New futures for cosmological models.

The discovery of accelerated expansion of the Universe opened up the possibility of new scenarios for the doom of our space-time, besides eternal expansion and a final contraction. In this paper, we review the chances that may await our universe. In particular, there are new possible singular fates (sudden singularities, big rip, etc.), but there also other evolutions that cannot be considered as singular. In addition to this, some of the singular fates are not strong enough in the sense that the space-time can be extended beyond the singularity. For deriving our results, we make use of generalized power and asymptotic expansions of the scale factor of the Universe. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.

f(R) gravity modifications: from the action to the data.

It is a very well established matter nowadays that many modified gravity models can offer a sound alternative to General Relativity for the description of the accelerated expansion of the universe. But it is also equally well known that no clear and sharp discrimination between any alternative theory and the classical one has been found so far. In this work, we attempt at formulating a different approach starting from the general class of f(R) theories as test probes: we try to reformulate f(R) Lagrangian terms as explicit functions of the redshift, i.e., as f(z). In this context, the f(R) setting to the consensus cosmological model, the [Formula: see text]CDM model, can be written as a polynomial including just a constant and a third-order term. Starting from this result, we propose various different polynomial parameterizations f(z), including new terms which would allow for deviations from [Formula: see text]CDM, and we thoroughly compare them with observational data. While on the one hand we have found no statistically preference for our proposals (even if some of them are as good as [Formula: see text]CDM by using Bayesian Evidence comparison), we think that our novel approach could provide a different perspective for the development of new and observationally reliable alternative models of gravity.

Forecast and analysis of the cosmological redshift drift.

The cosmological redshift drift could lead to the next step in high-precision cosmic geometric observations, becoming a direct and irrefutable test for cosmic acceleration. In order to test the viability and possible properties of this effect, also called Sandage-Loeb (SL) test, we generate a model-independent mock data set in order to compare its constraining power with that of the future mock data sets of Type Ia Supernovae (SNe) and Baryon Acoustic Oscillations (BAO). The performance of those data sets is analyzed by testing several cosmological models with the Markov chain Monte Carlo (MCMC) method, both independently as well as combining all data sets. Final results show that, in general, SL data sets allow for remarkable constraints on the matter density parameter today [Formula: see text] on every tested model, showing also a great complementarity with SNe and BAO data regarding dark energy parameters.

Modified gravity revealed along geodesic tracks.

The study of the dynamics of a two-body system in modified gravity constitutes a more complex problem than in Newtonian gravity. Numerical methods are typically needed to solve the equations of geodesics. Despite the complexity of the problem, the study of a two-body system in f(R) gravity leads to a new exciting perspective hinting the right strategy to adopt in order to probe modified gravity. Our results point out some differences between the semiclassical (Newtonian) approach, and the relativistic (geodesic) one thus suggesting that the latter represents the best strategy for future tests of modified theories of gravity. Finally, we have also highlighted the capability of forthcoming observations to serve as smoking gun of modified gravity revealing a departure from GR or further reducing the parameter space of f(R) gravity.

Recognizing Axionic Dark Matter by Compton and de Broglie Scale Modulation of Pulsar Timing.

Light axionic dark matter, motivated by string theory, is increasingly favored for the "no weakly interacting massive particle era". Galaxy formation is suppressed below a Jeans scale of ≃10^{8} M_{⊙} by setting the axion mass to m_{B}∼10^{-22} eV, and the large dark cores of dwarf galaxies are explained as solitons on the de Broglie scale. This is persuasive, but detection of the inherent scalar field oscillation at the Compton frequency ω_{B}=(2.5 months)^{-1}(m_{B}/10^{-22} eV) would be definitive. By evolving the coupled Schrödinger-Poisson equation for a Bose-Einstein condensate, we predict the dark matter is fully modulated by de Broglie interference, with a dense soliton core of size ≃150 pc, at the Galactic center. The oscillating field pressure induces general relativistic time dilation in proportion to the local dark matter density and pulsars within this dense core have detectably large timing residuals of ≃400 nsec/(m_{B}/10^{-22} eV). This is encouraging as many new pulsars should be discovered near the Galactic center with planned radio surveys. More generally, over the whole Galaxy, differences in dark matter density between pairs of pulsars imprints a pairwise Galactocentric signature that can be distinguished from an isotropic gravitational wave background.

Measuring the speed of light with baryon acoustic oscillations.

In this Letter, we describe a new method to use baryon acoustic oscillations (BAO) to derive a constraint on the possible variation of the speed of light. The method relies on the fact that there is a simple relation between the angular diameter distance (D(A)) maximum and the Hubble function (H) evaluated at the same maximum-condition redshift, which includes speed of light c. We note the close analogy of the BAO probe with a laboratory experiment: here we have D(A) which plays the role of a standard (cosmological) ruler, and H^{-1}, with the dimension of time, as a (cosmological) clock. We evaluate if current or future missions such as Euclid can be sensitive enough to detect any variation of c.

Constructing phantom cosmologies from standard scalar field universes.

We illustrate how form-invariance transformations can be used for constructing phantom cosmologies from standard scalar field universes. First we discuss how to relate two flat Friedmann-Robertson-Walker cosmologies with different barotropic indexes gamma and gamma;. Then we consider the particular case gamma;=-gamma, and we show that, if the matter content is interpreted in terms of self-interacting scalar fields, then the corresponding transformation provides the link between a standard and a phantom cosmology. After that, we illustrate the method by considering models with exponential potentials. Finally, we also show that the mentioned duality persists even if the typical brane-world modifications to the Friedmann equation are considered.