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arXiv:2006.03946v2 ; The knowledge of the universe future is of fundamental importance for any advanced civilization. We study the future of the singular dark universe where thermal effects due to the Hawking radiation on the apparent horizon of the FRW universe are taken in the consideration. It is shown that the dark universe which ends up as finite-time Type I and Type III singularity or the infinite-time Little Rip singularity transits to the finite-time Type II singularity thanks to account of the thermal effects. However, Type II and IV singular universe does not change the qualitative behavior. The combined account of the quantum and thermal effects shows that depending on the specific features of the universe only one of the effects is dominant. When (conformal matter) quantum effects are dominant, the future singularity is usually removed while for dominant thermal effects the universe final state is Type II singularity. ; This work is partially supported by MEXT, Japan KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas "Cosmic Acceleration" No. 15H05890 (S.N.) and the JSPS, Japan Grant-in-Aid for Scientific Research (C) No. 18K03615 (S.N.). This work was done partially in the framework of the Russian Government Program of Competitive Growth of the Kazan Federal University. ; Peer reviewed

The present paper represents an attempt for a very generic string inspired theory of gravitation, based on a stringy action in the teleparallel gravity which includes a specific functional which depends on the scalar field and its kinetic energy, as well as the torsion and boundary terms, embedding also possible effects from the teleparallel Gauss–Bonnet invariants. We focus our study in FLRW cosmology. After we deduce the cosmological equations for the associated generic theory of gravitation, we focus on string inspired couplings which are studied by considering different analytical techniques. The first analytical technique is based on the linear stability theory, by introducing proper dimensionless variables which enables us to study the structure of the phase space and the associated physical effects. In this case we have obtained different cosmological solutions which corresponds to matter and dark energy dominated solutions, achieving a possible transition between matter and dark energy dominated epochs. For each type of cosmological solutions we have discussed the corresponding physical features, attaining viable constraints for the coupling constants due to dynamical effects. The dynamical study of the physical features included also a numerical analysis by fine–tuning the initial conditions deep into the matter era, obtaining possible trajectories for the effective equation of state for specific coupling functions. ; This article is based upon work from CANTATA COST (European Cooperation in Science and Technology) action CA15117, EU Framework Programme Horizon 2020. SB is supported by Mobilitas Pluss N◦MOBJD423 by the Estonian government. PR acknowledges the Inter University Centre for Astronomy and Astrophysics (IUCAA), Pune, India for granting visiting associateship. MM would like to thank V. Baran for support. SDO is partially supported by Russian Ministry of Science and High Education, project No FEWF-2020-003. The authors thank Tomi S. Koivisto for spotting an important typo in the manuscript.

Two inhomogeneous single-fluid models for the Universe, which are able to naturally solve the H0 tension problem, are discussed. The analysis is based on a Bayesian Machine Learning approach that uses a generative process. The method here adopted allows for constraint of the free parameters of each model by making use of the model itself only. The observable is taken to be the Hubble parameter, obtained from the generative process. Using the full advantages of our method, the models are constrained for two redshift ranges. Namely, first this is done with mock H(z) data over z∈[0,2.5], thus covering known H(z) observational data, which are most helpful to validate the fit results. Then, aiming to extend to redshift ranges to be covered by the most recent ongoing and future planned missions, the models are constrained for the range z∈[0,5], too. Full validation of the results for this extended redshift range will have to wait for some years, for when higher-redshift H(z) data become available. This makes our models fully falsifiable. In addition, our second model is able to explain the BOSS reported value for H(z) at z=2.34. ; The work was carried out with the financial support of the Ministry of Education and Science of the Republic of Kazakhstan, Grant No. BR05236277 (S. D. Odintsov and R.Myrzakulov), Grant No. AP05135123 (R.Myrzakulov) and Grant No. 0118RK00935 while S. D. Odintsov was visiting ENU. This work has been partially supported by MINECO (Spain), Projects No. FIS2016-76363-P and No. PID2019–104397 GB-I00, and by AGAUR (Catalan Government), Project No. 2017-SGR-247. ; Peer reviewed

In this paper we shall investigate the propagation of gravitational waves in a flat Friedman-Robertson-Walker background, in the context of a string motivated corrected Einstein gravity. Particularly, we shall consider a misalignment axion Einstein gravity in the presence of a string originating Chern-Simons coupling of the axion field to the Chern-Pontryagin density in four dimensions. We shall focus our study on the propagation of the gravitational waves, and we shall investigate whether there exists any difference in the propagation of the polarization states of the gravitational waves. As we demonstrate, the dispersion relations are different in the right-handed mode and the left-handed mode. Finally, we compare the propagation of the axion Chern-Simons Einstein theory with that of standard F(R) gravity. ; This work is supported by MINECO (Spain), FIS2016-76363-P, and by project 2017 SGR247 (AGAUR, Catalonia) (S. D. O). This work is also supported by MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas "Cosmic Acceleration" No. 15H05890 (S. N.) and the JSPS Grant-in-Aid for Scientific Research (C) No. 18K03615 (S. N.). This work is supported by the DAAD program Hochschulpartnerschaften mit Griechenland (Projekt No. 57340132) (V. K. O). V. K. O is indebted to Professor K. Kokkotas for his hospitality in the IAAT, University of Tübingen. The work of A. P. is performed according to the Russian Government Program of Competitive Growth of Kazan Federal University. The work of A. P. was also supported by the Russian Foundation for Basic Research Grant No 19-02-00496. ; Peer reviewed