We analyze the evolution of a Friedmann-Robertson-Walker spacetime within the framework of $f(R)$ metric gravity using an exponential model. We show that $f(R)$ gravity may lead to a vanishing effective cosmological constant in the far future (i.e. $R\rightarrow 0$) and yet produce a transient accelerated expansion at present time with a potentially viable cosmological history. This is in contrast with several $f(R)$ models which, while viable, produce in general a non-vanishing effective cosmological constant asymptotically in time ($R\rightarrow 4Λ_{\rm eff}$). We also show that relativistic {stars in asymptotically flat spacetimes can be supported within this framework without encountering any singularity, notably in the Ricci scalar $R$.
We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists up to the time where the norm of the Riemann tensor diverges. Restricting to initial metrics which belong to this class and are rotationally symmetric, we prove that if the sectional curvature in planes tangent to the orbits of symmetry is initially nonpositive, the flow starting from such an initial metric exists for all time. Moreover, if the sectional curva…
We introduce a novel theory of gravity based on the inverse of the Ricci tensor, that we call the anticurvature tensor. We derive the general equations of motion for any Lagrangian function of the curvature and anticurvature scalars. We then demonstrate a no-go theorem: no Lagrangian that contains terms linear in any positive or negative power of the anticurvature scalar can drive an evolution from deceleration to acceleration, as required by observations. This effectively rules out many realizations of this theory, as we illustrate in detail in a particular case. Finally, we speculate on how …
In this paper we study a class of wormhole solutions called generalized Ellis-Bronnikov wormholes in the context of asymptotically safe gravity (ASG). These solutions are characterized by two parameters: an even number $n$ and the wormhole throat radius $r_t$. The particular case $n=2$ recovers the usual Ellis-Bronnikov spacetime, which has already been addressed in the literature. We analyzed the nature of matter in the wormhole's throat, and in nearby regions, of these generalized solutions with $n>2$, using three curvature scalars in the ASG approach, namely, the Ricci scalar, squared Ricci…
Late-Time Cosmic Acceleration in Ricci-Gauss-Bonnet Gravity via Gradient Descent Optimization
Vellore Institute of Technology（维洛尔理工学院）；Birla Institute of Technology and Science-Pilani, Hyderabad Campus（印度理工学院海德拉巴校区）；University of Nizwa（尼兹瓦大学）；Khazar University（阿塞拜疆国家大学）
We report exact black hole solutions in asymptotically flat or (A)dS four-dimensional spacetime with a conformally coupled self-interacting scalar field in $f(R)$ gravity. We first consider the asymptotically flat model $f(R) = R -2α\sqrt{R}$ and derive an exact black hole solution. Then, we consider the asymptotically (A)dS model $f(R) =R -2 Λ-2 α\sqrt{R-4 Λ}$ and derive an exact black hole solution. In both cases the modified gravity parameter $α$, which has the dimension of the inverse mass, cannot be set to zero and the self-interacting potential is determined from the Klein-Gordon equatio…
A recently proposed Asymptotically Safe cosmology provides an elegant mechanism towards understanding the nature of dark energy and its associated cosmic coincidence problem. The underlying idea is that the accelerated expansion of the universe can occur due to infrared quantum gravity modifications at intermediate astrophysical scales (galaxies or galaxy clusters) which produce local anti-gravity sources. In this cosmological model no extra unproven energy scales or fine-tuning are used. In this study the Asymptotically Safe model is confronted with the most recent observational data from low…
Cosmology of f(Q,L_m) gravity with Holographic Ricci Dark Energy: Early-Time Inflation and Late-Time Acceleration and RGUP Corrected Observables
Amity University Kolkata（阿米提大学加尔各答分校）；Ahram Canadian University, Faculty of Engineering, Basic Science Department（艾哈兰加拿大大学工程学院基础科学系）；The Egyptian Center for Theoretical Physics (ECTP)（埃及理论物理中心）
We discuss the recently suggested Ricci-Gauss-Bonnet holographic dark energy in Chern-Simons modified gravity. We have tested some general forms of the scale factor $a(t)$, and used two physically reasonable forms which have been proved to be consistent with observations. Both solutions predict a sign flipping in the evolution of cosmic pressure which is positive during the early-time deceleration and negative during the late-time acceleration. This sign flipping in the evolution of cosmic pressure helps in explaining the cosmic deceleration-acceleration transition, and it has appeared in othe…
Following the holographic principle, which suggests that the energy density of dark energy may be proportional inversely to the area of the event horizon of the Universe, we have proposed a new energy density of dark energy through the acceleration of particle horizon scaled by the length of this parameter. This model depends only on one free parameter beta=0-1.99. For beta's near zero, the deviation of the model compared with the Lambda CDM model is tangible while for values beta=1.99, the suggested model has no conflict with Lambda CDM theory. Regardless of the value of beta, the model prese…
A formalism for the appearance of dark energy in the matter dominated era, leading to a persistent de Sitter expansion at the late time is proposed. Our framework is a hybrid quintessence model with a non-minimal coupling to the Ricci scalar. Coupling to the curvature triggers the dark energy evolution, while the coupling of scalar fields drives this evolution to a de Sitter stable fixed point. These occur via successive $Z_2$ symmetry breakings.
We prove uniqueness and existence theorems for four-dimensional asymptotically flat, Ricci-flat, gravitational instantons with a torus symmetry. In particular, we prove that such instantons are uniquely characterised by their rod structure, which is data that encodes the fixed point sets of the torus action. Furthermore, we establish that for every admissible rod structure there exists an instanton that is smooth up to possible conical singularities at the axes of symmetry. The proofs involve adapting the methods that are used to establish black hole uniqueness theorems, to a harmonic map form…
Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein Hilbert action. Here we develop the Hamiltonian formalism of a nonlocal model by considering only terms to quadratic order in Ricci tensor and Ricci scalar. We also show how to count the degree of freedom using Hamiltonian formalism in this model.
We construct the Carrollian equivalent of the relativistic energy--momentum tensor, based on variation of the action with respect to the elementary fields of the Carrollian geometry. We prove that, exactly like in the relativistic case, it satisfies conservation equations that are imposed by general Carrollian covariance. In the flat case we recover the usual non-symmetric energy--momentum tensor obtained using Nœther procedure. We show how Carrollian conservation equations emerge taking the ultra-relativistic limit of the relativistic ones. We introduce Carrollian Killing vectors and build as…
In this paper, we investigate the simplest wormhole solution - the Ellis-Bronnikov one - in the context of the Asymptotically Safe Gravity (ASG) at the Planck scale. We work with three models, which employ Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field equations by turning the Newton constant into a running coupling constant. For all the cases, we check the radial energy conditions of the wormhole solution and compare them with those valid in General Relativity (GR). We verify that asymptotic safety guarantees that the Ellis-Bronnikov wormhole can satisfy the r…
