Are f(R) dark energy models cosmologically viable?

Corrected Thermodynamics of Black Holes in f(R) Gravity with Electrodynamic Field and Cosmological Constant

The thermodynamics of black holes (BHs) and their corrections have become a hot topic in the study of gravitational physics, with significant progress made in recent decades. In this paper, we study the thermodynamics and corrections of spherically symmetric BHs in models f(R)=R+αR2 and f(R)=R+2γR+8Λ under the f(R) theory, which includes the electrodynamic field and the cosmological constant. Considering thermal fluctuations around equilibrium states, we find that, for both f(R) models, the corrected entropy is meaningful in the case of a negative cosmological constant (anti-de Sitter-RN spacetime) with Λ=-1. It is shown that when the BHs' horizon radius is small, thermal fluctuations have a more significant effect on the corrected entropy. Using the corrected entropy, we derive expressions for the relevant corrected thermodynamic quantities (such as Helmholtz free energy, internal energy, Gibbs free energy, and specific heat) and calculate the effects of the correction terms. The results indicate that the corrections to Helmholtz free energy and Gibbs free energy, caused by thermal fluctuations, are remarkable for small BHs. In addition, we explore the stability of BHs using specific heat. The study reveals that the corrected BH thermodynamics exhibit locally stable for both models, and corrected systems undergo a Hawking-Page phase transition. Considering the requirement on the non-negative volume of BHs, we also investigate the constraint on the EH radius of BHs.

On the Evolution of the Hubble Constant with the SNe Ia Pantheon Sample and Baryon Acoustic Oscillations: A Feasibility Study for GRB-Cosmology in 2030

The difference from 4 to 6 σ in the Hubble constant (H0) between the values observed with the local (Cepheids and Supernovae Ia, SNe Ia) and the high-z probes (Cosmic Microwave Background obtained by the Planck data) still challenges the astrophysics and cosmology community. Previous analysis has shown that there is an evolution in the Hubble constant that scales as f(z)=H0/(1+z)η, where H0 is H0(z=0) and η is the evolutionary parameter. Here, we investigate if this evolution still holds by using the SNe Ia gathered in the Pantheon sample and the Baryon Acoustic Oscillations. We assume H0=70kms−1Mpc−1 as the local value and divide the Pantheon into three bins ordered in increasing values of redshift. Similar to our previous analysis but varying two cosmological parameters contemporaneously (H0, Ω0m in the ΛCDM model and H0, wa in the w0waCDM model), for each bin we implement a Markov-Chain Monte Carlo analysis (MCMC) obtaining the value of H0 assuming Gaussian priors to restrict the parameters spaces to values we expect from our prior knowledge of the current cosmological models and to avoid phantom Dark Energy models with w<−1. Subsequently, the values of H0 are fitted with the model f(z). Our results show that a decreasing trend with η∼10−2 is still visible in this sample. The η coefficient reaches zero in 2.0 σ for the ΛCDM model up to 5.8 σ for w0waCDM model. This trend, if not due to statistical fluctuations, could be explained through a hidden astrophysical bias, such as the effect of stretch evolution, or it requires new theoretical models, a possible proposition is the modified gravity theories, f(R). This analysis is meant to further cast light on the evolution of H0 and it does not specifically focus on constraining the other parameters. This work is also a preparatory to understand how the combined probes still show an evolution of the H0 by redshift and what is the current status of simulations on GRB cosmology to obtain the uncertainties on the Ω0m comparable with the ones achieved through SNe Ia.

Dynamical Analysis and Cosmological Evolution in Weyl Integrable Gravity

We investigate the cosmological evolution for the physical parameters in Weyl integrable gravity in a Friedmann–Lemaître–Robertson–Walker universe with zero spatial curvature. For the matter component, we assume that it is an ideal gas, and of the Chaplygin gas, from the Weyl integrable gravity a scalar field is introduced by a geometric approach which provides an interaction with the matter component.We calculate the stationary points for the field equations and we study their stability properties. Furthermore, we solve the inverse problem for the case of an ideal gas and prove that the gravitational field equations can follow from the variation of a Lagrangian function. Finally, variational symmetries are applied for the construction of analytic and exact solutions.

Physical Acceptability of the Renyi, Tsallis and Sharma-Mittal Holographic Dark Energy Models in the f(T,B) Gravity under Hubble’s Cutoff

In the present article, we investigate the physical acceptability of the spatially homogeneous and isotropic Friedmann–Lemâitre–Robertson–Walker line element filled with two fluids, with the first being pressureless matter and the second being different types of holographic dark energy. This geometric and material content is considered within the gravitational field equations of the f(T,B) (where T is the torsion scalar and the B is the boundary term) gravity in Hubble’s cut-off. The cosmological parameters, such as the Equation of State (EoS) parameter, during the cosmic evolution, are calculated. The models are stable throughout the universe expansion. The region in which the model is presented is dependent on the real parameter δ of holographic dark energies. For all δ≥4.5, the models vary from ΛCDM era to the quintessence era.

Reconstructed f(R) Gravity and Its Cosmological Consequences in theChameleon Scalar Field with a Scale Factor Describing the Pre-Bounce Ekpyrotic Contraction

The present study reports a reconstruction scheme for f(R) gravity with the scale factor a(t)∝(t*−t)2c2 describing the pre-bounce ekpyrotic contraction, where t* is the big crunch time. The reconstructed f(R) is used to derive expressions for density and pressure contributions, and the equation of state parameter resulting from this reconstruction is found to behave like “quintom”. It has also been observed that the reconstructed f(R) has satisfied a sufficient condition for a realistic model. In the subsequent phase, the reconstructed f(R) is applied to the model of the chameleon scalar field, and the scalar field ϕ and the potential V(ϕ) are tested for quasi-exponential expansion. It has been observed that although the reconstructed f(R) satisfies one of the sufficient conditions for realistic model, the quasi-exponential expansion is not available due to this reconstruction. Finally, the consequences of pre-bounce ekpyrotic inflation in f(R) gravity are compared to the background solution for f(R) matter bounce.

Unified Inflation and Late-Time Accelerated Expansion with Exponential and R2 Corrections in Modified Gravity

Modified gravity models with and exponential function of curvature and R 2 corrections are proposed. At low curvature, the model explains the matter epoch and the late time accelerated expansion while at the inflation epoch the leading term is R 2 . At R → 0 the cosmological constant disappears, giving unified description of inflation and dark energy in pure geometrical context. The models satisfy the stability conditions, pass local tests and are viable in the ( r , m ) -plane, where the trajectories connect the saddle matter dominated critical point ( r = − 1 , m = 0 ) with the late time de Sitter attractor at r = − 2 and 0 < m ≤ 1 . Initial conditions were found, showing that the density parameters evolve in a way consistent with current cosmological observations, predicting late time behavior very close to the Λ CDM with future universe evolving towards the de Sitter attractor.

A Modified Dynamical Model of Cosmology I Theory

Wheeler (1964) had formulated Mach’s principle as the boundary condition for general relativistic field equations. Here, we use this idea and develop a modified dynamical model of cosmology based on imposing Neumann boundary condition on cosmological perturbation equations. Then, it is shown that a new term appears in the equation of motion, which leads to a modified Poisson equation. In addition, a modified Hubble parameter is derived due to the presence of the new term. Moreover, it is proved that, without a cosmological constant, such a model has a late time-accelerated expansion with an equation of state converging to w < − 1 . Also, the luminosity distance in the present model is shown to differ from that of the Λ C D M model at high redshifts. Furthermore, it is found that the adiabatic sound speed squared is positive in radiation-dominated era and then converges to zero at later times. Theoretical implications of the Neumann boundary condition have been discussed, and it is shown that, by fixing the value of the conjugate momentum (under certain conditions), one could derive a similar version of modified dynamics. In a future work, we will confine the free parameters of the Neumann model based on hype Ia Supernovae, Hubble parameter data, and the age of the oldest stars.

Testing viable f(R) models with the angular-diameter distance to compact quasar cores

We consider here some popular f(R) models generally viewed as possible alternatives to the existence of dark energy in General Relativity. For each of these, we compute the redshift z _max at which the angular diameter distance d _A (z) is expected to reach its maximum value. This turning point in d _A (z) was recently measured in a model-independent way using compact quasar cores and was found to occur at z _max = 1.70 ± 0.20. We compare the predictions of z _max for the f(R) models with this observed value to test their viability at a deeper level than has been attempted thus far, thereby quantifying an important observational difference between such modified gravity scenarios and standard Lambda Cold Dark Matter (ΛCDM) cosmology. Our results show that, while the most popular f(R) models today are consistent with this measurement to within 1σ, the turning point z _max will allow us to prioritize these alternative gravity theories as the measurement precision continues to improve, particularly with regard to how well they mitigate the tension between the predictions of ΛCDM and the observations. For example, while the Hu-Sawicki version of f(R) increases this tension, the Starobinky model reduces it.

Cosmological Bounce and Some Other Solutions in Exponential Gravity

In this work, we present some cosmologically relevant solutions using the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in metric f ( R ) gravity where the form of the gravitational Lagrangian is given by 1 α e α R . In the low curvature limit this theory reduces to ordinary Einstein-Hilbert Lagrangian together with a cosmological constant term. Precisely because of this cosmological constant term this theory of gravity is able to support nonsingular bouncing solutions in both matter and vacuum background. Since for this theory of gravity f ′ and f ″ is always positive, this is free of both ghost instability and tachyonic instability. Moreover, because of the existence of the cosmological constant term, this gravity theory also admits a de-Sitter solution. Lastly we hint towards the possibility of a new type of cosmological solution that is possible only in higher derivative theories of gravity like this one.

Cosmology and fundamental physics with the Euclid satellite

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015-2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid's Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom-a review

Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples of such modifications. These theories exhibit, in general, more degrees of freedom than those found in standard general relativity; counting, identifying, and retrieving the description/representation of such dynamical variables is currently an open problem, and a decidedly nontrivial one. In this work we review, via both formal arguments and custom-made examples, the most relevant methods to unveil the gravitational degrees of freedom of a given model, discussing the merits, subtleties and pitfalls of the various approaches.

Phase space of modified Gauss-Bonnet gravity

We investigate the evolution of non-vacuum Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f(R) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations.

Cosmology and Fundamental Physics with the Euclid Satellite

Euclid is a European Space Agency medium-class mission selected for launch in 2019 within the Cosmic Vision 2015-2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid's Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

The expansion of the universe observed with supernovae

Over the last 20 years, supernovae have become a key tool to constrain the expansion history of the Universe through the construction of Hubble diagrams, using luminosity distances to supernovae belonging to the 'Ia' subtype. This technique was key for the discovery that the expansion of the Universe is now accelerating. We review the principle and difficulties of the measurements, the classification and diversity of supernovae, and the physics of explosion. We discuss the systematic uncertainties affecting the cosmological conclusions with some emphasis on photometric calibration. We describe the major supernova cosmology surveys, the presented analyses and their conclusions, together with the present status of the field. We conclude on the expectations for the near future.

f(R) Theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.