General Relativistic Cosmology Research Articles

On the uniqueness of ΛCDM-like evolution for homogeneous and isotropic cosmology in General Relativity

We address the question of the uniqueness of spatially flat ΛCDM-like evolution for FLRW cosmologies in General Relativity, i.e. whether any model other than the spatially flat ΛCDM can give rise to the same type of scale factor evolution. Firstly, we elaborate on what we exactly imply by a ΛCDM-like evolution or kinematic/cosmographic degeneracy with the ΛCDM model, using the lessons from the statefinder diagnostic. Then, we consider two models with interaction in the dark sector: coupled fluid-fluid model and coupled quintessence model. We enforce the kinematic degeneracy with the spatially flat ΛCDM model via the cosmographic condition j=1 (j being the jerk parameter), which in turn fixes the function of the interaction term that is a priori unspecified. We argue that in General Relativity this cosmographic condition is consistent only with spatial flatness. Employing a dynamical system approach, we show that the spatially flat coupled fluid-fluid interacting models kinematically degenerate with ΛCDM must necessarily be based on a phantom fluid, whereas the set of physically viable spatially flat coupled quintessence models with power law or exponential potential kinematically degenerate to ΛCDM is of measure zero. Our analysis establishes that coupled fluid-fluid models with non-phantom fluids or coupled quintessence models with power law and exponential potential can never reproduce a cosmological evolution similar to that of the ΛCDM. The astrophysical consequences of our findings are qualitatively discussed in light of observational cosmological tensions.

Singularity formation in asymptotically safe cosmology with inhomogeneous equation of state

Interest in cosmological singularities has remarkably grown in recent times, particularly on future singularities with the discovery of late-time acceleration of the universe and dark energy. While such explorations have previously been done in various modified gravity and quantum gravitationally inspired cosmologies (besides standard general relativistic cosmology), no such an endeavour has been taken up till now in the realms of renormalization group approaches to cosmology and we have hence took up on this journey. In this work, we consider the formation of cosmological singularities in an asymptotically safe cosmology where the cut off scale is proportional to the Hubble parameter. We consider a well motivated inhomogeneous form of the equation of state(EOS) as well. We firstly delve into some basics of this cosmology and show that such a scenario permits a transition between phantom and quintessence forms of universal evolution. We then show that one can have Type I - Type IV singularities in such a cosmology for various version of the EOS and that the singularities can occur both in finite and infinite time. The conditions in which these singularities occur is significantly different than how they occur in the standard cosmology, with the formulations being even more involved. Interestingly this difference comes about without the need of any free parameters in the cosmological models, which is usually what one observes when one goes for the same pursuit via various modified gravity/ QG inspired cosmological approaches. Furthermore, we showed that usual singularity removal methods like conformal anomaly effects and f(R) gravity effects do not offer much hope for singularity removal in this cosmology.

Type V singularities with inhomogeneous equations of state

Interest in cosmological singularities has remarkably grown in recent times, particularly on future singularities with the discovery of late-time acceleration of the universe and dark energy. Recent work has seen a proper classification of such singularities into strong and weak based on their strength, with weak singularities being the likes of sudden, w and big freeze singularities and strong singularities like the big rip. This has led to a classification of such singularities in various types like Big rip is Type 1, w-singularity is type V etc. While singularities of type I-type IV have been discussed vividly by taking into account inhomogeneous equations of state (EOS), the same has not been attempted for type V singularities. So in this work we have discussed in detail about the formation of type V singularities in various cosmologies after considering inhomogeneous equations of state. We consider two inhomogeneous forms of the EOS in the context of four different cosmological backgrounds; standard general relativistic cosmology, an asymptotically safe cosmology, a cosmology inspired by modified area-entropy relations, generalized uncertainty principles, holographic renormalization and Chern-Simons gravity (all of which can be coincidentally described by the same form of the modified Friedmann equation) and an f(R) gravity cosmology. We show in detail that one sees some very big differences in the occurrence conditions of type V singularities when one makes such considerations. In the particular case of the f(R) gravity cosmology, we see that the type V singularities get completely removed. This work goes to show that the creation and formation of type V singularities is influenced most strongly by the form of the equation of state that one considers, way more so than what background cosmology one chooses.

Rejuvenating the hope of a swampland consistent inflated multiverse with tachyonic inflation in the high-energy RS-II braneworld

The swampland conjectures from string theory have had some really interesting implications on cosmology, in particular on inflationary models. Some models of inflation have been shown to be incompatible with these criteria while some have been shown to be severely fine-tuned, with most of these problems arising in single field inflationary models in a General relativistic cosmology. Recent works have although optimistically shown that single field models in more general cosmologies can be consistent with these conjectures and hence there is an optimism that not all such models lie in the swampland. However, a paradigm of inflation which has been shown to not be perfectly okay with the conjectures is eternal inflation. So in this work, we discuss tachyonic inflation in the high-energy RS-II Braneworld scenario in the context of the swampland conjectures while also considering the possibility of swampland consistent eternal inflation. We show that our concerned regime evades all the prominent swampland issues for single field inflation being virtually unscathed. After this, we show that the main conflicts of eternal inflation with the swampland can easily be resolved in the considered tachyonic scenario and in particular, we also discuss the exciting prospect of a Generalized Uncertainty Principle facilitating the notion of Swampland consistent eternal inflation. Our work as a whole reignites the possibility that there can be a swampland (and possibly, quantum gravitationally) consistent picture of a “Multiverse”.

Type V singularities in non-standard cosmological backgrounds

Interest in cosmological singularities has remarkably grown in recent times, particularly on future singularities with the discovery of late-time acceleration of the universe and dark energy. Recent work has seen a proper classification of such singularities into strong and weak based on their strength, with weak singularities being the likes of sudden, w and big freeze singularities and strong singularities like the big rip. While there has been an expansive literature which has discussed the occurrence of Type I-IV in many non-standard cosmologies, w-singularities have not yet been explored in exotic cosmological settings. So in this work we pursue the same and discuss the status quo of w-singularities in a variety of non-standard cosmologies. We consider the RS-II Braneworld cosmology, an F(R) gravity cosmology which gives viable late time acceleration. We also consider cosmologies due to modified area-entropy relations, generalized uncertainty principles, holographic renormalization and Chern-Simons gravity( all of which can be coincidentally described by the same form of the modified Friedmann equation). We show that w-singularities will occur in exactly the same conditions in all these vividly different cosmological settings as they do in the usual general relativistic cosmology if one considers a power series expansion ansatz for the scale factor. We also show that if one considers an exponential form of the scale factor then while Type V singularities in the RS-II Braneworld and Chern-Simons cosmologies occur in the same conditions as in the standard cosmology case, there is a significant difference in the conditions when one considers the f(R) gravity case. These results are surprising overall, as one would usually not expect cosmological singularities to occur in almost the same conditions in non-standard cosmologies as they do in the usual standard cosmology.

General relativity’s energy and positivity: a brief history

I give a brief review of the search for a proper definition of energy in General Relativity (GR), a far from trivial quest, which was only completed after four and a half decades. The equally (or perhaps more) difficult task of establishing its positivity—it was to take another 15 plus years—will then be summarized. Extension to cosmological GR is included. Mention is made of some recent offshoots. An invitation to submit a review to the Proceedings of the Royal Society prompts revisiting a subject of central importance both to GR and to my own past research—its energy definition and positivity. While there are no loose ends left, a summary may be of some use to students and non-experts. Exposure to introductory GR is useful. We will divide this survey into two unequal parts: first, the original GR without a cosmological constant, then extend it to the rather different two cases of Λ ≠ 0 .

Einstein\u2013Yang\u2013Mills theory: gauge invariant charges and linearization instability

We construct the gauge-invariant electric and magnetic charges in Yang–Mills theory coupled to cosmological general relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser (Phys Lett B 116:259–263, 1982). For non-vanishing background gauge fields, the charges receive non-trivial contribution from the gravity part. In addition, we study the constraints on the first order perturbation theory and establish the conditions for linearization instability: that is the validity of the first order perturbation theory.

Particle Pair Production in Cosmological General Relativity—Redux

We model the universe on the interaction of two cosmic particles based on the Cosmological General Relativity (CGR) of Carmeli and obtain a theoretical value for the Hubble constant h at zero distance and no gravity. CGR is a 5-dimensional theory of time t, space x, y, z and velocity v. A minimum cosmic acceleration a0=dv/dt=c/τ results from a linearized version of CGR, where c is the vacuum speed of light and τ is the Hubble-Carmeli time constant. The force due to the Carmeli acceleration a0 counteracts the Newtonian gravitational force between the two particles. Each particle is unstable and disintegrates into baryons, leptons and radiation. By the uniform expansion of the black body radiation field, we obtain the expression , where A is a constant, T0 is the temperature of the cosmic microwave background black body, Ωbphys is the physical baryon density parameter and pc ≈3.086×1018cm·pc-1. Using standard values for T0 and Ωbphys we obtain a value τ=(4.15121±0.00206) ×1017s, which gives a value for the Hubble constant at zero distance and no gravity of h=1/τ=(74.33982±0.03694)km·s-1·Mpc-1. From the value for τ, we get the age of the universe of (13.15467 ± 0.00653) × 109 years.

The role of an invariant IR cutoff in late time cosmological dynamics

We study the role of an invariant infra-red cutoff in the late time cosmological dynamics. This low energy cutoff originates from the existence of a minimal measurable uncertainty as a result of the curvature of background manifold, and can be encoded in an extended uncertainty relation. Inspired by black hole entropy-area relation, we extend the analysis to the thermodynamics of apparent horizon of the universe. By treating both the Newtonian and general relativistic cosmologies, we show that the contribution of infra-red cutoff in the equations of dynamics can be interpreted as an effective fluid which is capable of explaining late time cosmic speed up and even transition to a phantom phase of expansion. We use the latest observational data from PLANCK2018 to constrain the parameter of an extended uncertainty relation.

Strong Constraints on Cosmological Gravity from GW170817 and GRB 170817A.

The detection of an electromagnetic counterpart (GRB 170817A) to the gravitational-wave signal (GW170817) from the merger of two neutron stars opens a completely new arena for testing theories of gravity. We show that this measurement allows us to place stringent constraints on general scalar-tensor and vector-tensor theories, while allowing us to place an independent bound on the graviton mass in bimetric theories of gravity. These constraints severely reduce the viable range of cosmological models that have been proposed as alternatives to general relativistic cosmology.

Averaged universe confronted with cosmological observations: A fully covariant approach

One of the outstanding problems in general relativistic cosmology is that of the averaging. That is, how the lumpy universe that we observe at small scales averages out to a smooth Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The root of the problem is that averaging does not commute with the Einstein equations that govern the dynamics of the model. This leads to the well-know question of backreaction in cosmology. In this work, we approach the problem using the covariant framework of Macroscopic Gravity (MG). We use its cosmological solution with a flat FLRW macroscopic background where the result of averaging cosmic inhomogeneities has been encapsulated into a backreaction density parameter denoted $\Omega_\mathcal{A}$. We constrain this averaged universe using available cosmological data sets of expansion and growth including, for the first time, a full CMB analysis from Planck temperature anisotropy and polarization data, the supernovae data from Union 2.1, the galaxy power spectrum from WiggleZ, the weak lensing tomography shear-shear cross correlations from the CFHTLenS survey and the baryonic acoustic oscillation data from 6Df, SDSS DR7 and BOSS DR9. We find that $-0.0155 \le \Omega_\mathcal{A} \le 0$ (at the 68\% CL) thus providing a tight upper-bound on the backreaction term. We also find that the term is strongly correlated with cosmological parameters such $\Omega_\Lambda$, $\sigma_8$ and $H_0$. While small, a backreaction density parameter of a few percent should be kept in consideration along with other systematics for precision cosmology.

Compact objects in Horndeski gravity

Horndeski gravity holds a special position as the most general extension of Einstein’s theory of general relativity (GR) with a single scalar degree of freedom and second-order field equations. Because of these features, Horndeski gravity is an attractive phenomenological playground to investigate the consequences of modifications of GR in cosmology and astrophysics. We present a review of the progress made so far in the study of compact objects (black holes (BHs) and neutron stars (NSs)) within Horndeski gravity. In particular, we review our recent work on slowly rotating BHs and present some new results on slowly rotating NSs.

On the emergence of accelerating cosmic expansion inf(R)theories of gravity

We consider cosmological modelling in $f(R)$ theories of gravity, using both top-down and bottom-up constructions. The top-down models are based on Robertson-Walker geometries, and the bottom-up constructions are built by patching together sub-horizon-sized regions of perturbed Minkowski space. Our results suggest that these theories do not provide a theoretically attractive alternative to the standard general relativistic cosmology. We find that the only $f(R)$ theories that can admit an observationally viable weak-field limit have large-scale expansions that are observationally indistinguishable from the Friedmann solutions of General Relativity with $\Lambda$. Such theories do not alleviate any of the difficulties associated with $\Lambda$, and cannot produce any new behaviour in the cosmological expansion without simultaneously destroying the Newtonian approximation to gravity on small scales.

General relativistic corrections and non-Gaussianity in large-scale structure

General relativistic cosmology cannot be reduced to linear relativistic perturbations superposed on an isotropic and homogeneous (Friedmann–Robertson–Walker) background, even though such a simple scheme has been successfully applied to analyse a large variety of phenomena (such as cosmic microwave background primary anisotropies, matter clustering on large scales, weak gravitational lensing, etc). The general idea of going beyond this simple paradigm is what characterizes most of the efforts made in recent years: the study of second and higher-order cosmological perturbations including all general relativistic contributions—also in connection with primordial non-Gaussianities—the idea of defining large-scale structure observables directly from a general relativistic perspective, the various attempts to go beyond the Newtonian approximation in the study of nonlinear gravitational dynamics, by using e.g., post-Newtonian treatments, are all examples of this general trend. Here we summarize some of these directions of investigation, with the aim of emphasizing future prospects in this area of cosmology, both from a theoretical and observational point of view.

How well is our Universe described by an FLRW model?

Extremely well! In the ΛCDM model, the spacetime metric, gab, of our Universe is approximated by an FLRW metric, , to about one part in 104 or better on both large and small scales, except in the immediate vicinity of very strong field objects, such as black holes. However, derivatives of gab are not close to derivatives of , so there can be significant differences in the behavior of geodesics and huge differences in curvature. Consequently, observable quantities in the actual Universe may differ significantly from the corresponding observables in the FLRW model. Nevertheless, as we shall review here, we have proven general results showing that—within the framework of our approach to treating backreaction—the large matter inhomogeneities that occur on small scales cannot produce significant effects on large scales, so satisfies Einsteinʼs equation with the averaged stress–energy tensor of matter as its source. We discuss the flaws in some other approaches that have suggested that large backreaction effects may occur. As we also will review here, with a suitable ‘dictionary,’ Newtonian cosmologies provide excellent approximations to cosmological solutions to Einsteinʼs equation (with dust and a cosmological constant) on all scales. Our results thereby provide strong justification for the mathematical consistency and validity of the ΛCDM model within the context of general relativistic cosmology.

Cosmological General Relativity with Scale Factor and Dark Energy

In this paper the four-dimensional space-velocity Cosmological General Relativity of Carmeli is developed by a general solution to the Einstein field equations. The metric is given in the Tolman form and the vacuum mass density is included in the energy-momentum tensor. The scale factor redshift equation is obtained, forming the basis for deriving the various redshift-distance relations of cosmological analysis. A linear equation of state dependent on the scale factor is assumed to account for the effects of an evolving dark energy in the expansion of the universe. Modeling simulations are provided for a few combinations of mass density, vacuum density and state parameter values over a sample of high redshift SNe Ia data. Also, the Carmeli cosmological model is derived as a special case of the general solution.

Cosmology: The search for twenty-four (or more) functions

We enumerate the $4(1+F)+2S$ independent arbitrary functions of space required to describe a general relativistic cosmology containing an arbitrary number of noninteracting fluid ($F$) and scalar fields ($S$). Results are also given for arbitrary space dimension and for higher-order gravity theories, where the number increases to $16+4F+2S$. Both counts are subject to assumptions about whether the dark energy is a cosmological constant. A more detailed analysis is provided when global homogeneity is assumed and the functions become constants. This situation is also studied in the case where the flat and open universes have compact spatial topologies. This changes the relative generalities significantly and places new constraints on the types of expansion anisotropy that are permitted. The most general compact homogeneous universes containing Friedmann models are spatially flat and described by $8+4F+2S$ constants. Comparisons are made with the simple six-parameter lambda-CDM model and physical interpretations provided for the parameters needed to describe the most general cosmological models.

Cosmology in a certain vector-tensor theory of gravitation

We study relevant cosmological topics in the framework of a certain vector-tensor theory of gravitation (hereafter VT). This theory is first compared with the so-called extended electromagnetism (EE). These theories have a notable resemblance and both explain the existence of a cosmological constant. It is shown that, in EE, a positive dark energy density requires a Lagrangian leading to quantum ghosts, whereas VT is free from these ghosts. On account of this fact, the remainder of the paper is devoted to study cosmology in the framework of VT. Initial conditions, at high redshift, are used to solve the evolution equations of all the VT scalar modes. In particular, a certain scalar mode characteristic of VT -which does not appear in general relativity (GR)- is chosen in such a way that it evolves separately. In other words, the scalar modes of the standard model based on GR do not affect the evolution of the VT characteristic mode; however, this scalar mode influences the evolution of the standard GR ones. Some well known suitable codes (CMBFAST and COSMOMC) have been modified to include our VT initial conditions and evolution equations, which are fully general. One of the resulting codes -based on standard statistical methods- has been used to fit VT predictions and observational evidences about both Ia supernovae and cosmic microwave background anisotropy. Seven free parameters are used in this fit. Six of them are often used in GR cosmology and the seventh one is characteristic of VT. From the statistical analysis it follows that VT seems to be advantageous against GR in order to explain cosmological observational evidences.

A Valid Finite Bounded Expanding Carmelian Universe Without Dark Matter

The solution of Einstein's field equations in Cosmological General Relativity (CGR), where the Galaxy is at the center of a finite yet bounded spherically symmetrical isotropic gravitational field, is identical with the unbounded solution. This leads to the conclusion that the Universe may be viewed as a finite expanding white hole. The fact that CGR has been successful in describing the distance modulus verses redshift data of the high-redshift type Ia supernovae means that the data cannot distinguish between unbounded models and those with finite bounded radii of at least $c \tau$. Also it is shown that the Universe is spatially flat at the current epoch and has been at all past epochs where it was matter dominated.

EXPLAINING THE SUPERNOVA DATA WITHOUT ACCELERATING EXPANSION

The 2011 Nobel Prize in Physics was awarded "for the discovery of the accelerating expansion of the universe through observations of distant supernovae." However, it is not the case that the type Ia supernova data necessitates accelerating expansion. Since we do not have a successful theory of quantum gravity, we should not assume general relativity (GR) will survive unification intact, especially on cosmological scales where tests are scarce. We provide a simple example of how GR cosmology may be modified to produce a decelerating Einstein-de Sitter cosmology (EdS) that accounts for the Union2 Compilation data as well as the accelerating ΛCDM (EdS plus a cosmological constant).