Cosmological models in two spacetime dimensions

2014

Latin indices from the beginning of the alphabet, a, b, c, and so on generally run over four spacetime indices 0, 1, 2, 3, where v 0 denotes the time component of the vector v a. An exception to this convention occurs in paper V and the related section in chapter 5 where they label spatial coordinate indices from 1 to 3. Greek indices from the beginning of the alphabet, α, β, γ, and so on generally run over three spatial indices 1, 2, 3, and are used to label components relative an orthonormal frame, except in paper V where they label spacetime components from 1 to 4. Greek indices from the middle of the alphabet, μ, ν, and so on are used to label spacetime coordinate components. Latin indices from the middle of the alphabet, i, j, k, and so on are used to label spatial coordinate components, or as in paper IV, components relative a group invariant frame. Repeated upper and lower indices are summed over, unless otherwise indicated. The metric has signature − + + +. Units for which 8πG = 1 and c = 1, where G is the gravitational constant and c is the speed of light, are used throughout the thesis. Vectors and tensors are represented by symbols in bold font, x, 0, g, T for example, where the dimension and rank should be discernable from the context. 2 The cosmological constant was first introduced by Einstein [23] as a way to obtain a static universe, but was abandoned by him when it was discovered that the universe is expanding, only later to be revived in light of the new observations of an accelerating universe. 3 The names dark matter/energy are a bit misleading. It may sound like dark matter is completely black, absorbing all light, but in reality it is totally transparent, not interacting with light or normal matter at all, except through its gravitational pull (and possibly through weak interactions that are of no relevance on astronomical scales). More appropriate names would be invisible matter/energy. 4 Aleksander Aleksanderoviq Friedman's last name is sometimes translated Friedmann and sometimes Friedman.

A cosmological model of homogeneous and isotropic spatially flat Universe with gravitating self-interacting scalar field is considered. The exact solution, admitting an analytical exit from inflationary stage into a radiation era and a matter dominated epoch, is obtained by virtue of ``fine turning of the potential'' method. We found that an inflationary stage is supported by decay of higgs bosons in the framework of the solution obtained. Freidmann's regim is associated with adiabatical expantion of the Universe, filled by the matter with special equation of state. Thus we presented the exact solution which solve the problem of transition from an inflationary to a radiation eras or long standing `exit' problem.

Nuclear Physics B, 1987

A cosmological model with an additional term A(x)g~, in the energy-momentum tensor is introduced. Its structure is specified by the assumption that the energy density of the universe equals its critical value. The model so determined has k = 1, is singularity-free and does not possess the horizon, entropy, monopole or cosmological-constant problems of the standard hot bang cosmology. The whole universe is found to be causally connected slightly after Planck time. There exists a period of phase transition during part of which the pressure is negative. The model displays a flow of energy from curvature to matter such that the entropy of matter is not conserved.

nipne.ro

A new class of exact solutions of Einstein's field equations with a perfect fluid source, variable gravitational coupling G and cosmological term for FRW spacetime in higher dimensions is obtained. The nature of the variables G(t), (t), and the energy density (t) have been examined for three cases. It is shown that in these models particle horizon exist and the cosmological term is decaying with time. Further, it is observed that new class of solutions include some previous cases in four-dimensional space-time. The results of the present studies are well within the range of observational limits.

2006

We investigate a possibility for construction of the conventional Friedmann cosmology for our observable Universe if underlying theory is multidimensional Kaluza-Klein model endowed with a perfect fluid. We show that effective Friedmann model obtained by dynamical compactification of the multidimensional one is faced with too strong variations of the fundamental "constants". From other hand, models with stable compactification of the internal space are free from this problem and also result in conventional 4D cosmological behavior for our Universe. We prove a no-go theorem which shows that stable compactification of the internal spaces is possible only if equations of state in the external and internal spaces are properly adjusted to each other. With a proper choice of parameters (fine tuning), effective cosmological constant in this model provides the late time acceleration of the Universe. The fine tuning problem is resolved in the case of the internal spaces in the form of orbifolds with branes in fixed points. However, in this case the effective potential is too flat (mass gravexcitons is very small) to provide necessary constancy of the effective fundamental "constants".

1993

A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach de Sitter space. The action for this theory is obtained by a higher derivative modification of Einstein's theory. We expect that our model can easily be generalized to solve the singularity problem also for anisotropic cosmologies.

Arxiv preprint arXiv:0903.4775, 2009

We consider perturbative modifications of the Friedmann equations in terms of energy density corresponding to modified theories of gravity proposed as an alternative route to comply with the observed accelerated expansion of the universe. Assuming that the present matter content of the universe is a pressureless fluid, the possible singularities that may arise as the final state of the universe are surveyed. It is shown that, at most, two coefficients of the perturbative expansion of the Friedman equations are relevant for the analysis. Some examples of application of the perturbative scheme are included.

Physics Letters B, 1986

A model of the universe with an additional term A(x)&,~ in the energy-momentum tensor is motivated and presented. The model is completely determined by the assumption that the energy density of the universe equals its critical value. It has k = 1 geometry, is free of the initial singularity and does not possess a horizon, entropy or monopole problem.

2010

In the late 1990s, observations of type Ia supernovae led to the astounding discovery that the universe is expanding at an accelerating rate. The explanation of this anomalous acceleration has been one of the great problems in physics since that discovery. We propose cosmological models that can simply and elegantly explain the cosmic acceleration via the geometric structure of the spacetime continuum, without introducing a cosmological constant into the standard Einstein field equation, negating the necessity for the existence of dark energy. In this geometry, the three fundamental physical dimensions length, time, and mass are related in new kind of relativity. There are four conspicuous features of these models: 1) the speed of light and the gravitational "constant" are not constant, but vary with the evolution of the universe, 2) time has no beginning and no end; i.e., there is neither a big bang nor a big crunch singularity, 3) the spatial section of the universe is a 3-sphere, and 4) in the process of evolution, the universe experiences phases of both acceleration and deceleration. One of these models is selected and tested against current cosmological observations, and is found to fit the redshiftluminosity distance data quite well.

Theoretical and Observational Cosmology, 1999

The aim of this set of lectures is a systematic presentation of a covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic covariant relations for a cosmological fluid, the present lectures cover some of the same ground as a previous set of Cargèse lectures [6], but they then go on to give (ii) the full set of corresponding tetrad equations, (iii) a classification of cosmological models with exact symmetries, (iv) a brief discussion of some of the most useful exact models and their observational properties, and (v) an introduction to the covariant and gauge invariant perturbation theory of almost-Friedmann-Lemaître-Robertson-Walker universes, with fluid descriptions for the matter and a kinetic theory description of the radiation.