String Gas Cosmology: Progress and Problems

String Gas Cosmology is a model of the evolution of the very early universe based on fundamental principles and key new degrees of freedom of string theory which are different from those of point particle field theories. In String Gas Cosmology the universe starts in a quasi-static Hagedorn phase during which space is filled with a gas of highly excited string states. Thermal fluctuations of this string gas lead to an almost scale-invariant spectrum of curvature fluctuations. Thus, String Gas Cosmology is an alternative to cosmological inflation as a theory for the origin of structure in the universe. This short review focuses on the building blocks of the model, the predictions for late time cosmology, and the main problems which the model faces.Comment: 17 pages, 4 figures, invited short review for the Special Issue of CQG on String Cosmology, typo correcte

Unconventional Cosmology

I review two cosmological paradigms which are alternative to the current inflationary scenario. The first alternative is the "matter bounce", a non-singular bouncing cosmology with a matter-dominated phase of contraction. The second is an "emergent" scenario, which can be implemented in the context of "string gas cosmology". I will compare these scenarios with the inflationary one and demonstrate that all three lead to an approximately scale-invariant spectrum of cosmological perturbations.Comment: 45 pages, 10 figures; invited lectures at the 6th Aegean Summer School "Quantum Gravity and Quantum Cosmology", Chora, Naxos, Greece, Sept. 12 - 17 2012, to be publ. in the proceedings; these lecture notes form an updated version of arXiv:1003.1745 and arXiv:1103.227

A rule of thumb for cosmological backreaction

In the context of second order perturbation theory, cosmological backreaction is seen to rescale both time and the scale factor. The issue of the homogeneous limit of long-wavelength perturbations is addressed and backreaction is quantified in terms of a gauge-invariant metric function that is the true physical degree of freedom in the homogeneous limit. The time integral of this metric function controls whether backreaction hastens or delays the expansion of the universe. As an example, late-time acceleration of the universe is shown to be inconsistent with a perturbative approach. Any tendency to accelerate the expansion requires negative non-adiabatic pressure fluctuations.Comment: 5 pages, references added, comment clarified in Introductio

One-loop corrections to the curvature perturbation from inflation

An estimate of the one-loop correction to the power spectrum of the primordial curvature perturbation is given, assuming it is generated during a phase of single-field, slow-roll inflation. The loop correction splits into two parts, which can be calculated separately: a purely quantum-mechanical contribution which is generated from the interference among quantized field modes around the time when they cross the horizon, and a classical contribution which comes from integrating the effect of field modes which have already passed far beyond the horizon. The loop correction contains logarithms which may invalidate the use of naive perturbation theory for cosmic microwave background (CMB) predictions when the scale associated with the CMB is exponentially different from the scale at which the fundamental theory which governs inflation is formulated.Comment: 28 pages, uses feynmp.sty and ioplatex journal style. v2: supersedes version published in JCAP. Some corrections and refinements to the discussion and conclusions. v3: Corrects misidentification of quantum correction with an IR effect. Improvements to the discussio

Cosmological Backreaction from Perturbations

We reformulate the averaged Einstein equations in a form suitable for use with Newtonian gauge linear perturbation theory and track the size of the modifications to standard Robertson-Walker evolution on the largest scales as a function of redshift for both Einstein de-Sitter and Lambda CDM cosmologies. In both cases the effective energy density arising from linear perturbations is of the order of 10^-5 the matter density, as would be expected, with an effective equation of state w ~ -1/19. Employing a modified Halofit code to extend our results to quasilinear scales, we find that, while larger, the deviations from Robertson-Walker behaviour remain of the order of 10^-5.Comment: 15 pages, 8 figures; replaced by version accepted by JCA

Accelerated expansion from structure formation

We discuss the physics of backreaction-driven accelerated expansion. Using the exact equations for the behaviour of averages in dust universes, we explain how large-scale smoothness does not imply that the effect of inhomogeneity and anisotropy on the expansion rate is small. We demonstrate with an analytical toy model how gravitational collapse can lead to acceleration. We find that the conjecture of the accelerated expansion being due to structure formation is in agreement with the general observational picture of structures in the universe, and more quantitative work is needed to make a detailed comparison.Comment: 44 pages, 1 figure. Expanded treatment of topics from the Gravity Research Foundation contest essay astro-ph/0605632. v2: Added references, clarified wordings. v3: Published version. Minor changes and corrections, added a referenc

Dark Energy from structure: a status report

The effective evolution of an inhomogeneous universe model in any theory of gravitation may be described in terms of spatially averaged variables. In Einstein's theory, restricting attention to scalar variables, this evolution can be modeled by solutions of a set of Friedmann equations for an effective volume scale factor, with matter and backreaction source terms. The latter can be represented by an effective scalar field (`morphon field') modeling Dark Energy. The present work provides an overview over the Dark Energy debate in connection with the impact of inhomogeneities, and formulates strategies for a comprehensive quantitative evaluation of backreaction effects both in theoretical and observational cosmology. We recall the basic steps of a description of backreaction effects in relativistic cosmology that lead to refurnishing the standard cosmological equations, but also lay down a number of challenges and unresolved issues in connection with their observational interpretation. The present status of this subject is intermediate: we have a good qualitative understanding of backreaction effects pointing to a global instability of the standard model of cosmology; exact solutions and perturbative results modeling this instability lie in the right sector to explain Dark Energy from inhomogeneities. It is fair to say that, even if backreaction effects turn out to be less important than anticipated by some researchers, the concordance high-precision cosmology, the architecture of current N-body simulations, as well as standard perturbative approaches may all fall short in correctly describing the Late Universe.Comment: Invited Review for a special Gen. Rel. Grav. issue on Dark Energy, 59 pages, 2 figures; matches published versio

The Effect of Large-Scale Inhomogeneities on the Luminosity Distance

We study the form of the luminosity distance as a function of redshift in the presence of large scale inhomogeneities, with sizes of order 10 Mpc or larger. We approximate the Universe through the Swiss-cheese model, with each spherical region described by the Tolman-Bondi metric. We study the propagation of light beams in this background, assuming that the locations of the source and the observer are random. We derive the optical equations for the evolution of the beam area and shear. Through their integration we determine the configurations that can lead to an increase of the luminosity distance relative to the homogeneous cosmology. We find that this can be achieved if the Universe is composed of spherical void-like regions, with matter concentrated near their surface. For inhomogeneities consistent with the observed large scale structure, the relative increase of the luminosity distance is of the order of a few percent at redshifts near 1, and falls short of explaining the substantial increase required by the supernova data. On the other hand, the effect we describe is important for the correct determination of the energy content of the Universe from observations.Comment: 27 pages, 5 figures Revised version. References added. Conclusions clarifie