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arXiv:1507.04684 (cross-list from gr-qc) [pdf, other]

Consistency of non-flat $Λ$CDM model with the new result from BOSS

Suresh Kumar

Comments: 5 pages, 1 figure

Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO)

Using 137,562 quasars in the redshift range $2.1\leq z\leq3.5$ from the Data Release 11 (DR11) of the Baryon Oscillation Spectroscopic Survey (BOSS) of Sloan Digital Sky Survey (SDSS)-III, the BOSS-SDSS collaboration estimated the expansion rate $H(z=2.34)=222\pm7$ km/s/Mpc of Universe, and reported that this value is in tension with the predictions of flat $\Lambda$CDM model at around 2.5$\sigma$ level. In this letter, we briefly describe some attempts made in the literature to relieve the tension, and show that the tension can naturally be alleviated in non-flat $\Lambda$CDM model with positive curvature. However, this idea confronts with the inflation paradigm which predicts almost a spatially flat Universe. Nevertheless, the theoretical consistency of the non-flat $\Lambda$CDM model with the new result from BOSS deserves attention of the community.

4 Conclusion Following [8], we noticed that the lower values of H(z) at higher redshifts can be achieved in phenomenological models of interacting dark sector as discussed in Subsection 2.1. Therefore, the new result from BOSS could be an indication of interaction in the dark sector as pointed out in [8]. The lower values of H(z) at higher redshifts can also be accommodated in modified ΛCDM model via screening mechanism as illustrated in Subsection 2.2, following [9]. Motivated by the screening idea, we have considered the non-flat ΛCDM model with positive curvature. We have found that this model successfully accommodates the lower value of H(z) at higher z suggested by BOSS. Thus, in this work, we have briefly described some ideas/suggestions made in the literature to relieve the tension arising from the new result of BOSS, and showed that a non-flat ΛCDM model with positive curvature is also capable of accommodating the lower value of H(z) at higher z from BOSS. From the theoretical consistency of the non-flat ΛCDM model with the new result from BOSS as illustrated in Section 3, one may interpret that the new result from BOSS could be an indication of non-flat Universe with positive curvature. It might be possible that we are estimating a value of cosmological constant screened by the curvature term. It is also possible that the general relativity framework of ΛCDM model is not adequate, and requires modified theories of gravity to take into account [9]. In nutshell, if the non-flat ΛCDM model is true, then one needs to discover the physics of inflation that can produce a Universe with large spatial curvature. On the other hand, if the Universe is spatially flat, one needs to understand the physics of dark energy different from the cosmological constant. Considering overall scenario, it is clear that we do not have a model of the Universe in harmony with different observational probes. The new result from BOSS is, of course, a smoking gun for exploring new physics, and its theoretical consistency with the non-flat ΛCDM model deserves attention of the community.

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# Is the universe curved.

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