the polarization angle and converts E to B. The polarization angle could not be rotated more than –59 < Δα < 24 (95% CL) between the decoupling and the present epoch. We find the limit on the total mass of massive neutrinos of ∑m ν < 0.67 eV(95%CL), which is free from the uncertainty in the normalization of the large-scale structure data. The number of relativistic degrees of freedom (dof), expressed in units of the effective number of neutrino species, is constrained as N eff = 4.4 ± 1.5 (68%), consistent with the standard value of 3.04. Finally, quantitative limits on physically-motivated primordial non-Gaussianity parameters are –9 < f local NL < 111 (95% CL) and –151 < f equil NL < 253 (95% CL) for the local and equilateral models, respectively.

https://iopscience.iop.org/article/10.1088/0067-0049/180/2/330/pdf

Five-year wilkinson microwave anisotropy probe observations: cosmological interpretation

We have discovered 16 Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to provide the first conclusive evidence for cosmic deceleration that preceded the current epoch of cosmic acceleration. These objects, discovered during the course of the GOODS ACS Treasury program, include 6 of the 7 highest redshift SNe Ia known, all at z > 1.25, and populate the Hubble diagram in unexplored territory. The luminosity distances to these objects and to 170 previously reported SNe Ia have been determined using empirical relations between light-curve shape and luminosity. A purely kinematic interpretation of the SN Ia sample provides evidence at the greater than 99% confidence level for a transition from deceleration to acceleration or, similarly, strong evidence for a cosmic jerk. Using a simple model of the expansion history, the transition between the two epochs is constrained to be at z = 0.46 ± 0.13. The data are consistent with the cosmic concordance model of ΩM ≈ 0.3, ΩΛ ≈ 0.7 (χ = 1.06) and are inconsistent with a simple model of evolution or dust as an alternative to dark energy. For a flat universe with a cosmological constant, we measure ΩM = 0.29 ± (equivalently, ΩΛ = 0.71). When combined with external flat-universe constraints, including the cosmic microwave background and large-scale structure, we find w = -1.02 ± (and w < -0.76 at the 95% confidence level) for an assumed static equation of state of dark energy, P = wρc2. Joint constraints on both the recent equation of state of dark energy, w0, and its time evolution, dw/dz, are a factor of ~8 more precise than the first estimates and twice as precise as those without the SNe Ia discovered with HST. Our constraints are consistent with the static nature of and value of w expected for a cosmological constant (i.e., w0 = -1.0, dw/dz = 0) and are inconsistent with very rapid evolution of dark energy. We address consequences of evolving dark energy for the fate of the universe.

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Type Ia supernova discoveries at z > 1 from the Hubble Space Telescope: Evidence for past deceleration and constraints on dark energy evolution

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology, and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories that include higher-order curvature invariants, and specifically the particular class of $f(R)$ theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. Here $f(R)$ theories of gravity are reviewed in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented---metric, Palatini, and metric affine---and the following topics are discussed: motivation; actions, field equations, and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; and astrophysical applications.

f ( R ) theories of gravity

We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z = 1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multiband photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results: {Omega}{sub M} = 0.263 {+-} 0.042 (stat) {+-} 0.032 (sys) for a flat {Lambda}CDM model; and w = -1.023 {+-} 0.090 (stat) {+-} 0.054 (sys) for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations.

/pdf/the-supernova-legacy-survey-measurement-of-omega-m-omega-tobumct4pw.pdf

The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda,and w from the First Year Data Set

We have discovered 21 new Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to trace the history of cosmic expansion over the last 10 billion yr. These objects, which include 13 spectroscopicallyconfirmedSNeIaat z � 1,werediscoveredduring14epochsofreimagingoftheGOODSfieldsNorthand South over 2 yr with the Advanced Camera for Surveys on HST. Together with a recalibration of our previous HSTdiscovered SNe Ia, the full sample of 23 SNe Ia at z � 1 provides the highest redshift sample known. Combining these data with previous SN Ia data sets, we measured Hz ðÞ at discrete, uncorrelated epochs, reducing the uncertainty of Hz >1 ðÞ from 50% to under 20%, strengthening the evidence for a cosmic jerk—the transition from deceleration in the past to acceleration in thepresent. The uniqueleverage of theHSThigh-redshift SNe Ia provides thefirstmeaningful constraint on the dark energy equation-of-state parameter at z � 1. The result remains consistent with a cosmological constant [ wz ðÞ ¼� 1] and rules out rapidly evolving dark energy (dw/dz 31). The defining property of dark energy, its negative pressure, appears to be present at z > 1, in the epoch preceding acceleration, with � 98% confidenceinourprimaryfit.Moreover,thez > 1sample-averagedspectralenergydistributionisconsistentwiththat of thetypicalSNIaoverthelast10Gyr,indicatingthatanyspectralevolutionofthepropertiesof SNeIawithredshift is still below our detection threshold.

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New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing Constraints on the Early Behavior of Dark Energy*

We present photometric and spectroscopic observations of 23 high redshift supernovae spanning a range of z=0.34-1.03, 9 of which are unambiguously classified as Type Ia. These supernovae were discovered during the IfA Deep Survey, which began in September 2001 and observed a total of 2.5 square degrees to a depth of approximately m=25-26 in RIZ over 9-17 visits, typically every 1-3 weeks for nearly 5 months, with additional observations continuing until April 2002. We give a brief description of the survey motivations, observational strategy, and reduction process. This sample of 23 high-redshift supernovae includes 15 at z>0.7, doubling the published number of objects at these redshifts, and indicates that the evidence for acceleration of the universe is not due to a systematic effect proportional to redshift. In combination with the recent compilation of Tonry et al. (2003), we calculate cosmological parameter density contours which are consistent with the flat universe indicated by the CMB (Spergel et al. 2003). Adopting the constraint that Omega_total = 1.0, we obtain best-fit values of (Omega_m, Omega_Lambda)=(0.33, 0.67) using 22 SNe from this survey augmented by the literature compilation. We show that using the empty-beam model for gravitational lensing does not eliminate the need for Omega_Lambda > 0. Experience from this survey indicates great potential for similar large-scale surveys while also revealing the limitations of performing surveys for z>1 SNe from the ground.

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J. P. Henry

Papers

23 High Redshift Supernovae from the IfA Deep Survey: Doubling the SN Sample at z>0.7