Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests (1205.3421v3)

Abstract: 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 $F(R)$ Ho\v{r}ava-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 paper demonstrates the equivalence of various dark energy models through alternative representations like scalar fields, holographic energy, and modified gravity.
• It validates the ΛCDM and dark fluid scenarios by employing cosmography tests that align with current observational data.
• The study paves the way for unified models of cosmic acceleration and inspires future research with refined observational techniques.

Dark Energy Cosmology and Its Equivalent Descriptions

The paper "Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests" provides a comprehensive summary of various dark energy cosmologies and their equivalent representations through different theoretical models. The paper of dark energy is crucial to understanding the current accelerated expansion of the universe, and this paper explores several key models, including the widely accepted $\Lambda$CDM model, as well as less conventional approaches like Little Rip and Pseudo-Rip universes, and phantom and quintessence cosmologies.

The paper begins with a detailed examination of the $\Lambda$CDM model, which incorporates a cosmological constant $\Lambda$ and cold dark matter (CDM) to account for cosmic acceleration. This model is also compared with several observational tests, affirming its consistency with current data. Beyond the $\Lambda$CDM paradigm, the researchers explore alternative models such as dark fluid scenarios characterized by a generalized equation of state (EoS), highlighting how these can mimic $\Lambda$CDM behavior under current observations.

Notably, the authors demonstrate equivalence between different dark energy models by utilizing frameworks like scalar fields, holographic dark energy, and modified gravity theories such as $F(R)$ and $f(T)$ theories. These equivalent descriptions are crucial as they provide alternative insights and potential solutions to the dark energy problem. In particular, the paper effectively shows that single and multiple scalar field theories, tachyon scalar fields, and geometric approaches can be intertwined to offer diverse perspectives on dark energy.

The second part of the paper focuses on an equivalent class of dark energy models that include $F(R)$ gravity, $F(R)$ Ho\v{r}ava-Lifshitz gravity, and teleparallel $f(T)$ gravity. These approaches extend beyond general relativity, offering alternative mechanisms to explain cosmic acceleration through modifications in the gravitational field equations.

Significant attention is given to cosmography as a tool for testing different dark energy models. The authors argue that accurate data analysis can resolve degeneracies among parameters, enhancing the capacity to distinguish between competing cosmological models. This aspect is vital as it appeals to ongoing and future observational missions aimed at further constraining the dark energy equation of state.

Key implications of this research include the potential for developing unified models that accommodate various cosmic acceleration mechanisms while remaining consistent with observations. The exploration of equivalent descriptions opens new routes for theoretical investigations and practical applications in cosmology.

Furthermore, the paper invites future work to refine these models, particularly in light of emerging observational data from large-scale surveys. The pursuit of novel gravitational theories that encompass dark energy phenomena remains a vibrant field of research, likely to yield deeper insights into the fundamental nature of our universe.

In conclusion, this paper is a notable contribution to the literature on dark energy cosmology, admirably synthesizing complex theoretical models and observational insights. Through demonstrating the equivalence of multiple models, the authors provide a valuable roadmap for future exploration in understanding the enigmatic dark energy component driving the current accelerated expansion of the universe.