Modified Gravity Cosmology: From Inflation to Dark Energy

We study a string-inspired cosmological model from the symmetries point of view. We start by deducing the form that each physical quantity must take so that the field equations, in the string frame, admit self-similar solutions. In the same way, we formalize the use of power-law solutions (less restrictive than the self-similar ones) by studying the wave equation for the dilaton through the Lie group method. Furthermore, we show how to generate more solutions by using this approach. As examples, we calculate exact solutions to several cosmological models in the four-dimensional NS-NS (Neveu-Schwarz-Neveu-Schwarz) sector of low-energy effective string theory coupled to a dilaton and an axion-like H-field within the string frame background, with FRW and the Bianchi Type II metrics. We also study the existence of Noether symmetries, which allow us to determine the form of the physical quantities in the framework of FRW geometry and to find exact cosmological solutions. Full article

In the chameleon mechanism, a field (typically scalar) has a mass that depends on the matter density of the environment: the larger is the matter density, the larger is the mass of the chameleon. We briefly review some aspects of chameleonic theories. In particular, in a typical class of these theories, we discuss the lagrangian, the role of conformal transformations, the equation of motion and the thin-shell effect. We also discuss f ( R ) theories and chameleonic quantum gravity. Full article

We develop a cosmological model based on a quadratic equation of state \(p/c^2=-(\alpha+1){\rho^2}/{\rho_P}+\alpha\rho-(\alpha+1)\rho_ {\Lambda}\), where \(\rho_P\) is the Planck density and \(\rho_{\Lambda}\) the cosmological density, ``unifying'' vacuum energy and dark energy in the spirit of a generalized Chaplygin gas model. For \(\rho\rightarrow \rho_P\), it reduces to \(p=-\rho_P c^2\) leading to a phase of early accelerating expansion (early inflation) with a constant density equal to the Planck density \(\rho_P=5.16 \times 10^{99}\, {\rm g}/{\rm m}^3\) (vacuum energy). For \(\rho_{\Lambda}\ll\rho\ll \rho_P\), we recover the standard linear equation of state \(p=\alpha \rho c^2\) describing radiation (\(\alpha=1/3\)) or pressureless matter (\(\alpha=0\)) and leading to an intermediate phase of decelerating expansion. For \(\rho\rightarrow \rho_{\Lambda}\), we get \(p=-\rho_{\Lambda} c^2\) leading to a phase of late accelerating expansion (late inflation) with a constant density equal to the cosmological density \(\rho_{\Lambda}=7.02\times 10^{-24}\, {\rm g}/{\rm m}^3\) (dark energy). The pressure is successively negative (vacuum energy), positive (radiation and matter), and negative again (dark energy). We show a nice ``symmetry'' between the early universe (vacuum energy \(+\) \(\alpha\)-fluid) and the late universe (\(\alpha\)-fluid \(+\) dark energy). In our model, they are described by two polytropic equations of state with index \(n=+1\) and \(n=-1\) respectively. Furthermore, the Planck density \(\rho_P\) in the early universe plays a role similar to the cosmological density \(\rho_{\Lambda}\) in the late universe. They represent fundamental upper and lower density bounds differing by \(122\) orders of magnitude. The cosmological constant ``problem'' may be a false problem. We study the evolution of the scale factor, density, and pressure. Interestingly, our quadratic equation of state leads to a fully analytical model describing the evolution of the universe from the early inflation (Planck era) to the late accelerating expansion (de Sitter era). These two phases are bridged by a decelerating algebraic expansion (\(\alpha\)-era). Our model does not present any singularity at \(t=0\) and exists eternally in the past (although it may be incorrect to extrapolate the solution to the infinite past). On the other hand, it admits a scalar field interpretation based on an inflaton, quintessence, or tachyonic field. Our model generalizes the standard \(\Lambda\)CDM model by incorporating naturally a phase of early inflation that avoids the primordial singularity. Furthermore, it describes the early inflation, the intermediate decelerating expansion, and the late accelerating expansion of the universe simultaneously in terms of a single equation of state. We determine the corresponding scalar field potential that unifies the inflaton and quintessence potentials. Full article

In this paper, we explore the interior dynamics of neutral and charged black holes in f(R) gravity. We transform f(R) gravity from the Jordan frame into the Einstein frame and simulate scalar collapses in flat, Schwarzschild, and Reissner-Nordström geometries. In simulating scalar collapses in Schwarzschild and Reissner-Nordström geometries, Kruskal and Kruskal-like coordinates are used, respectively, with the presence of f′ and a physical scalar field being taken into account. The dynamics in the vicinities of the central singularity of a Schwarzschild black hole and of the inner horizon of a Reissner-Nordström black hole is examined. Approximate analytic solutions for different types of collapses are partially obtained. The scalar degree of freedom Φ, transformed from f′, plays a similar role as a physical scalar field in general relativity. Regarding the physical scalar field in f(R) case, when dΦ/dt is negative (positive), the physical scalar field is suppressed (magnified) by Φ, where t is the coordinate time. For dark energy f(R) gravity, inside black holes, gravity can easily push f′ to 1. Consequently, the Ricci scalar R becomes singular, and the numerical simulation breaks down. This singularity problem can be avoided by adding an R² term to the original f(R) function, in which case an infinite Ricci scalar is pushed to regions where f′ is also infinite. On the other hand, in collapse for this combined model, a black hole, including a central singularity, can be formed. Moreover, under certain initial conditions, f′ and R can be pushed to infinity as the central singularity is approached. Therefore, the classical singularity problem, which is present in general relativity, remains in collapse for this combined model. Full article

High-precision observational data have confirmed with startling evidence that the Universe is currently undergoing a phase of accelerated expansion. This phase, one of the most important and challenging current problems in cosmology, represents a new imbalance in the governing gravitational equations. Historically, physics has addressed such imbalances by either identifying sources that were previously unaccounted for or by altering the gravitational theory. Several candidates, responsible for this expansion, have been proposed in the literature, in particular dark energy models and modified gravity models, amongst others. Outstanding questions are related to the nature of this so-called “dark energy” that is driving this acceleration, and whether it is due to the vacuum energy or a dynamical field. On the other hand, the late-time cosmic acceleration may be due to modifications of general relativity. In this work, we explore a generalised modified gravity theory, namely ƒ(R,Φ, X) gravity, where R is the Ricci scalar, R is a scalar field and X is a kinetic term. This theory contains a wide range of dark energy and modified gravity models. We considered specific models and applications to the late-time cosmic acceleration. Full article

We review properties of solutions in bigravity theory for a specific case where two metric tensors, \(g_{\mu \nu}\) and \(f_{\mu \nu}\), satisfy proportional relation \(f_{\mu \nu}=C^{2}g_{\mu \nu}\). For this condition, we find that the solutions describing the asymptotically de Sitter space-time can be obtained and investigate the perturbation around the Schwarzschild–de Sitter solutions and corresponding anti-evaporation. We discuss the stability under special perturbations related to the anti-evaporation and the importance of the non-diagonal components of the metric in bigravity. Full article

In this paper, we establish the correspondence between ghost-free bimetric theory and a class of higher derivative gravity actions, including conformal gravity and new massive gravity. We also characterize the relation between the respective equations of motion and classical solutions. We illustrate that, in this framework, the spin-2 ghost of higher derivative gravity at the linear level is an artifact of the truncation to a four-derivative theory. The analysis also gives a relation between the proposed partially massless (PM) bimetric theory and conformal gravity, showing, in particular, the equivalence of their equations of motion at the four-derivative level. For the PM bimetric theory, this provides further evidence for the existence of an extra gauge symmetry and the associated loss of a propagating mode away from de Sitter backgrounds. The new symmetry is an extension of Weyl invariance, which may suggest the candidate PM bimetric theory as a possible ghost-free completion of conformal gravity. Full article

A new gravity model with the function F(R) = (1/β) arctan (βR – β²R²) instead of the Ricci scalar in the Einstein–Hilbert action, describing inflation of the Universe, is suggested and analyzed. We obtain constant curvature solutions of the model in the Jordan frame. Performing the conformal transformation of the metric, the potential and the mass of a scalar degree of freedom in the Einstein frame are found. The slow-roll and cosmological parameters of the model are evaluated. It was demonstrated that the index of the scalar spectrum power law, n_s, is in agreement with the PLANCK data. Full article

The quasi-static solutions of the matter density perturbation in various dark energy models and modified gravity models have been investigated in numerous papers. However, the oscillating solutions in those models have not been investigated enough so far. In this paper, we review the behavior of the oscillating solutions, which have a possibility to unveil the difference between the models of the late-time accelerated expansion of the Universe, by using appropriate approximations. Full article

In this short review, I discuss basic qualitative characteristics of quantum non-Abelian gauge dynamics in the non-stationary background of the expanding Universe in the framework of the standard Einstein–Yang–Mills formulation. A brief outlook of existing studies of cosmological Yang–Mills fields and their properties will be given. Quantum effects have a profound impact on the gauge field-driven cosmological evolution. In particular, a dynamical formation of the spatially-homogeneous and isotropic gauge field condensate may be responsible for both early and late-time acceleration, as well as for dynamical compensation of non-perturbative quantum vacua contributions to the ground state of the Universe. The main properties of such a condensate in the effective QCD theory at the flat Friedmann–Lemaítre–Robertson–Walker (FLRW) background will be discussed within and beyond perturbation theory. Finally, a phenomenologically consistent dark energy can be induced dynamically as a remnant of the QCD vacua compensation arising from leading-order graviton-mediated corrections to the QCD ground state. Full article

Recently, the phenomenology of f(R) gravity has been scrutinized. This scrutiny has been motivated by the possibility to account for the self-accelerated cosmic expansion without invoking dark energy sources. Besides, this kind of modified gravity is capable of addressing the dynamics of several self-gravitating systems alternatively to the presence of dark matter. It has been established that both metric and Palatini versions of these theories have interesting features but also manifest severe and different downsides. A hybrid combination of theories, containing elements from both these two formalisms, turns out to be also very successful accounting for the observed phenomenology and is able to avoid some drawbacks of the original approaches. This article reviews the formulation of this hybrid metric-Palatini approach and its main achievements in passing the local tests and in applications to astrophysical and cosmological scenarios, where it provides a unified approach to the problems of dark energy and dark matter. Full article

Over the past few decades, general relativity and the concordance ΛCDM model have been successfully tested using several different astrophysical and cosmological probes based on large datasets (precision cosmology). Despite their successes, some shortcomings emerge due to the fact that general relativity should be revised at infrared and ultraviolet limits and to the fact that the fundamental nature of dark matter and dark energy is still a puzzle to be solved. In this perspective, ƒ(R) gravity has been extensively investigated, being the most straightforward way to modify general relativity and to overcame some of the above shortcomings. In this paper, we review various aspects of ƒ(R) gravity at extragalactic and cosmological levels. In particular, we consider a cluster of galaxies, cosmological perturbations and N-body simulations, focusing on those models that satisfy both cosmological and local gravity constraints. The perspective is that some classes of ƒ(R) models can be consistently constrained by the large-scale structure. Full article

The purpose of this short review is to describe cosmological models with a linear inhomogeneous time-dependent equation of state (EoS) for dark energy, when dark fluid is coupled with dark matter. This may lead to a bounce cosmology. We consider equivalent descriptions in terms of the EoS parameters for an exponential, a power-law, or a double-exponential law for the scale factor a. Stability issues are discussed by considering small perturbations around the critical points for the bounce, in the early as well as in the late, universe. The latter part of the paper is concerned with dark energy coupled with dark matter in viscous fluid cosmology. We allow the bulk viscosity ζ = ζ(H, t) to be a function of the Hubble parameter and the time, and consider the Little Rip, the Pseudo Rip, and the bounce universe. Analytic expressions for characteristic properties of these cosmological models are obtained. Full article