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

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

Modified Gravity and Cosmology

Supermassive black holes (BHs) have been found in 85 galaxies by dynamical modeling of spatially resolved kinematics. The Hubble Space Telescope revolutionized BH research by advancing the subject from its proof-of-concept phase into quantitative studies of BH demographics. Most influential was the discovery of a tight correlation between BH mass and the velocity dispersion σ of the bulge component of the host galaxy. Together with similar correlations with bulge luminosity and mass, this led to the widespread belief that BHs and bulges coevolve by regulating each other's growth. Conclusions based on one set of correlations from in brightest cluster ellipticals to in the smallest galaxies dominated BH work for more than a decade. New results are now replacing this simple story with a richer and more plausible picture in which BHs correlate differently with different galaxy components. A reasonable aim is to use this progress to refine our understanding of BH-galaxy coevolution. BHs with masses of 105−106M...

https://www.annualreviews.org/doi/suppl/10.1146/annurev-astro-082708-101811/suppl_file/aa51_kormendy_supmat.pdf

Coevolution (Or Not) of Supermassive Black Holes and Host Galaxies

This is the Supplemental Material to Kormendy and Ho 2013, ARAA, 51, 511 (arXiv:1304.7762). Section S1 summarizes indirect methods that are used to estimate black hole (BH) masses for galaxies with active nuclei (AGNs). Section S2 lists the observational criteria that are used to classify classical and pseudo bulges. The (pseudo)bulge classifications used in the main paper are not based on physical interpretation; rather, they are based on these observational criteria. Section S3 supplements the BH database in Section 5 of the main paper and Section S4 here. It discusses corrections to galaxy and BH parameters, most importantly to 2MASS K-band apparent magnitudes. It presents evidence that corrections are needed because 2MASS misses light at large radii when the images of galaxies subtend large angles on the sky or have shallow outer brightness gradients. Section S4 reproduces essentially verbatim the first part of Section 5 in the main paper, the BH database. It includes the list of BH and host-galaxy properties (Tables 2 and 3). Its most important purpose is to provide all of the notes on individual objects.

Coevolution (Or Not) of Supermassive Black Holes and Host Galaxies: Supplemental Material

There is accumulating evidence that (fundamental) scalar fields may exist in nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. As with white dwarfs and neutron stars, a limiting mass exists similarly, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation; however, modifications of general relativity, as in the case of Jordan?Brans?Dicke theory as a low-energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to the constituent mass, an effective radius and a large particle number. Due to the Heisenberg principle, a completely stable branch exists, and as a coherent state, it allows for rotating solutions with quantized angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.

https://iopscience.iop.org/article/10.1088/0264-9381/20/20/201/pdf

General relativistic boson stars

In inflationary scenarios with more than one scalar field, inflation may proceed even if each of the individual fields has a potential too steep for that field to sustain inflation on its own We show that scalar fields with exponential potentials evolve so as to act cooperatively to assist inflation, by finding solutions in which the energy densities of the different scalar fields evolve in fixed proportion Such scaling solutions exist for an arbitrary number of scalar fields, with different slopes for the exponential potentials, and we show that these solutions are the unique late-time attractors for the evolution We determine the density perturbation spectrum produced by such a period of inflation, and show that with multiple scalar fields the spectrum is closer to the scale-invariant than the spectrum that any of the fields would generate individually

Assisted inflation

There is accumulating evidence that (fundamental) scalar fields may exist in Nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. Similarly as for white dwarfs and neutron stars, there exists a limiting mass, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and the spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation, however, modifications of general relativity, as in the case of Jordan-Brans-Dicke theory as a low energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to constituent mass, an effective radius, and a large particle number. Due to the Heisenberg principle, there exists a completely stable branch, and as a coherent state, it allows for rotating solutions with quantised angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: Possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.

Franz E. Schunck

Papers

General relativistic boson stars

Assisted inflation

TOPICAL REVIEW: General relativistic boson stars

Rotating boson star as an effective mass torus in general relativity

Boson stars: alternatives to primordial black holes?