[en] In the quest for precision cosmology, one must ensure that the cosmology is accurate as well. We discuss figures of merit for determining from observations whether the dark energy is a cosmological constant or dynamical, with special attention to the best determined equation of state value, at the 'pivot' or decorrelation redshift. We show this is not necessarily the best lever on testing consistency with the cosmological constant, and moreover is subject to bias. The standard parametrization of w(a)=w₀ + w_a(1-a) by contrast is quite robust, as tested by extensions to higher order parametrizations and modified gravity. Combination of complementary probes gives strong immunization against inaccurate, but precise, cosmology

[en] Under the generic designation of unimodular theory, two theoretical models of gravity are considered: the unimodular gravity and the TDiff theory. Our approach is primarily pedagogical. We aim to describe these models both from a geometric and a field-theoretical point of view. In addition, we explore connections with the cosmological-constant problem and outline some applications. We do not discuss the application of this theory to the quantization of gravity

[en] A dynamical realization of the most general $N=4$ superconformal group in one dimension $D(2,1;\mathrm{\alpha <!--\; ??\; -->})$ is discussed in which the group parameter α is linked to the cosmological constant.

[en] A detailed study of the various cosmological aspects in massive gravity theory has been presented in the present work. For the homogeneous and isotropic FLRW model, the deceleration parameter has been evaluated, and, it has been examined whether there is any transition from deceleration to acceleration in recent past, or not. With the proper choice of the free parameters, it has been shown that the massive gravity theory is equivalent to Einstein gravity with a modified Newtonian gravitational constant together with a negative cosmological constant. Also, in this context, it has been examined whether the emergent scenario is possible, or not, in massive gravity theory. Finally, we have done a cosmographic analysis in massive gravity theory

[en] The theory of the inflationary multiverse changes the way we think about our place in the world. According to its most popular version, our world may consist of infinitely many exponentially large parts, exhibiting different sets of low-energy laws of physics. Since these parts are extremely large, the interior of each of them behaves as if it were a separate universe, practically unaffected by the rest of the world. This picture, combined with the theory of eternal inflation and anthropic considerations, may help to solve many difficult problems of modern physics, including the cosmological constant problem. In this article I will briefly describe this theory and provide links to the some hard to find papers written during the first few years of the development of the inflationary multiverse scenario. (key issues review)

[en] We prove the consistency of the Goedel metric with the Horava-Lifshitz gravity whose action involves terms with z=1, z=2, and z=3. We show that, for different relations between the parameters of the theory, this consistency is achieved for different classes of matter; in particular, for the small cosmological constant, it is achieved only for the exotic matter--that is, ghosts or phantom matter.

[en] Horava-Lifshitz gravity with ''detailed balance'' but without the projectability assumption is discussed. It is shown that detailed balance is quite efficient in limiting the proliferation of couplings in Horava–Lifshitz gravity, and that its implementation without the projectability assumption leads to a theory with sensible dynamics. However, the (bare) cosmological constant is restricted to be large and negative

[en] It is shown that in some multi-supergraviton models, the contributions to the effective potential due to a non-trivial topology can be positive, giving rise in this way to a positive cosmological constant, as demanded by cosmological observations

[en] Treating the metric as a classical background field, we show that the cosmological constant does not run with the renormalization scale-contrary to some claims in the literature

[en] We develop Maggiore and Mancarella non-local model by using new function, $\mathrm{f}({\mathrm{m}}^2\frac{\mathrm{R}}{{\mathrm{◻<!--\; ???\; -->}}^2})$ and we obtained analytical hyperbolic tangent function. This new model has expansion history exactly as same as ΛCDM (Lambda Cold Dark Matter) with same matter content, but without cosmological constant or dark energy. However, background evolution in our model and ΛCDM are the same, but these models may be distinguishable in structure formation or observation that will contain additional information more than background level. (paper)