We investigate the cosmological evolution of a mimetic matter model with arbitrary scalar potential. The cosmological reconstruction---which is the method for constructing a model for an arbitrary evolution of the scale factor---is explicitly performed for different choices of potential. The cases where the mimetic matter model shows the evolution as cold dark matter (CDM), the $w\mathrm{CDM}$ model, dark matter and dark energy with a dynamical $Om(z)$ [where $Om(z)\ensuremath{\equiv}[(H(z)/{H}_{0}{)}^{2}\ensuremath{-}1]/[(1+z{)}^{3}\ensuremath{-}1]$], and phantom dark energy with a phantom-nonphantom crossing are presented in detail. The cosmological perturbations for such evolutions are studied in the mimetic matter model. For instance, the evolution behavior of the matter density contrast (which is different than the usual one, i.e., $\stackrel{\ifmmode\ddot\else\textasciidieresis\fi{}}{\ensuremath{\delta}}+2H\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\delta}}\ensuremath{-}{\ensuremath{\kappa}}^{2}\ensuremath{\rho}\ensuremath{\delta}/2=0$) is investigated. The possibility of a peculiar evolution of $\ensuremath{\delta}$ in the model under consideration is shown. Special attention is paid to the behavior of the matter density contrast near the future singularity, where the decay of perturbations may occur much earlier than the singularity.

Cosmological perturbations in a mimetic matter model

Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we relate this form of geometry to the broader metric-affine approach to forming gravitational theories where we describe a systematic way of constructing consistent teleparallel theories that respect certain physical conditions such as local Lorentz invariance. We first use teleparallel gravity to formulate a teleparallel equivalent of general relativity which is dynamically equivalent to general relativity but which may have different behaviors for other scenarios, such as quantum gravity. After setting this foundation, we describe the plethora of modified teleparallel theories of gravity that have been proposed in the literature. In the second part of the Review, we first survey works in teleparallel astrophysics literature where we focus on the open questions in this regime of physics. We then discuss the cosmological consequences for the various formulations of teleparallel gravity. We do this at background level by exploring works using various approaches ranging from dynamical systems to Noether symmetries, and more. Naturally, we then discuss perturbation theory, firstly by giving a concise approach in which this can be applied in teleparallel gravity theories and then apply it to a number of important theories in the literature. Finally, we examine works in observational and precision cosmology across the plethora of proposal theories. This is done using some of the latest observations and is used to tackle cosmological tensions which may be alleviated in teleparallel cosmology. We also introduce a number of recent works in the application of machine learning to gravity, we do this through deep learning and Gaussian processes, together with discussions about other approaches in the literature.

Teleparallel Gravity: From Theory to Cosmology

The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological singularities in classical and quantum cosmology. We discuss the classification of singularities from the geometrical point of view and from the point of view of the behavior of finite size objects, crossing such singularities. We discuss in some detail quantum and classical cosmology of models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus dust), of models based on the Born–Infeld-type fields and of the model of a scalar field with a potential inversely proportional to the field itself. We dwell also on the phenomenon of the phantom divide line crossing in the scalar field models with cusped potentials. Then we discuss the Friedmann equations modified by quantum corrections to the effective action of the models under considerations and the influence of such modification on the nature and the existence of soft singularities. We review also quantum cosmology of models, where the initial quantum state of the universe is presented by the density matrix (mixed state). Finally, we discuss the exotic singularities arising in the braneworld cosmological models.

Quantum cosmology and late-time singularities

The standard cosmology strongly relies upon the Cosmological Principle, which consists on the hypotheses of large scale isotropy and homogeneity of the Universe. Testing these assumptions is, therefore, crucial to determining if there are deviations from the standard cosmological paradigm. In this paper, we use the latest type Ia supernova compilations, namely JLA and Union2.1 to test the cosmological isotropy at low redshift ranges ($z<0.1$). This is performed through a Bayesian selection analysis, in which we compare the standard, isotropic model, with another one including a dipole correction due to peculiar velocities. We find that the Union2.1 sample favors the dipole-corrected model, but the opposite happens for the JLA. Nonetheless, the velocity dipole results are in good agreement with previous analyses carried out with both datasets. We conclude that there are no significant indications for large anisotropic signals from nearby supernova compilations, albeit this test should be greatly improved with the upcoming cosmological surveys.

Isotropy of low redshift type Ia supernovae: A Bayesian analysis

Teleparallel Gravity offers the possibility of reformulating gravity in terms of torsion by exchanging the Levi-Civita connection with the Weitzenbock connection which describes torsion rather than curvature. Surprisingly, Teleparallel Gravity can be formulated to be equivalent to general relativity for a appropriate setup. Our interest lies in exploring an extension of this theory in which the Lagrangian takes the form of $f(T,B)$ where T and B are two scalars that characterize the equivalency with general relativity. In this work, we explore the possible of reproducing well-known cosmological bouncing scenarios in the flat Friedmann-Lemaitre-Robertson-Walker geometry using this approach to gravity. We study the types of gravitational Lagrangians which are capable of reconstructing analytical solutions for symmetric, oscillatory, superbounce, matter bounce, and singular bounce settings. These new cosmologically inspired models may have an effect on gravitational phenomena at other cosmological scales.

/pdf/cosmological-bouncing-solutions-in-f-t-b-gravity-551iafmzaj.pdf

Cosmological bouncing solutions in f(T,B) gravity

We discuss combined constraints, coming from the cosmic microwave background shift parameter $\mathcal{R}$, the baryon acoustic oscillations distance parameter $\mathcal{A}$, and from the latest type Ia supernovae data, imposed on cosmological models which allow sudden future singularities of pressure We show that due to their weakness such sudden singularities may happen in the very near future and that at present they can mimic standard dark energy models

Cosmological tests of sudden future singularities

Current observational evidence does not yet exclude the possibility that dark energy could be in the form of phantom energy. A universe consisting of a phantom constituent will be driven toward a drastic end known as the `Big Rip' singularity where all the matter in the universe will be destroyed. Motivated by this possibility, other evolutionary scenarios have been explored by Barrow, including the phenomena which he called Sudden Future Singularities (SFS). In such a model it is possible to have a blow up of the pressure occurring at sometime in the future evolution of the universe while the energy density would remain unaffected. The particular evolution of the scale factor of the universe in this model that results in a singular behaviour of the pressure also admits acceleration in the current era. In this paper we will present the results of our confrontation of one example class of SFS models with the available cosmological data from high redshift supernovae, baryon acoustic oscillations (BAO) and the cosmic microwave background (CMB). We then discuss the viability of the model in question as an alternative to dark energy.

Sudden Future Singularity models as an alternative to Dark Energy

Current observational evidence does not yet exclude the possibility that dark energy could be in the form of phantom energy. A universe consisting of a phantom constituent will be driven towards a drastic end known as the ‘Big Rip’ singularity where all the matter in the universe will be destroyed. Motivated by this possibility, other evolutionary scenarios have been explored by Barrow, including the phenomena which he called Sudden Future Singularities (SFSs). In such a model it is possible to have a blow up of the pressure occurring at sometime in the future evolution of the universe while the energy density would remain unaffected. The particular evolution of the scale factor of the universe in this model that results in a singular behaviour of the pressure also admits acceleration in the current era. In this paper we will present the results of our confrontation of one example class of SFS models with the available cosmological data from high-redshift SNe, baryon acoustic oscillations (BAOs) and the cosmic microwave background (CMB). We then discuss the viability of the model in question as an alternative to dark energy.

/pdf/sudden-future-singularity-models-as-an-alternative-to-dark-5968tejrma.pdf

Sudden Future Singularity models as an alternative to dark energy

We contribute another anisotropy study to this field of research using Type Ia supernovae (SNe Ia). In this work, we utilise the power spectrum calculation method and apply it to both the current SNe Ia data and simulation. Using the Union2.1 data set at all redshifts, we compare the spectrum of the residuals of the observed distance moduli to that expected from an isotropic universe affected by the Union2.1 observational uncertainties at low multipoles. Through this comparison we find a dipolar anisotropy with tension of less that $2\sigma$ towards $l =171^\circ \pm 21^\circ$ and $b=-26^\circ \pm 28^\circ$ which is mainly induced by anisotropic spatial distribution of the SNe with $z > 0.2$ rather than being a cosmic effect. Furthermore, we find a tension of $\sim 4\sigma$ at $\ell=4$ between the two spectra. Our simulations are constructed with the characteristics of the upcoming surveys like the Large Synoptic Survey Telescope (LSST), which shall bring us the largest SNe Ia collection to date. We make predictions for the amplitude of a possible dipolar anisotropy that would be detectable by future SNe Ia surveys.

Supernovae anisotropy power spectrum

We contribute another anisotropy study to this field of research using Supernovae Type Ia (SNe Ia). In this work, we utilise the power spectrum calculation method and apply it to both the current SNe Ia data and simulation. Our simulations are constructed with the characteristics of the upcoming survey of the Large Synoptic Survey Telescope (LSST), which shall bring us the largest SNe Ia collection to date. We make predictions for the amplitude of a possible dipole anisotropy or anisotropy in higher multipole moments that would be detectable by the LSST.

Hoda Ghodsi

Papers

Cosmological tests of sudden future singularities

Sudden Future Singularity models as an alternative to Dark Energy

Sudden Future Singularity models as an alternative to dark energy

Supernovae anisotropy power spectrum

Supernovae anisotropy power spectrum