Cosmology based on f ( R ) gravity with O (1)eV sterile neutrino
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TION OF PLASMAS, PARTICLE BEAMS, AND RADIATION WITH MATTER
Cosmology Based on f(R) Gravity with O(1) eV Sterile Neutrino1 A. Chudaykin* Institute for Nuclear Research, Russian Academy of Sciences, pr. Shestidesyatiletiya Oktyabrya 7a, Moscow, 117312 Russia *e-mail: [email protected] Received September 30, 2015
Abstract—We confront different up to date cosmological data with different gravity models of the Universe with one additional massive sterile neutrino [1].
Keywords: modified gravity, galaxy clusters, neutrino masses from cosmology DOI: 10.1134/S1063778816100057
1. INTRODUCTION The Dark Energy (DE) fraction is considered lately as evolving and unstable by analogy with the inflation stage in the early Universe. We use f(R) gravity [2], which modifies General Relativity (GR) by replacing the scalar curvature (Ricci curvature) R with a new phenomenological function f(R) in the Einstein-Hilbert action. Cosmology based on modified gravity can explain cosmic acceleration today without introducing cosmological constant Λ, so f (0) = 0 . New theory must be viable and theoretically consistent and therefore it should satisfy following conditions in the relevant region of R [3]
f '(R) > 0,
f ''(R) > 0,
(1)
and for R R0
f (R) − R R,
f '(R) − 1 1,
f ''(R)R 1, (2)
where prime denotes a derivative with respect to argument R and R0 is the present Ricci curvature in the Universe. The last three conditions are necessary to provide the correct Newtonian limit for the matterdominated stage in the past and smallness of non-GR corrections to a space-time background metric of compact astrophysical objects at present epoch. In cosmological model based on f(R) gravity and standard cosmology metric fluctuations evolve differently: matter density perturbations in modified gravity grow faster on scales smaller than the Compton wave1 The article is published in the original.
length of the scalar on field that occurs at recent redshifts. Therefore if we add one additional sterile neutrino in f(R) gravity, the net result can be zero because modified gravity and rest mass of sterile species play opposite roles in the evolution of matter density perturbations on small scales [4]. Indeed, small massive particle suppress structure formation below Jeans length through free-streaming effect. We add one sterile neutrino with mass O(1) eV to Standard Model by mixing with active ones. Importantly, the recent research of the primordial helium abundance permits the existence of one extra neutrino species [5]: an effective number of neutrinos is N eff = 3 . 58 ± 0 . 40(2σ). The light sterile neutrinos are required by various anomalies results in neutrino oscillation experiments [6]. In particular, the so-called gallium anomaly observed by GALLEX [7] and SAGE [8] experiments is nicely explained if the electron neutrino oscillations into sterile neutrino of 1 . 5 eV mass exist [9]. 2. BACKGROUND UNIVERSE The f(R) gravity is defined by the following action
S = 1 2 d 4 x − g f (R) + S m, 2κ
∫
(3)
where κ 2 /(8π) ≡ G is the Newton
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