Resolution of cosmological singularity in Ho\v{r}ava-Lifshitz cosmology

The standard $\Lambda$CDM model despite its agreement with observational data still has some issues unaddressed, lie the problem of initial singularity. Solving that problem usually requires modifications of general relativity. However, there appeared the Ho\v{r}ava-Lifshitz (HL) theory of gravity, in which equations governing cosmological evolution include a new term scaling similarly as dark radiation term in the Friedmann equations, enabling a bounce of the universe instead of initial singularity. This review describes past works on a stability of such a bounce in different formulations of HL theory, initial detailed balance scenario and further projectable versions containing higher than quadratic term to the original action.Comment: Submitted to Universe. Rewritten in order to remove repetitions from the previous paper

Comparing the dynamics of diagonal and general Bianchi IX spacetime

We make comparison of the dynamics of the diagonal and nondiagonal Bianchi IX models in the evolution towards the cosmological singularity. Apart from the original variables, we use the Hubble normalized ones commonly applied in the examination of the dynamics of homogeneous models. Applying the dynamical systems method leads to the result that in both cases the continuous space of critical points is higher dimensional and they are of the nonhyperbolic type. This is a generic feature of the dynamics of both cases and seems to be independent on the choice of phase space variables. The topologies of the corresponding critical spaces are quite different. We conjecture that the nondiagonal case may carry a new type of chaos different from the one specific to the usually examined diagonal one.Comment: 25 pages, 2 figures, version including numerical simulations of dynamic

Nonadiabatic bounce and an inflationary phase in the quantum mixmaster universe

Following our previous paper, Bergeron et al, Smooth quantum dynamics of the mixmaster universe, Phys. Rev. D 92, 061302(R) (2015), concerning the quantization of the vacuum Bianchi IX model and the Born-Huang-Oppenheimer framework, we present a further analysis of the dynamical properties of the model. Consistently with the deep quantum regime, we implement the harmonic approximation of the anisotropy potential. We thus obtain manageable dynamical equations. We study the quantum anisotropic oscillations during the bouncing phase of the universe. Neglecting the backreaction from transitions between quantum anisotropy states we obtain analytical results. In particular, we identify a parameter which is associated with dynamical properties of the quantum model and describes a sort of phase transition. Once the parameter exceeds its critical value, the Born-Huang-Oppenheimer approximation breaks down. The application of the present result to a simple model of the Universe indicates that the parameter indeed exceeds its critical value and that there takes place a huge production of anisotropy at the bounce. This in turn must lead to a sustained phase of accelerated expansion, an inflationary phase. The quantitative inclusion of backreaction shall be examined in a follow-up paper based on the vibronic approach.Comment: 32 pages, 9 figure

Vibronic framework for quantum mixmaster universe

Following our previous papers concerning the quantization of the vacuum Bianchi-IX model within or beyond the Born-Oppenheimer and adiabatic approximation, we develop a more elaborate analysis of the dynamical properties of the model based the vibronic approach utilized in molecular physics. As in the previous papers, we restrict our approach to the harmonic approximation of the anisotropy potential in order to obtain resoluble analytical expressions.Comment: 29 pages, 12 figure

On the energy flow of λ\lambda in Ho\v{r}ava-Lifshitz cosmology

Ho\v{r}ava-Lifshitz gravity has been proposed as a ghost-free quantum gravity model candidate with an anisotropic UV-scaling between space and time. We present here a cosmological background analysis of two different formulations of the theory, with particular focus on the running of the parameter $\lambda$. Using a large dataset consisting of Cosmic Microwave Background data from {\it Planck}, Pantheon+ supernovae catalogue, SH0ES Cepheid variable stars, Baryon acoustic oscillations (BAO), Cosmic Chronometers, and gamma-ray bursts (GRB), we arrive at new bounds on the cosmological parameters, in particular $\lambda$, which describes deviation from classical general relativity. For the detailed balance scenario we arrive at the bound $\lambda=1.02726\pm0.00012$, and for beyond detailed balance the limit reads $\lambda=0.9949^{+0.0045}_{-0.0046}$. We also study the influence of different data sets and priors, and we find that removing low-redshift data generally moves $\lambda$ closer towards UV values, whilst simultaneously widening the error bars. In the detailed balance scenario, this effect is more noticeable, and $\lambda$ takes on values that are significantly below unity, which corresponds to the infrared limit of the theory.Comment: 16 pages, 2 tables, 1 figur