Higher-order theories of gravity matched with large-scale structure and cosmological observations

The so-called f(R)-gravity could, in principle, explain the accelerated expansion of the Universe without adding unknown forms of dark energy/dark matter, but more simply extending the general relativity by generic functions of the Ricci scalar. However, as a part of several phenomenological models, there is no final f(R)-theory capable of fitting all the observations and addressing all the issues related to the presence of dark energy and dark matter. Astrophysical observations are pointing out huge amounts of “dark matter” and “dark energy” needed to explain the observed large-scale structures and cosmic accelerating expansion. Up to now, no experimental evidence has been found, at a fundamental level, to explain such mysterious components. The problem could be completely reversed considering dark matter and dark energy as “shortcomings” of general relativity.     

Disappearing cosmological constant in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

For higher-derivative f(R) gravity, where R is the Ricci scalar, a class of models is proposed, which produce viable cosmology different from the ACDM at recent times and satisfy cosmological, Solar System, and laboratory tests. These models have both flat and de Sitter spacetimes as particular solutions in the absence of matter. Thus, a cosmological constant is zero in a flat spacetime, but appears effectively in a curved one for sufficiently large R. A “smoking gun” for these models would be a small discrepancy in the values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations. On the other hand, a new problem for dark energy models based on f(R) gravity is pointed out, which is connected with the possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe. The text was submitted by the author in English.     

A kinematical approach to conformal cosmology

We present an alternative cosmology based on conformal gravity, as originally introduced by H. Weyl and recently revisited by P. Mannheim and D. Kazanas. Unlike past similar attempts our approach is a purely kinematical application of the conformal symmetry to the Universe, through a critical reanalysis of fundamental astrophysical observations, such as the cosmological redshift and others. As a result of this novel approach we obtain a closed-form expression for the cosmic scale factor R(t) and a revised interpretation of the space–time coordinates usually employed in cosmology. New fundamental cosmological parameters are introduced and evaluated. This emerging new cosmology does not seem to possess any of the controversial features of the current standard model, such as the presence of dark matter, dark energy or of a cosmological constant, the existence of the horizon problem or of an inflationary phase. Comparing our results with current conformal cosmologies in the literature, we note that our kinematic cosmology is equivalent to conformal gravity with a cosmological constant at late (or early) cosmological times. The cosmic scale factor and the evolution of the Universe are described in terms of several dimensionless quantitites, among which a new cosmological variable δ emerges as a natural cosmic time. The mathematical connections between all these quantities are described in details and a relationship is established with the original kinematic cosmology by L. Infeld and A. Schild. The mathematical foundations of our kinematical conformal cosmology will need to be checked against current astrophysical experimental data, before this new model can become a viable alternative to the standard theory.     

Early Universe with Variable Gravitational and Cosmological Constants

Einstein field equations are considered in zero-curvature Robertson–Walker (R–W) cosmology with perfect fluid source and time-dependent gravitational and cosmological “constants.” Exact solutions of the field equations are obtained by using the ’gamma-law' equation of state p = (γ − 1)ρ in which γ varies continuously with cosmological time. The functional form of γ (R) is used to analyze a wide range of cosmological solutions at early universe for two phases in cosmic history: inflationary phase and Radiation-dominated phase. The corresponding physical interpretations of the cosmological solutions are also discussed.     

Riemann-Christoffel Flows

A geometric flow based in the Riemann-Christoffel curvature tensor that in two dimensions has some common features with the usual Ricci flow is presented. For n dimensional spaces this new flow takes into account all the components of the intrinsic curvature. For four dimensional Lorentzian manifolds it is found that the solutions of the Einstein equations associated to a “detonant” sphere of matter, as well, as a Friedman-Roberson-Walker cosmological model are examples of Riemann-Christoffel flows. Possible generalizations are mentioned.     

Curvature Inspired Cosmological Scenario

Using modified gravity with non-linear terms of curvature, R ² and R ^(2+r) (with r being a positive real number and R being the scalar curvature), cosmological scenario, beginning at the Planck scale, is obtained. Here a unified picture of cosmology is obtained from f(R)-gravity. In this scenario, universe begins with power-law inflation followed by deceleration and acceleration in the late universe as well as possible collapse of the universe in future. It is different from f(R)-dark energy models with non-linear curvature terms assumed as dark energy. Here, dark energy terms are induced by linear as well as non-linear terms of curvature in Friedmann equation being derived from modified gravity. It is also interesting to see that, in this model, dark radiation and dark matter terms emerge spontaneously from the gravitational sector. It is found that dark energy, obtained here, behaves as quintessence in the early universe and phantom in the late universe. Moreover, analogous to brane-tension in brane-gravity inspired Friedmann equation, a tension term λ arises here being called as cosmic tension, It is found that, in the late universe, Friedmann equation (obtained here) contains a term −ρ ²/2λ (ρ being the phantom energy density) analogous to a similar term in Friedmann equation with loop quantum effects, if λ>0 and brane-gravity correction when λ<0.     

Dark energy and gravity

I review the problem of dark energy focussing on cosmological constant as the candidate and discuss what it tells us regarding the nature of gravity. Section 1 briefly overviews the currently popular “concordance cosmology” and summarizes the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as a candidate and emphasizes why no other approach really solves the conceptual problems usually attributed to cosmological constant. Section 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract certain key ingredients which must be present in any viable solution. In the conventional approach, the equations of motion for matter fields are invariant under the shift of the matter Lagrangian by a constant while gravity breaks this symmetry. I argue that until the gravity is made to respect this symmetry, one cannot obtain a satisfactory solution to the cosmological constant problem. Hence cosmological constant problem essentially has to do with our understanding of the nature of gravity. Section 3 discusses such an alternative perspective on gravity in which the gravitational interaction—described in terms of a metric on a smooth spacetime—is an emergent, long wavelength phenomenon, and can be described in terms of an effective theory using an action associated with normalized vectors in the spacetime. This action is explicitly invariant under the shift of the matter energy momentum tensor T _ab → T _ab + Λ _gab and any bulk cosmological constant can be gauged away. Extremizing this action leads to an equation determining the background geometry which gives Einstein’s theory at the lowest order with Lanczos–Lovelock type corrections. In this approach, the observed value of the cosmological constant has to arise from the energy fluctuations of degrees of freedom located in the boundary of a spacetime region.     

Cosmology

Precise astronomical observations of the cosmic expansion and the anisotropies of the cosmic microwave background have confirmed the simple cosmological “big bang” models. They have also produced evidence for a strange composition of the cosmic matter and energy density. The known baryons contribute only 5 percent to the cosmic substrate, while 25 percent are due to unknown dark matter particles, and 70 percent seem to come from a mysterious dark energy component which presently acts like a cosmological constant accelerating the cosmic expansion.     

Physics of Dark Energy Particles

We consider the astrophysical and cosmological implications of the existence of a minimum density and mass due to the presence of the cosmological constant. If there is a minimum length in nature, then there is an absolute minimum mass corresponding to a hypothetical particle with radius of the order of the Planck length. On the other hand, quantum mechanical considerations suggest a different minimum mass. These particles associated with the dark energy can be interpreted as the “quanta” of the cosmological constant. We study the possibility that these particles can form stable stellar-type configurations through gravitational condensation, and their Jeans and Chandrasekhar masses are estimated. From the requirement of the energetic stability of the minimum density configuration on a macroscopic scale one obtains a mass of the order of 10⁵⁵ g, of the same order of magnitude as the mass of the universe. This mass can also be interpreted as the Jeans mass of the dark energy fluid. Furthermore we present a representation of the cosmological constant and of the total mass of the universe in terms of ‘classical’ fundamental constants.     

Black Hole Thermodynamics of Hořava-Lifshitz and IR Modified Ho řava-Lifshitz Gravity Theory

Recently, a renormalizable model of gravity has been proposed by Hoř ava, which might be an ultraviolet completion of general relativity and it reduces to Einstein gravity with a non-vanishing cosmological constant in infrared approximation. Kehagias and Sfetsos have added a relevant operator proportional to the 3D geometry Ricci scalar to the original Hoř ava-Lifshitz theory action, which “softly” deviated from detailed-balance. This does not modify the ultraviolet properties of the theory. However, it modifies the infrared approximation and the Minkowski vacuum can be allowed in the infrared Hořava-Lifshitz gravity theory. The static spherical symmetric black hole solutions have been obtained in the Hořava-Lifshitz and infrared Hořava-Lifshitz gravity theory. Based on the metric of the black holes, Hawking radiation of massless scalar particles is investigated using Damour-Ruffini method. Then the black hole thermodynamics property will also be discussed.     

Archaic Universe and Cosmological Model: “Big-Bang” as Nucleation by Vacuum

In this work, we examine in depth the physical aspects of the archaic universe described by Euclidean 5-sphere geometry, by using Projective Relativity techniques. We hypothesize that the expansion of the Universe was “ignited” by primordial R processes, and that the big bang consisted of a spatially extended nucleation process which took place at the end of a pre-cosmic phase, characterized by the evolution parameter x₀\underline{x}_{0}. This parameter, which can be considered a quantum precursor of ordinary physical time, is a coordinate of Euclidean 5-sphere metrics. It is so possible to avoid many of the difficulties with standard model and to get rid of ad hoc assumptions. A complete solution to Projective General Relativity (PGR) equations is provided, so as to establish univocal relations between the scale factor R(τ) and cosmic time τ. In this way, the physics and geometry of the cosmological model are specified completely.     

Exact solutions in gravity with a sigma model source

We consider a D-dimensional model of gravity with non-linear “scalar fields” as a matter source. The model is defined on the product manifold M, which contains n Einstein factor spaces. General cosmological type solutions to the field equations are obtained when n − 1 factor spaces are Ricci-flat, e.g. when one space M ₁ of dimension d ₁ > 1 has nonzero scalar curvature. The solutions are defined up to solutions to geodesic equations corresponding to a sigma model target space. Several examples of sigma models are presented. A subclass of spherically symmetric solutions is studied and a restricted version of “no-hair theorem” for black holes is proved. For the case d ₁ = 2 a subclass of latent soliton solutions is singled out.     

Basic properties of the Einstein equations with a Ricci-Scalar-Dependent cosmological term

Basic properties of the Einstein equations modified by a cosmological Λ-term dependent on the Ricci scalar R are considered. We show that in addition to a nonzero divergence of the energy-momentum tensor of the matter and the consequent cold matter mass nonconservation as the Universe expands, this model suggests a significant modification of the equations for the gravitational potential and particle acceleration in the Newtonian approximation. These circumstances allow the necessary criteria for possible functional dependences Λ(R) to be formulated. Nevertheless, by introducing a variable Λ-term, we can look at the problems of dark matter and dark energy anew. In particular, we show that the model in which the cosmological term depends linearly on the Ricci scalar (this corresponds to the approximation of a more complex dependence in the case of low matter densities) makes it possible to satisfactorily describe the rotation curves of galaxies without invoking the dark matter hypothesis and to construct a cosmological model with a variable vacuum energy density, in qualitative agreement with the present views of the early Universe.     

Dark energy,induced gravity and broken scale invariance

We study the cosmological evolution of an induced gravity model with a self-interacting scalar field σ and in the presence of matter and radiation. Such model leads to Einstein gravity plus a cosmological constant as a stable attractor among homogeneous cosmologies and is therefore a viable dark-energy (DE) model for a wide range of scalar field initial conditions and values for its positive γ   coupling to the Ricci curvature γσ²R$\gamma {\sigma }^{2}R$.     

Genesis of Dark Energy: Dark Energy as Consequence of Release and Two-Stage Tracking of Cosmological Nuclear Energy

Recent observations on Type-Ia supernovae and low density (Ω _m =0.3) measurement of matter including dark matter suggest that the present-day universe consists mainly of repulsive-gravity type ‘exotic matter’ with negative-pressure often said ‘dark energy’ (Ω _x =0.7). But the nature of dark energy is mysterious and its puzzling questions, such as why, how, where and when about the dark energy, are intriguing. In the present paper the authors attempt to answer these questions while making an effort to reveal the genesis of dark energy and suggest that ‘the cosmological nuclear binding energy liberated during primordial nucleo-synthesis remains trapped for a long time and then is released free which manifests itself as dark energy in the universe’. It is also explained why for dark energy the parameter w=-\frac23w=-\frac{2}{3} . Noting that w=1 for stiff matter and w=\frac13w=\frac{1}{3} for radiation; w=-\frac23w=-\frac{2}{3} is for dark energy because “−1” is due to ‘deficiency of stiff-nuclear-matter’ and that this binding energy is ultimately released as ‘radiation’ contributing “ +\frac13+\frac{1}{3} ”, making w=-1+\frac13=-\frac23w=-1+\frac{1}{3}=-\frac{2}{3} . When dark energy is released free at Z=80, w=-\frac23w=-\frac{2}{3} . But as on present day at Z=0 when the radiation-strength-fraction (δ), has diminished to δ→0, the w=-1+d\frac13=-1w=-1+\delta\frac{1}{3}=-1 . This, almost solves the dark-energy mystery of negative pressure and repulsive-gravity. The proposed theory makes several estimates/predictions which agree reasonably well with the astrophysical constraints and observations. Though there are many candidate-theories, the proposed model of this paper presents an entirely new approach (cosmological nuclear energy) as a possible candidate for dark energy.     

Some adventures in the search for a modified gravity explanation of cosmic acceleration

The discovery of cosmic acceleration has raised the intriguing possibility that we are witnessing the first breakdown of General Relativity on cosmological scales. In this article I will briefly review current attempts to construct theoretically consistent and observationally viable modifications of gravity that are capable of describing the accelerating universe. I will discuss f(R) models, and their obvious extensions, and the DGP model as an example of extra-dimensional implementations. I will then briefly describe the Galileon models and their very recent multifield and curved space extensions—a class of four-dimensional effective field theories encoding extra dimensional modifications to gravity.     

Scale Transformation,Modified Gravity,and Brans-Dicke Theory

A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless matter with non-vanishing modified terms together with dynamical cosmological and gravitational coupling terms. The obtained modified Einstein equations are neither those in f(R) metric formalism nor the ones in f(ℛ) Palatini formalism, whereas the modified source terms are formally equivalent to those of f(R)=\frac12R²f({\mathcal{R}})=\frac{1}{2}{\mathcal{R}}^{2} gravity in Palatini formalism. The correspondence between the present model, the modified gravity theory, and Brans-Dicke theory with w = -\frac32\omega=-\frac{3}{2} is explicitly shown, provided the dilaton field is condensated to its vacuum state.