https://www.physics.rutgers.edu/grad/690/Padmanabhan-2003.pdf

Cosmological constant—the weight of the vacuum

Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Λ-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Λ-term. We discuss the current observational situation focusing on cosmological tests of Λ including the age of the universe, high redshift supernovae, gravitational lensing, galaxy clustering and the cosmic microwave background. We also review the theoretical debate surrounding Λ: the generation of Λ in models with spontaneous symmetry breaking and through quantum vacuum polarization effects — mechanisms which are known to give rise to a large value of Λ hence leading to the "cosmological constant problem." More recent attempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modelling a dynamical Λ-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small Λ-term are briefly reviewed. A comprehensive bibliography of recent work on Λ is provided.

http://cds.cern.ch/record/385991/files/9904398.pdf

The Case for a Positive Cosmological Λ-Term

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

There is now strong evidence that the current energy density of the Universe is dominated by dark energy with an equation of state w

/pdf/cosmological-structure-formation-in-a-homogeneous-dark-3k2r3039lo.pdf

Cosmological structure formation in a homogeneous dark energy background

I use the most recent cosmic microwave background (CMB) anisotropy measurements to constrain the leading cold dark matter models in the ?m-?? plane. A narrow triangular region is preferred. This triangle is elongated in such a way that its intersection with even conservative versions of recent supernovae, cluster mass-to-light ratios, and double radio source constraints is small and provides the current best limits in the ?m-?? plane: ??${Λ}$ -->$t SUBgt {Λ}t/SUBgt $ -->=0.62 ? 0.16 and ? -->m=0.24 ? 0.10. This complementarity between the CMB and other observations rules out ??${Λ}$ -->$t SUBgt {Λ}t/SUBgt $ -->=0 models at more than the 99% confidence level.

The Cosmic Microwave Background and Observational Convergence in the Ωm-ΩΛ Plane

The authors review the equations, notational choices, and confusing terminology of the Friedmann (zero-pressure) and Lema\^{\i}tre cosmological models, retaining cgs units as far as practical and in particular retaining units ${\mathrm{cm}}^{\ensuremath{-}2}$ for the present Gaussian curvature ${K}_{0}$ of three-space. They integrate the Friedmann equation numerically, requiring solutions to match the present Hubble parameter ${H}_{0}$ and mass-density ("closure") parameter ${\ensuremath{\Omega}}_{0}$ at present time ${t}_{0}=0$, and generate families of curves showing the scale factor $R(\ensuremath{\tau})$ (with ${R}_{0}=1$) vs $\ensuremath{\tau}$ (time in units ${H}_{0}^{\ensuremath{-}1}$) for fixed ${\ensuremath{\Omega}}_{0}$ and various values of the cosmological constant $\ensuremath{\Lambda}$ (in units ${H}_{0}^{2}$). These unusual graphs show the continuity of the solutions and the physical significance of $\ensuremath{\Lambda}$. Families for several values of ${\ensuremath{\Omega}}_{0}$ exhibit known but unfamiliar features. The authors also show the family of "standard models" ($\ensuremath{\Lambda}=0$) and the family satisfying the "inflationary constraint" (${K}_{0}=0$). They obtain new and simple formulas for the critical value ${\ensuremath{\Lambda}}_{s}({H}_{0},{\ensuremath{\Omega}}_{0})$, which separates models with a big bang from those without. Their definition of ${\ensuremath{\Lambda}}_{s}$ at fixed ${H}_{0}$ and ${\ensuremath{\Omega}}_{0}$ differs from usual practice but proves useful. These formulas also give the quasistatic scale factor ${R}_{s}$ and redshift ${z}_{s}$ for the corresponding Eddington-Lema\^{\i}tre model, and give ${R}_{s}$ and ${z}_{s}$ approximately for the neighboring "Lema\^{\i}tre coasting models," which have $\ensuremath{\Lambda}l{\ensuremath{\Lambda}}_{s}$. The conventional wisdom that $\ensuremath{\Lambda}={\ensuremath{\Lambda}}_{c}(1+\ensuremath{\varepsilon})$ for the coasting models applies to a different characteristic value ${\ensuremath{\Lambda}}_{c}$. A quasistatic state in the future, with a second critical value ${\ensuremath{\Lambda}}_{s2}$, is possible if ${\ensuremath{\Omega}}_{0}g1$. The parameters ${\ensuremath{\Omega}}_{0}$, $\frac{\ensuremath{\Lambda}}{{H}_{0}^{2}}$, $\frac{{\ensuremath{\Lambda}}_{s}}{{H}_{0}^{2}}$, and $\frac{{\ensuremath{\Lambda}}_{s2}}{{H}_{0}^{2}}$ can be used to classify the Friedmann models.

James E. Felten

Papers

Scale factors R ( t ) and critical values of the cosmological constant Λ in Friedmann universes