There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We report measurements of the mass density, Omega_M, and
cosmological-constant energy density, Omega_Lambda, of the universe based on
the analysis of 42 Type Ia supernovae discovered by the Supernova Cosmology
Project. The magnitude-redshift data for these SNe, at redshifts between 0.18
and 0.83, are fit jointly with a set of SNe from the Calan/Tololo Supernova
Survey, at redshifts below 0.1, to yield values for the cosmological
parameters. All SN peak magnitudes are standardized using a SN Ia lightcurve
width-luminosity relation. The measurement yields a joint probability
distribution of the cosmological parameters that is approximated by the
relation 0.8 Omega_M - 0.6 Omega_Lambda ~= -0.2 +/- 0.1 in the region of
interest (Omega_M <~ 1.5). For a flat (Omega_M + Omega_Lambda = 1) cosmology we
find Omega_M = 0.28{+0.09,-0.08} (1 sigma statistical) {+0.05,-0.04}
(identified systematics). The data are strongly inconsistent with a Lambda = 0
flat cosmology, the simplest inflationary universe model. An open, Lambda = 0
cosmology also does not fit the data well: the data indicate that the
cosmological constant is non-zero and positive, with a confidence of P(Lambda >
0) = 99%, including the identified systematic uncertainties. The best-fit age
of the universe relative to the Hubble time is t_0 = 14.9{+1.4,-1.1} (0.63/h)
Gyr for a flat cosmology. The size of our sample allows us to perform a variety
of statistical tests to check for possible systematic errors and biases. We
find no significant differences in either the host reddening distribution or
Malmquist bias between the low-redshift Calan/Tololo sample and our
high-redshift sample. The conclusions are robust whether or not a
width-luminosity relation is used to standardize the SN peak magnitudes.

/pdf/measurements-of-omega-and-lambda-from-42-high-redshift-z1htxv5kgf.pdf

Measurements of Omega and Lambda from 42 High-Redshift Supernovae

We present spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.16 " z " 0.62. The luminosity distances of these objects are determined by methods that employ relations between SN Ia luminosity and light curve shape. Combined with previous data from our High-z Supernova Search Team and recent results by Riess et al., this expanded set of 16 high-redshift supernovae and a set of 34 nearby supernovae are used to place constraints on the following cosmo- logical parameters: the Hubble constant the mass density the cosmological constant (i.e., the (H 0 ), () M ), vacuum energy density, the deceleration parameter and the dynamical age of the universe ) " ), (q 0 ), ) M \ 1) methods. We estimate the dynamical age of the universe to be 14.2 ^ 1.7 Gyr including systematic uncer- tainties in the current Cepheid distance scale. We estimate the likely e†ect of several sources of system- atic error, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. Presently, none of these e†ects appear to reconcile the data with and ) " \ 0 q 0 " 0.

/pdf/observational-evidence-from-supernovae-for-an-accelerating-2hxji77uix.pdf

Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant

https://biblio.ugent.be/publication/685594/file/1130605.pdf

Review of Particle Physics

The combination of seven-year data from WMAP and improved astrophysical data rigorously tests the standard cosmological model and places new constraints on its basic parameters and extensions. By combining the WMAP data with the latest distance measurements from the baryon acoustic oscillations (BAO) in the distribution of galaxies and the Hubble constant (H0) measurement, we determine the parameters of the simplest six-parameter ΛCDM model. The power-law index of the primordial power spectrum is ns = 0.968 ± 0.012 (68% CL) for this data combination, a measurement that excludes the Harrison–Zel’dovich–Peebles spectrum by 99.5% CL. The other parameters, including those beyond the minimal set, are also consistent with, and improved from, the five-year results. We find no convincing deviations from the minimal model. The seven-year temperature power spectrum gives a better determination of the third acoustic peak, which results in a better determination of the redshift of the matter-radiation equality epoch. Notable examples of improved parameters are the total mass of neutrinos, � mν < 0.58 eV (95% CL), and the effective number of neutrino species, Neff = 4.34 +0.86 −0.88 (68% CL), which benefit from better determinations of the third peak and H0. The limit on a constant dark energy equation of state parameter from WMAP+BAO+H0, without high-redshift Type Ia supernovae, is w =− 1.10 ± 0.14 (68% CL). We detect the effect of primordial helium on the temperature power spectrum and provide a new test of big bang nucleosynthesis by measuring Yp = 0.326 ± 0.075 (68% CL). We detect, and show on the map for the first time, the tangential and radial polarization patterns around hot and cold spots of temperature fluctuations, an important test of physical processes at z = 1090 and the dominance of adiabatic scalar fluctuations. The seven-year polarization data have significantly improved: we now detect the temperature–E-mode polarization cross power spectrum at 21σ , compared with 13σ from the five-year data. With the seven-year temperature–B-mode cross power spectrum, the limit on a rotation of the polarization plane due to potential parity-violating effects has improved by 38% to Δα =− 1. 1 ± 1. 4(statistical) ± 1. 5(systematic) (68% CL). We report significant detections of the Sunyaev–Zel’dovich (SZ) effect at the locations of known clusters of galaxies. The measured SZ signal agrees well with the expected signal from the X-ray data on a cluster-by-cluster basis. However, it is a factor of 0.5–0.7 times the predictions from “universal profile” of Arnaud et al., analytical models, and hydrodynamical simulations. We find, for the first time in the SZ effect, a significant difference between the cooling-flow and non-cooling-flow clusters (or relaxed and non-relaxed clusters), which can explain some of the discrepancy. This lower amplitude is consistent with the lower-than-theoretically expected SZ power spectrum recently measured by the South Pole Telescope Collaboration.

/pdf/seven-year-wilkinson-microwave-anisotropy-probe-wmap-19dgu0rhy7.pdf

Seven-year wilkinson microwave anisotropy probe (wmap *) observations: cosmological interpretation

We show that cosmic acceleration can arise due to very tiny corrections to the usual gravitational action of general relativity, of the form ${R}^{\ensuremath{-}n}$ with $ng0.$ This model eliminates the need for a nonzero cosmological constant or any other form of dark energy, attributing a purely gravitational origin to the acceleration of the universe.

https://arxiv.org/pdf/astro-ph/0306438.pdf

Is Cosmic Speed-Up Due to New Gravitational Physics?

This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy.

/pdf/the-cosmological-constant-4ljm1nl1cq.pdf

The Cosmological Constant

Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first covers the foundations of the theory and mathematical formalism, providing an approachable introduction to what can often be an intimidating subject. Three major applications of general relativity are then discussed: black holes, perturbation theory and gravitational waves, and cosmology. Students will learn the origin of how spacetime curves (the Einstein equation) and how matter moves through it (the geodesic equation). They will learn what black holes really are, how gravitational waves are generated and detected, and the modern view of the expansion of the universe. A brief introduction to quantum field theory in curved spacetime is also included. A student familiar with this book will be ready to tackle research-level problems in gravitational physics.

/pdf/spacetime-and-geometry-an-introduction-to-general-relativity-6syqtusxxl.pdf

Spacetime and Geometry: An Introduction to General Relativity

The cosmological constant problem is examined in the context of both astronomy and physics. Effects of a nonzero cosmological constant are discussed with reference to expansion dynamics, the age of the universe, distance measures, comoving density of objects, growth of linear perturbations, and gravitational lens probabilities. The observational status of the cosmological constant is reviewed, with attention given to the existence of high-redshift objects, age derivation from globular clusters and cosmic nuclear data, dynamical tests of Omega sub Lambda, quasar absorption line statistics, gravitational lensing, and astrophysics of distant objects. Finally, possible solutions to the physicist's cosmological constant problem are examined.

The Cosmological constant

Models of dark energy are conveniently characterized by the equation-of-state parameter $w=p/\ensuremath{\rho},$ where $\ensuremath{\rho}$ is the energy density and p is the pressure. Imposing the dominant energy condition, which guarantees stability of the theory, implies that $wg~\ensuremath{-}1.$ Nevertheless, it is conceivable that a well-defined model could (perhaps temporarily) have $wl\ensuremath{-}1 ,$ and indeed such models have been proposed. We study the stability of dynamical models exhibiting $wl\ensuremath{-}1$ by virtue of a negative kinetic term. Although naively unstable, we explore the possibility that these models might be phenomenologically viable if thought of as effective field theories valid only up to a certain momentum cutoff. Under our most optimistic assumptions, we argue that the instability time scale can be greater than the age of the universe, but only if the cutoff is at or below ${10}^{\ensuremath{-}3}\mathrm{eV}.$ We conclude that it is difficult, although not necessarily impossible, to construct viable models of dark energy with $wl\ensuremath{-}1;$ observers should keep an open mind, but the burden is on theorists to demonstrate that any proposed new models are not ruled out by rapid vacuum decay.

https://arxiv.org/pdf/astro-ph/0301273.pdf

Sean M. Carroll

Papers

Is Cosmic Speed-Up Due to New Gravitational Physics?

The Cosmological Constant

Spacetime and Geometry: An Introduction to General Relativity

The Cosmological constant

Can the dark energy equation - of - state parameter w be less than -1?