Singular fate of the universe in modified theories of gravity

A theory of exponential modified gravity which explains both early-time inflation and late-time acceleration, in a unified way, is proposed. The theory successfully passes the local tests and fulfills the cosmological bounds and, remarkably, the corresponding inflationary era is proven to be unstable. Numerical investigation of its late-time evolution leads to the conclusion that the corresponding dark energy epoch is not distinguishable from the one for the ΛCDM model. Several versions of this exponential gravity, sharing similar properties, are formulated. It is also shown that this theory is non-singular, being protected against the formation of finite-time future singularities. As a result, the corresponding future universe evolution asymptotically tends, in a smooth way, to de Sitter space, which turns out to be the final attractor of the system.

Entropy, 2012

Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaître-Robertson-Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f (R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied.

We obtain the analogues of the Friedman equations in an emergent gravity scenario in the presence of dark energy. The background metric is taken to be Friedman-Lemaitre-Robertson-Walker (FLRW). We show that if $\dot\phi ^{2}$ is the dark energy density (in units of the critical density) then (a) for total energy density greater than the pressure (non-relativistic scenario, matter domination) the deceleration parameter $q(t)\approx\frac {1}{2} [1 + 27 \dot\phi ^{2}+...] > \frac{1}{2}$ (b) for total energy density equal to 3 times the pressure (relativistic case, radiation domination), the deceleration parameter $q(t)\approx 1 + 18\dot\phi ^{2} +... > 1$ and (c) for total energy density equal to the negative of the pressure (dark energy scenario), the deceleration parameter $q(t)< -1$. Our results indicate that many aspects of standard cosmology can be accommodated with the presence of dark energy right from the beginning of the universe where the time parameter $t\equiv \fra...

Astrophysics and Space Science, 2010

This paper is devoted to study the gravitational charged perfect fluid collapse in the Friedmann universe models with cosmological constant. For this purpose, we assume that the electromagnetic field is so weak that it does not introduce any distortion into the geometry of the spacetime. The results obtained from the junction conditions between the Friedmann and the Reissner-Nordström de-Sitter spacetimes are used to solve the field equations. Further, the singularity structure and mass effects of the collapsing system on time difference between the formation of apparent horizons and singularity have been studied. This analysis provides the validity of Cosmic Censorship Hypothesis. It is found that the electric field affects the area of apparent horizons and their time of formation.

We study cosmologies in modified theories of gravity considering Lagrangian density fðRÞ which is a polynomial function of scalar curvature ðRÞ in the Einstein-Hilbert action in vacuum. The field equation obtained from the modified action corresponding to a Robertson-Walker metric is highly nonlinear and not simple enough to obtain analytic solution. Consequently we adopt a numerical technique to study the evolution of the Friedmann-Robertson-Walker universe. A number of evolutionary phases of the Universe including the present accelerating phase are found to exist in the higher derivative theories of gravity. The cosmological solutions obtained here are new and interesting. We study a modified theory of gravity as a toy model to explore the past and the present, and to predict the future evolution. It is found that all the models analyzed here can reproduce the current accelerating phase of expansion of the Universe. The duration of the present accelerating phase is found to depend on the coupling constants of the gravitational action. The physical importance of the coupling parameters considered in the action are also discussed.

2011

This is a thesis on general relativity. It analyzes dynamical properties of Einstein’s field equations in cosmology and in the vicinity of spacetime singularities in a number of different situations. Different techniques are used depending on the particular problem under study; dynamical systems methods are applied to cosmological models with spatial homogeneity; Hamiltonian methods are used in connection with dynamical systems to find global monotone quantities determining the asymptotic states; Fuchsian methods are used to quantify the structure of singularities in spacetimes without symmetries. All these separate methods of analysis provide insights about different facets of the structure of the equations, while at the same time they show the relationships between those facets when the different methods are used to analyze overlapping areas. The thesis consists of two parts. Part I reviews the areas of mathematics and cosmology necessary to understand the material in part II, whi...

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.

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.

Journal of Cosmology and Astroparticle Physics, 2010

We study F (R) modified gravity models which are capable of driving the accelerating epoch of the Universe at the present time whilst not destroying the standard Big Bang and inflationary cosmology. Recent studies have shown that a weak curvature singularity with |R| → ∞ can arise generically in viable F (R) models of present dark energy (DE) signaling an internal incompleteness of these models. In this work we study how this problem is cured by adding a quadratic correction with a sufficiently small coefficient to the F (R) function at large curvatures. At the same time, this correction eliminates two more serious problems of previously constructed viable F (R) DE models: unboundedness of the mass of a scalar particle (scalaron) arising in F (R) gravity and the scalaron overabundance problem. Such carefully constructed models can also yield both an early time inflationary epoch and a late time de Sitter phase with vastly different values of R. The reheating epoch in these combined models of primordial and present dark energy is completely different from that of the old R + R 2 /6M 2 inflationary model, mainly due to the fact that values of the effective gravitational constant at low and intermediate curvatures are different for positive and negative R. This changes the number of e-folds during the observable part of inflation that results in a different value of the primordial power spectrum index. 1. Introduction 1 2. Review of cosmological evolution 7 2.1 Non-linear oscillations and existence of a "sudden" singularity with |R| → ∞ 8 2.2 General viable F (R) models of present DE 11 2.3 Determination of the Hubble parameter 12 2.4 Structure of a singularity with F ′′ (R) = 0 for a finite R 13 3. Avoiding the weak singularity and solving the problems of F (R) DE models 13 4. Inflation and late time acceleration from one F (R) function 17 4.1 New problem 18 4.2 Resolution of the problem and the improved AB model 19 4.3 de Sitter attractors 19 4.4 Slow-roll inflation 20 4.5 Reheating 21 4.5.1 Evolution of H(t) without backreaction 22 4.5.2 Effect of backreaction 27 4.6 Cosmological evolution 29 5. Conclusions and discussion 32

The European Physical Journal C, 2010

We study all four types of finite-time future singularities emerging in late-time accelerating (effective quintessence/phantom) era from F(R, G)-gravity, where R and G are the Ricci scalar and the Gauss-Bonnet invariant, respectively. As an explicit example of F(R, G)-gravity, we also investigate modified Gauss-Bonnet gravity, so-called F (G)-gravity. In particular, we reconstruct the F (G)-gravity and F(R, G)-gravity models where accelerating cosmologies realizing the finite-time future singularities emerge. Furthermore, we discuss a possible way to cure the finite-time future singularities in F (G)-gravity and F(R, G)-gravity by taking into account higher-order curvature corrections. The example of non-singular realistic modified Gauss-Bonnet gravity is presented.