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 review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Dynamics of dark energy

Physics welcomes the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, \ensuremath{\Lambda}; today the concept is termed dark energy or quintessence. Physics also suggests that dark energy could be dynamical, allowing for the arguably appealing picture of an evolving dark-energy density approaching its natural value, zero, and small now because the expanding universe is old. This would alleviate the classical problem of the curious energy scale of a millielectron volt associated with a constant \ensuremath{\Lambda}. Dark energy may have been detected by recent cosmological tests. These tests make a good scientific case for the context, in the relativistic Friedmann-Lema\^{\i}tre model, in which the gravitational inverse-square law is applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one-quarter of the critical Einstein--de Sitter value. The case for detection of dark energy is not yet as convincing but still serious; we await more data, which may be derived from work in progress. Planned observations may detect the evolution of the dark-energy density; a positive result would be a considerable stimulus for attempts at understanding the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.

/pdf/the-cosmological-constant-and-dark-energy-1w78acsak0.pdf

The Cosmological Constant and Dark Energy

http://risa.stanford.edu/teaching/362/particledarkmatter.pdf

Particle dark matter: Evidence, candidates and constraints

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.

/pdf/type-ia-supernova-discoveries-at-z-1-from-the-hubble-space-2dypo50ta3.pdf

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

Spherically symmetric gravitational equilibria of self-interacting scalar fields $\ensuremath{\varphi}$ with interaction potential $V(\ensuremath{\varphi})=\frac{1}{4}\ensuremath{\lambda}{|\ensuremath{\varphi}|}^{4}$ are determined. Surprisingly, the resulting configuration may differ markedly from the noninteracting case even when $\ensuremath{\lambda}\ensuremath{\ll}1$. Contrary to generally accepted astrophysical folklore, it is found that the maximum masses of such boson stars may be comparable to the Chandrasekhar mass for fermions of mass ${m}_{\mathrm{fermion}}\ensuremath{\sim}{\ensuremath{\lambda}}^{\ensuremath{-}\frac{1}{4}}{m}_{\mathrm{boson}}$.

Boson Stars: Gravitational Equilibria of Self-Interacting Scalar Fields

We consider radio bursts that originate from extragalactic neutron stars (NSs) by addressing three questions about source distances. What are the physical limitations on coherent radiation at GHz frequencies? Do they permit detection at cosmological distances? How many bursts per NS are needed to produce the inferred burst rate 10 3 -10 4 sky 1 day 1 ? The burst rate is comparable to the NS formation rate in a Hubble volume, requiring only one per NS if they are bright enough. However, radiation physics causes us to favor a closer population. More bursts per NS are then required but repeats in 10 to 100 yr could still be negligible. Bursts are modeled as sub-ns, coherent shot pulses superposed incoherently to produce msduration 1 Jy amplitudes; each shot-pulse can be much weaker than the burst amplitude, placing less restrictive requirements on the emission process. Nonetheless, single shot pulses are similar to the extreme, unresolved (< 0:4 ns) MJy shot pulse seen from the Crab pulsar, which is consistent with coherent curvature radiation emitted near the light cylinder by an almost neutral clump with net charge 10 21 e and total energy & 10 23 ergs. Bursts from Gpc distances require incoherent superposition of 10 12 d 2 shot pulses or a total energy & 10 35 d 2 erg. The energy reservoir near the light cylinder limits the detection distance to . few 100 Mpc for a fluence 1 Jy ms unless conditions are more extreme than for the Crab pulsar. Similarly, extreme single pulses from ordinary pulsars and magnetars could be detectable from throughout the Local Group and perhaps farther. Contributions to dispersion measures from galaxy clusters will be significant for some of the bursts. We discuss tests for the signatures of bursts associated with extragalactic NSs.

Supergiant pulses from extragalactic neutron stars

The rotating vector model of pulsar polarization of Radhakrishnan and Cooke (1969) is extended here to include first-order special relativistic effects. The model predicts that the centroid of the position angle curve arrives later than the centroid of the intensity profile by 4r/c, where r is the emission radius. Application of the model to pulsars with well ordered position-angle swings and periods between 0.06 and 3.7 s give emission radii of not more than 2000 km for 0.43 and 1.4 GHz. Symmetry-breaking effects of the corotation velocity may help explain a general asymmetry found in pulsar intensity profiles and may strongly affect the intensity profiles of short-period pulsars. 66 refs.

A Relativistic Model of Pulsar Polarization

An analytical model is presented for the evolution of wide binaries in the Galaxy. The study is pertinent to the postulated solar companion, Nemesis, which may disturb the Oort cloud and cause catastrophic comet showers to strike the earth every 26 Myr. Distant gravitational encounters are modeled by Fokker-Planck coefficients for advection and diffusion of the orbital binding energy. It is shown that encounters with passing stars cause a diffusive evolution of the binding energy and semimajor axis. Encounters with subclumps in giant molecular clouds disrupt orbits to a degree dependent on the cumulative number of stellar encounters. The time scales of the vents and the limitations of scaling laws used are discussed. Results are provided from calculations of galactic distribution of wide binaries and the evolution of wide binary orbits. 38 references.

The Dynamical Fate of Wide Binaries in the Solar Neighborhood

Overall, brane inflation is compatible with the recent analysis of the Wilkinson microwave anisotropy probe (WMAP) data. Here we explore the constraints of WMAP and the 2dF Galaxy Redshift Survey (2dFGRS) data on the various brane inflationary scenarios. Brane inflation naturally ends with the production of cosmic strings, which may provide a way to distinguish these models observationally. We argue that currently available data cannot exclude a non-negligible contribution from cosmic strings definitively. We perform a partial statistical analysis of mixed models that include a subdominant contribution from cosmic strings. Although the data favor models without cosmic strings, we conclude that they cannot definitively rule out a cosmic-string-induced contribution of $\ensuremath{\sim}10%$ to the observed temperature, polarization and galaxy density fluctuations. These results imply that $G\ensuremath{\mu}\ensuremath{\lesssim}1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\sqrt{B\ensuremath{\lambda}/0.1},$ where $\ensuremath{\lambda}l~1$ is a measure of the intercommutation probability of the cosmic string networks and B measures the importance of perturbations induced by cosmic strings. We argue that, conservatively, the data available currently still permit $B\ensuremath{\lesssim}0.1.$ Precision measurements sensitive to the B-mode polarization produced by vector density perturbation modes driven by the string network could provide evidence for these models. Accurate determinations of ${n}_{s}(k),$ the scalar fluctuation index, could also distinguish among various brane inflation models.

/pdf/observational-constraints-on-cosmic-string-production-during-mpbzmsx7a1.pdf

Ira Wasserman

Papers

Boson Stars: Gravitational Equilibria of Self-Interacting Scalar Fields

Supergiant pulses from extragalactic neutron stars

A Relativistic Model of Pulsar Polarization

The Dynamical Fate of Wide Binaries in the Solar Neighborhood

Observational constraints on cosmic string production during brane inflation