We review different dark energy cosmologies. In particular, we present the ΛCDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the ΛCDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies for different fluids are explicitly realized, and their properties are also explored. It is shown that all the above dark energy universes may mimic the ΛCDM model currently, consistent with the recent observational data. Furthermore, special attention is paid to the equivalence of different dark energy models. We consider single and multiple scalar field theories, tachyon scalar theory and holographic dark energy as models for current acceleration with the features of quintessence/phantom cosmology, and demonstrate their equivalence to the corresponding fluid descriptions. In the second part, we study another equivalent class of dark energy models which includes F(R) gravity as well as F(R) Hořava-Lifshitz gravity and the teleparallel f(T) gravity. The cosmology of such models representing the ΛCDM-like universe or the accelerating expansion with the quintessence/phantom nature is described. Finally, we approach the problem of testing dark energy and alternative gravity models to general relativity by cosmography. We show that degeneration among parameters can be removed by accurate data analysis of large data samples and also present the examples.

Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests

We review different dark energy cosmologies. In particular, we present the $\Lambda$CDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the $\Lambda$CDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies for different fluids are explicitly realized, and their properties are also explored. It is shown that all the above dark energy universes may mimic the $\Lambda$CDM model currently, consistent with the recent observational data. Furthermore, special attention is paid to the equivalence of different dark energy models. We consider single and multiple scalar field theories, tachyon scalar theory and holographic dark energy as models for current acceleration with the features of quintessence/phantom cosmology, and demonstrate their equivalence to the corresponding fluid descriptions. In the second part, we study another equivalent class of dark energy models which includes $F(R)$ gravity as well as $F(R)$ Hořava-Lifshitz gravity and the teleparallel $f(T)$ gravity. The cosmology of such models representing the $\Lambda$CDM-like universe or the accelerating expansion with the quintessence/phantom nature is described. Finally, we approach the problem of testing dark energy and alternative gravity models to general relativity by cosmography. We show that degeneration among parameters can be removed by accurate data analysis of large data samples and also present the examples.

The strong discrepancy between local and early-time (inverse distance ladder) estimates of the Hubble constant H0 could be pointing towards new physics beyond the concordance ΛCDM model. Several attempts to address this tension through new physics rely on extended cosmological models, featuring extra free parameters beyond the six ΛCDM parameters. However, marginalizing over additional parameters has the effect of broadening the uncertainties on the inferred parameters (including H0), and it is often the case that within these models the H0 tension is addressed due to larger uncertainties rather than a genuine shift in the central value of H0. In this paper I consider an alternative viewpoint: what happens if a physical theory is able to fix the extra parameters to a specific set of nonstandard values? In this case, the degrees of freedom of the model are reduced with respect to the standard case where the extra parameters are free to vary. Focusing on the dark energy equation of state w and the effective number of relativistic species Neff, I find that physical theories able to fix w≈-1.3 or Neff≈3.95 would lead to an estimate of H0 from cosmic microwave background, baryon acoustic oscillation, and type Ia supernovae data in perfect agreement with the local distance ladder estimate, without broadening the uncertainty on the former. These two nonstandard models are, from a model-selection perspective, strongly disfavored with respect to the baseline ΛCDM model. However, models that predict Neff≈3.45 would be able to bring the tension down to 1.5σ while only being weakly disfavored with respect to ΛCDM, whereas models that predict w≈-1.1 would be able to bring the tension down to 2σ (at the cost of the preference for ΛCDM being definite). Finally, I estimate dimensionless multipliers relating variations in H0 to variations in w and Neff, which can be used to swiftly repeat the analysis of this paper in light of future more precise local distance ladder estimates of H0, should the tension persist. As a caveat, these results were obtained from the 2015 Planck data release, but these findings would be qualitatively largely unaffected were I to use more recent data.

New physics in light of the $H_0$ tension: an alternative view

We demonstrate that there appear finite-time future singularities in $f(T)$ gravity with $T$ being the torsion scalar. We reconstruct a model of $f(T)$ gravity with realizing the finite-time future singularities. In addition, it is explicitly shown that a power-law-type correction term ${T}^{\ensuremath{\beta}}$ ($\ensuremath{\beta}g1$) such as a ${T}^{2}$ term can remove the finite-time future singularities in $f(T)$ gravity. Moreover, we study $f(T)$ models with realizing inflation in the early universe, the $\ensuremath{\Lambda}\mathrm{CDM}$ model, little rip cosmology and pseudo-rip cosmology. It is demonstrated that the disintegration of bound structures for little rip and pseudo-rip cosmologies occurs in the same way as in gravity with corresponding dark energy fluid. We also discuss that the time-dependent matter instability in the star collapse can occur in $f(T)$ gravity. Furthermore, we explore thermodynamics in $f(T)$ gravity and illustrate that the second law of thermodynamics can be satisfied around the finite-time future singularities for the universe with the temperature inside the horizon being the same as that of the apparent horizon.

Reconstruction of f(T) gravity: Rip cosmology, finite-time future singularities, and thermodynamics

Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied.

Black Holes, Cosmological Solutions, Future Singularities, and Their Thermodynamical Properties in Modified Gravity Theories

We examine models in which the dark energy density increases with time (so that the equation-of-state parameter $w$ satisfies $wl\ensuremath{-}1$), but $w\ensuremath{\rightarrow}\ensuremath{-}1$ asymptotically, such that there is no future singularity. We refine previous calculations to determine the conditions necessary to produce this evolution. Such models can display arbitrarily rapid expansion in the near future, leading to the destruction of all bound structures (a ``little rip''). We determine observational constraints on these models and calculate the point at which the disintegration of bound structures occurs. For the same present-day value of $w$, a big rip with constant $w$ disintegrates bound structures earlier than a little rip.

The little rip

Models for little rip dark energy

If we assume that the cosmic energy density will remain constant or strictly increase in the future, then the possible fates for the universe can be divided into four categories based on the time asymptotics of the Hubble parameter $H(t)$: the cosmological constant, for which $H(t)=\mathrm{\text{constant}}$, the big rip, for which $H(t)\ensuremath{\rightarrow}\ensuremath{\infty}$ at finite time, the little rip, for which $H(t)\ensuremath{\rightarrow}\ensuremath{\infty}$ as time goes to infinity, and the pseudo-rip, for which $H(t)\ensuremath{\rightarrow}\mathrm{\text{constant}}$ as time goes to infinity. Here we examine the last of these possibilities in more detail. We provide models that exemplify the pseudo-rip, which is an intermediate case between the cosmological constant and the little rip. Structure disintegration in the pseudo-rip depends on the model parameters. We show that pseudo-rip models for which the density and Hubble parameter increase monotonically can produce an inertial force which does not increase monotonically, but instead peaks at a particular future time and then decreases.

Pseudo-rip: Cosmological models intermediate between the cosmological constant and the little rip

In this brief review, we examine the theoretical consistency and viability of phantom dark energy. Almost all data sets from cosmological probes are compatible with the dark energy of the phantom variety (i.e. equation-of-state parameter w < −1) and may even favor evolving dark energy, and since we expect every physical entity to have some kind of field description, we set out to examine the case for phantom dark energy as a field theory. We discuss the many attempts at frameworks that may mitigate and eliminate theoretical pathologies associated with phantom dark energy. We also examine frameworks that provide an apparent measurement w < −1 while avoiding the need for a phantom field theory.

The viability of phantom dark energy: A review

In this brief review, we examine the theoretical consistency and viability of phantom dark energy. Almost all data sets from cosmological probes are compatible with dark energy of the phantom variety (i.e., equation-of-state parameter $w<-1$) and may even favor evolving dark energy, and since we expect every physical entity to have some kind of field description, we set out to examine the case for phantom dark energy as a field theory. We discuss the many attempts at frameworks that may mitigate and eliminate theoretical pathologies associated with phantom dark energy. We also examine frameworks that provide an apparent measurement $w<-1$ while avoiding the need for a phantom field theory.

Kevin J. Ludwick

Papers

The little rip

Models for little rip dark energy

Pseudo-rip: Cosmological models intermediate between the cosmological constant and the little rip

The viability of phantom dark energy: A review

The Viability of Phantom Dark Energy: A Brief Review