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In this work, using a spherically symmetric metric, we investigate a minimally interacting holographic dark energy model within the framework of Saez-Ballester Theory. We predict that the dark energy component dominating the universe is of phantom type, which will lead the model universe to cosmic doomsday (big rip singularity). As big rip and holographic dark energy are incompatible with each other, we employ a higher dimensional scenario so that the cosmic doomsday is replaced by the de-Sitter phase. The model expands with a slow and uniform change of size during the early evolution, whereas the change becomes faster, agreeing with the present observation of the accelerated expansion. The present values of Hubble’s parameter and the dark energy EoS parameter are measured to be H = 67 and λ = − 1 . 00011 , which agree with the respective values H 0 = 67 . 36 ± 0 . 54 kms − 1 Mpc − 1 and λ = − 1 . 03 ± 0 . 03 of the most recent Planck 2018 result.

In this work, we present a Big Rip scenario within the framework of the generalized Brans-Dicke (GBD) theory. In the GBD theory, we consider an evolving BD parameter along with a self-interacting potential. An anisotropic background is considered to have a more general view of the cosmic expansion. The GBD theory with a cosmological constant is presented as an effective cosmic fluid within general relativity which favours a phantom field dominated phase. The model parameters are constrained so that the model provides reasonable estimates of the Hubble parameter and other recent observational aspects at the present epoch. The dynamical aspects of the BD parameter and the BD scalar field have been analysed. It is found that the present model witnesses a finite time doomsday at a time of tBR≃16.14Gyr, and for this scenario, the model requires a large negative value of the Brans-Dicke parameter.

Our current picture of how matter and radiation are distributed in the Universe on a large scale is derived from a wide variety of different types of observation. In this chapter, we concentrate upon the large-scale distribution of matter and radiation in the Universe and deal with galaxies and clusters of galaxies in Chaps. 3 and 4 respectively. The observations described in this chapter provide much of the essential underpinning of modern cosmological research.

The current paper is concerned with extracting a novel law for a varying polynomial deceleration parameter. This law covers each of Berman’s laws, a linearly varying deceleration parameter, a periodic Universe with a varying deceleration parameter of the second degree, and many other models. Additionally, this novel law tells us about the behavior of the Universe. Furthermore, it gives appropriate results with data (SNIa data and CMB shift), particularly of the late time of the Universe. In accordance with this law, one can expect several patterns in the evolution of the Universe like Big Rip, Big Crunch, periodic Universe, and dark energy.

The first part of this article develops [1] a closed universe model deploying by identical multiplication a Friedmann-Planck micro-universe; thus this one constitutes the grains of the vacuum of this universe. The quantum initial expansion of this is quadratic as a function of time. Using this model, calculating the density of matter at the present time gives a correct numerical result. The essential point is that during periods of expansion following the initial quadratic period, this model reveals a surprising phenomenon. The function expressing the radius curvature as a function of time depends on the individual mass of the heaviest elementary particles created at the end of the quadratic period. The model also leads to reflection on the dark matter. The second part imagines a new type of Big Rip based on the following hypothesis: when the acceleration of the Universe, caused by dark energy, reaches the value of Planck acceleration, destruction of the microscopic structure of the Universe occurs and is replaced by a macroscopic structure (photon spheres) identical to that of the initial Planck element. Thus a new Big Bang could begin on an immensely larger scale. This reasoning eventually leads to reflection on the origins of the Big Bang.

The gravitational field with torsion is being constructed by using the parametrized absolute parallelism geometry. A generalized law of variation of Hubble’s parameter in evolutionary cosmological models is used. The cosmological models under the influence of the gravitational field with torsion are obtained and discussed. A new model of the Universe is presented using a special class of Riemann–Cartan geometry. This model is oscillating with expansion and contraction at different stages. It behaves normally as the conventional Big Bang model in the first half-age until it reaches the moment of a Big Rip, then reverses its behavior as a result of a changes in the pressure and torsion until it reaches a Big Crunch at the end of the second half-age. We suppose that the Big Rip singularity is replaced by a regular maximum of the scale factor at the Big Rip due to a possible physical mechanism of quantum nature. The positivity condition for the energy density of matter leads to exclusion of open and closed universes.

MSc (Astrophysical Sciences), North-West University, Potchefstroom Campus In this study, cosmological models are considered, where dark matter and dark energy are coupled and may exchange energy through non-gravitational interactions with one other. These interacting dark energy (IDE) models are introduced to address problems with the standard ΛCDM model of cosmology, in which dark energy is assumed to be a cosmological constant. The central problem addressed in this study is the cosmic coincidence problem (regarding the presently measured coin- cidental ratio of dark matter to dark energy). Assuming two different linear dark energy couplings, Q1 = δH�dm and Q2 = δH�de, we find that interacting dark energy models may alleviate and even solve the cosmic coincidence problem by stabilising the ratio of dark matter to dark energy in both the past and future. Furthermore, we examine how these dark interactions affect crucial events in the expansion history of the universe. These events include the big bang and cosmic acceleration, as well as the radiation-matter and matter-dark energy equality. Besides studying the cosmological consequences of an interaction between the dark sectors, we also investigate the viability of IDE models on both theoretical and observational grounds. For both models considered, we find that negative energy densities are inevitable if energy flows from dark matter to dark energy and that consequently we should only seriously consider models where energy flows from dark energy to dark matter. To additionally ensure that these models are free from early time instabilities, we need to require that dark energy is in the ‘phantom’ (ω < −1) regime. This has the consequence that model Q1 = δH�dm will end with a future big rip singularity, while Q2 = δH�de may avoid this fate with the right choice of cosmological parameters. Cosmo- logical parameters for these models are obtained from type-Ia supernovae data using a previously developed Markov Chain Monte-Carlo (MCMC) simulation. The predicted expansion history from these models are then statistically compared to the supernovae data and the ΛCDM model, where we find that Q1 = δH�dm is statistically rejected, while Q2 = δH�de may be considered viable. Masters

A recent model predicting Omori’s law giving the number of aftershocks per unit time following an earthquake involves a differential equation analogous to the Friedmann equation of cosmology. The beforeshock phase is analogous to an accelerating universe approaching a Big Rip, the main shock to the Big Rip singularity, and the aftershock to a contracting universe. The analogy provides some physical intuition and Lagrangian and Hamiltonian formulations for Omori’s law and its generalizations.

From the Wheeler Dewitt solutions, the scale factor of the initial universe is discussed. In this study scale factors from Wheeler Dewitt solutions, loop quantum gravity, and phantom energy dominated stages are compared. Certain modifications have been attempted in scale factor and quantum potentials driven by canonical quantum gravity approaches. Their results are discussed in this work. Despite increment of phantom energy density avoidance of big rip is reported. Scale factors predicted from various models is discussed in this work. Relationship between scale factors and smooth continuation of aeon is discussed by the application of conformal cyclic cosmology. Quantum potentials for various models are correlated and a correction parameter is included on the cosmological constant. Phantom energy dominated, final stage non-singular evolution of the universe is reported. Eternal increment of phantom energy density without interacting with dark matter is reported for the consequence of evolution of the future universe. Also, the non-interacting solutions of phantom energy and dark matter are explained. As the evolution continues even after the final singularity is approached, the validity of conformal cyclic cosmology is predicted. Non zero values for the scale factor for the set of eigenvalues are reported with a graph

Some phantom cosmological models without big rip singularity have been constructed in a simple extended theory of gravity. In the geometrical part of the action, a minimally coupled linear function of the Ricci Scalar and the trace of the energy momentum tensor have been considered in place of the Ricci scalar. Four Little Rip and Pseudo Rip models have been investigated where the equation of state parameter evolves asymptotically and sufficiently rapidly to $-1$. The effect of the coupling constant of the extended gravity theory on the dynamics has been discussed. Possible wormhole solutions for the phantom models are obtained. The possibility of Big Trip in wormholes are discussed for the models., Comment: 12 pages

We propose a new class of cosmological unified dark sector models called "{\em Generalized Logotropic Models}". They depend on a free parameter $n$. The original logotropic model [P.H. Chavanis, Eur. Phys. J. Plus {\bf 130}, 130 (2015)] is a special case of our generalized model corresponding to $n=1$. In our scenario, the Universe is filled with a single fluid, a generalized logotropic dark fluid (GLDF), whose pressure $P$ includes higher order logarithmic terms of the rest-mass density $\rho_m$. The total energy density $\epsilon$ is the sum of the rest-mass energy density $\rho_m c^2$ and the internal energy density $u$ which play the role of dark matter energy density $\epsilon_m$ and dark energy density $\epsilon_{de}$, respectively. We investigate the cosmological behavior of the generalized logotropic models by focusing on the evolution of the energy density, scale factor, equation of state parameter, decceleration parameter and squared speed of sound. Low values of $n\le 3$ are favored. We also study the asymptotic behavior of the generalized logotropic models. In particular, we show that the model presents a phantom behavior and has three distinct ways of evolution depending on the value of $n$. For $n\le 2$, it leads to a little rip and for $n>2$ to a big rip. We predict the value of the big rip time as a function of $n$ without any free (undetermined) parameter., Comment: 26 pages, 5 figures

In this paper, we investigate the effects of torsion and shears within the framework of the gravitational field with torsion in early and late cosmology. General relativity and torsion field equations are constructed using absolute parallel geometry. The Big Rip model of the Universe has been presented using a special class of Riemann–Cartan geometry and the law of variation of Hubble’s parameter. The model does not depend on the curvature constant. The positive condition of the energy density of the matter is satisfied in this model. This cosmological model shows that the torsion and shear effect is strong at the beginning of the Big Bang and at the end of the universe. Through the examination of precise cases of the parameters and initial conditions, we can show that for suitable ranges of the parameters, the dynamic torsion scalar model can exhibit features similar to those of the currently observed accelerating universe. The relationship between the torsion and shear scalars is investigated, and their impact on the accelerating universe is addressed apart from the idea of dark energy.

Some cosmological models based on the gravitational theory $f(R) = R+\zeta R^2$, and on fluids obeying to the equations of state of Redlich-Kwong, Berthelot, and Dieterici are proposed for describing smooth transitions between different cosmic epochs. A dynamical system analysis reveals that these models contain fixed points which correspond to an inflationary, a radiation dominated and a late-time accelerating epoch, and a nonsingular bouncing solution, the latter being an asymptotic fixed point of the compactified phase space. The infinity of the compactified phase space is interpreted as a region in which the non-ideal behaviors of the previously mentioned cosmic fluids are suppressed. Physical constraints on the adopted dimensionless variables are derived by demanding the theory to be free from ghost and tachyonic instabilities, and a novel cosmological interpretation of such variables is proposed through a cosmographic analysis. The different effects of the equation of state parameters on the number of equilibrium solutions and on their stability nature are clarified. Some generic properties of these models, which are not sensitive to the particular fluid considered, are identified, while differences are critically examined by showing that the Redlich-Kwong scenario admits a second radiation-dominated epoch and a Big Rip Singularity., Comment: Matches published version

Non-minimally coupled scalar field models are well-known for providing interesting cosmological features. These include a late time dark energy behavior, a phantom dark energy evolution without singularity, an early time inflationary universe, scaling solutions, convergence to the standard $\Lambda$CDM, etc. While the usual stability analysis helps us determine the evolution of a model geometrically, bifurcation theory allows us to precisely locate the parameters' values describing the global dynamics without a fine-tuning of initial conditions. Using the center manifold theory and bifurcation analysis, we show that the general model undergoes a transcritical bifurcation, which predicts us to tune our models to have certain desired dynamics. We obtained a class of models and a range of parameters capable of describing a cosmic evolution from an early radiation era towards a late time dark energy era over a wide range of initial conditions. There is also a possible scenario of crossing the phantom divide line. We also find a class of models where the late time attractor mechanism is indistinguishable from that of a structurally stable general relativity based model; thus, we can elude the big rip singularity generically. Therefore, bifurcation theory allows us to select models that are viable with cosmological observations., Comment: 17 pages and 14 figs

The big rip, the little rip and the little sibling of the big rip are cosmological doomsdays predicted by some phantom dark energy models that could describe the future evolution of our Universe. When the universe evolves towards either of these future cosmic events all bounded structures and, ultimately, space-time itself are ripped apart. Nevertheless, it is commonly belief that quantum gravity effects may smooth or even avoid these classically predicted singularities. In this review, we discuss the classical and quantum occurrence of these riplike events in the scheme of metric $f(R)$ theories of gravity. The quantum analysis is performed in the framework of $f(R)$ quantum geometrodynamics. In this context, we analyse the fulfilment of the DeWitt criterion for the avoidance of these singular fates., Comment: Invited review submitted to Universe for the Special Issue on "Quantum Cosmology", ed. by Prof. Paulo Vargas Moniz, 32 pages, 3 tables. v2: typos fixed, references added, matches published version

In this article, we assume that the beginning of the universe was before the Big Bang. In the beginning, all matter in the universe was combined in an infinitesimal spherical shape. This sphere was compressed to an incomprehensible value for a period, and then exploded and expanded time and space. We are referring to the negative time before the Big Bang. The evolution of the universe before the Big Bang, passing through the moment of the explosion to the end of the universe at the Big Rip, has been studied. In this article, we try to answer the questions; did the universe exist before the Big Bang? What is the origin of the universe and how did it arise? What are the stages of the evolution of the universe until the moment of the Big Rip? What is the length of time for the stages of this development?

The little rip is a cosmological abrupt event predicted by some phantom dark energy models that could describe the future evolution of our Universe. This event can be interpreted as a big rip singularity delayed indefinitely, although in those models bounded structures will be destroyed in a finite cosmic time in the future. In this work, we analyse the little rip cosmology from a classical and quantum point of view within the scheme of alternative metric $f(R)$ theories of gravity. The quantum analysis is performed in the framework of $f(R)$ quantum geometrodynamics by means of the modified Wheeler-DeWitt equation. In this context, we show that the DeWitt criterion can be satisfied. Similar to what happens in general relativity, this result points towards the avoidance of the little rip in $f(R)$ quantum cosmology., 14 pages. v2: typos fixed, references added, matches published version

A rapid transition of the dark energy equation of state parameter $w$ at a transition redshift $z_t z_t$ to $w z_t$. Such a Late $w$ Phantom Transition ($LwPT$) avoids the discontinuity of $H(z)$ suggested in previous studies and thus does not require a step in the Pantheon Hubble diagram which is strongly constrained. We demonstrate that such an ultra low $z$ abrupt feature of $w(z)$ provides a better fit to cosmological data compared to smooth late time deformations of $H(z)$ that also address the Hubble tension. The strongly present day phantom dark energy behavior implied by this class of models hints towards a rapid approach of a Big Rip singularity which for $z_t=0.02$ will rip the universe in less than 3.5 billion years. Early hints of such effect may be observable in the dynamics of the nearest and largest bound systems ({\it e.g.} Virgo structures). The $LwPT$ can be generically induced by a phantom scalar field frozen by Hubble friction mimicking the cosmological constant and currently entering its ghost instability phase as Hubble friction decreases below the field dynamical scale.

We investigate the Bianchi type-V cosmological model with dark matter and anisotropic dark energy. It is assumed that the two sources minimally interact, so their energy-momentum tensors are conserved separately. The proportionality condition that relates the shear scalar $$(\sigma )$$ with the expansion scalar $$(\theta )$$ and the assumption of a diagonal energy–momentum tensor lead to some restriction on the metric functions. A special law is introduced for skewness parameter that describes the deviation of pressure from isotropy. This law can lead to models: the little rip, the big rip and the hybrid expansion. The hybrid expansion law provides a description of the transition of the Universe from deceleration to acceleration. The Universe behavior is discussed depending on the numerical parameters of the models.

Introducing an additional symmetry (δ symmetry) in the Einstein-Hilbert action, we obtain a gravitational field model (δ gravity) based on two symmetric tensors, gμv and gμv where an effective metric, given by gμv = gμv + gμv must be defined to describe the trajectories of massless particles. In previous papers, a truncated versions of δ gravity applied to cosmology was presented, where the δ symmetry was fixed in order to simplify the analysis of the model. The model predicts an accelerated expansion of the Universe without a cosmological constant or additional scalar fields, ending in a Big Rip. We present the full-fledged δ gravity, introducing a new kind of matter fields (δ matter) in order to preserve the δ symmetry. In this approach the prediction of the expansion of the Universe is preserved, but the value of the cosmological parameters improve greatly by the inclusion of δ matter. Additionally, δ matter gives us an excellent candidate for Dark Matter.

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., Comment: v2 with some minor changes and references added, matches the published version in Physics of the Dark Universe

We consider the possibility that the dark sector of our Universe contains a negative cosmological constant dubbed $\lambda$. For such models to be viable, the dark sector should contain an additional component responsible for the late-time accelerated expansion rate ($X$). We explore the departure of the expansion history of these models from the concordance $\Lambda$ Cold Dark Matter model. For a large class of our models the accelerated expansion is transient with a nontrivial dependence on the model parameters. All models with $w_X>-1$ will eventually contract and we derive an analytical expression for the scale factor $a(t)$ in the neighborhood of its maximal value. We find also the scale factor for models ending in a Big Rip in the regime where dustlike matter density is negligible compared to $\lambda$. We address further the viability of such models, in particular when a high $H_0$ is taken into account. While we find no decisive evidence for a nonzero $\lambda$, the best models are obtained with a phantom behavior on redshifts $z\gtrsim 1$ with a higher evidence for nonzero $\lambda$. An observed value for $h$ substantially higher than $0.70$ would be a decisive test of their viability., Comment: 12 pages, 5 figures, 4 tables. v3: Matches published version

We examine nonrelativistic particles that decay into relativistic products in big rip, little rip, and pseudo-rip models for the future evolution of the universe. In contrast to decays that occur in standard $\Lambda$CDM, the evolution of the ratio $r$ of the energy density of the relativistic decay products to the energy density of the initially decaying particles can decrease with time in all of these models. In big rip and little rip models, $r$ always goes to zero asymptotically, while this ratio evolves to infinity or a constant in pseudo-rip models., Comment: 4 pages, 3 figures, discussion and asymptotic analytic solution added

In this paper, we have considered a quadratic variation of the deceleration parameter ($q$) as a function of cosmic time ($t$) which describes a smooth transition from the decelerating phase of the Universe to an accelerating one and also show some distinctive feature from the standard model. The logical move of this article is against the behavior of the future Universe, \textit{i.e.} whether the Universe expands forever or ends with a Big Rip, and we observe that the outcome of the considered parametrization comes in favor of Big Rip future of the Universe. The whole set up of the parametrization and solution is taken in $f(R,T)$ theory of gravity for a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) geometry. Furthermore, we have considered the functional form of $f(R,T)$ function as $% f(R)+f(T)$, where a quadratic correction of the geometric term $R$ is adopted as the function $f(R)$, and a linear matter term $f(T)$. We have investigated some features of the model by examining the behavior of physical parameters. Our primary goal here is to discuss the physical dynamics of the model in $f(R,T)$ gravity. We have found, the EoS parameter also has the same singularity as that of the Hubble parameter \textit{i.e.} at the initial phase and at the Big Rip. The EoS parameter is explored in some detail for our choice of $f(R,T)$ function considered here. Different cases for $f(R,T)$ functional form for different values of the coupling parameters are discussed, and the evolution of the physical parameters is shown graphically., Comment: 14 pages, 3 figures with sub-figures

We explore the cosmological implications at effective level of matter creation effects in a dissipative fluid for a FLRW geometry; we also perform a statistical analysis for this kind of model. By considering an inhomogeneous Ansatz for the particle production rate we obtain that for created matter of dark matter type we can have a quintessence scenario or a future singularity known as little rip; in dependence of the value of a constant parameter, $\eta$, which characterizes the matter production effects. The dimensionless age of this kind of Universe is computed, showing that this number is greater than the standard cosmology value, this is typical of universes with presence of dark energy. The inclusion of baryonic matter is studied. By implementing the construction of the particle production rate for a dissipative fluid by considering two approaches for the expression of the bulk viscous pressure; we find that in Eckart model we have a big rip singularity leading to a catastrophic matter production and in the truncated version of the Israel-Stewart model such rate remains bounded leading to a quintessence scenario. For a non adiabatic dissipative fluid, we obtain a positive temperature and the cosmic expansion obeys the second law of thermodynamics., Comment: Improved version, accepted for publication in Phys. Rev. D. 12 pages, 4 figures

We consider different scenarios of the evolution of the universe, where the singularities or some non-analyticities in the geometry of the spacetime are present, trying to answer the following question: is it possible to conserve some kind of notion of particle corresponding to a chosen quantum field present in the universe when the latter approaches the singularity? We study scalar fields with different types of Lagrangians, writing down the second-order differential equations for the linear perturbations of these fields in the vicinity of a singularity. If both independent solutions are regular, we construct the vacuum state for quantum particles as a Gaussian function of the corresponding variable. If at least one of two independent solutions has a singular asymptotic behavior, then we cannot define the creation and the annihilation operators and construct the vacuum. This means that the very notion of particle loses sense. We show that at the approaching to the Big Rip singularity, particles corresponding to the phantom scalar field driving the evolution of the universe must vanish, while particles of other fields still can be defined. In the case of the model of the universe described by the tachyon field with a special trigonometric potential, where the Big Brake singularity occurs, we see that the (pseudo) tachyon particles do not pass through this singularity. Adding to this model some quantity of dust, we slightly change the characteristics of this singularity and tachyon particles survive. Finally, we consider a model with the scalar field with the cusped potential, where the phantom divide line crossing occurs. Here the particles are well defined in the vicinity of this crossing point., 13 pages, 1 figure. Final version to be published in PRD