arXiv:2002.08157v2 [gr-qc] 23 Feb 2020 One - Dimensional Gravitational Waves In Quadratic Gravity Taimur Mohammadi, * Behrooz Malekolkalami, † February 25, 2020 Abstract In this paper, the equation of one-dimensional GWs for quadratic action in an isotropic and perfect fluid with perturbed FRW background metric was investigated. It was seen the obtained equation has several solutions which the figures of the power spectrum obtained are almost identical for all of them and are decreasing in terms of the wavenumber. Keywords: Gravitational waves, Power Spectrum, Quadratic action, f (R) gravity. 1 Introduction Gravitational waves (GWs) are produced when mass undergoes acceleration, in other words when space - time are perturbed by the motion of a massive object, the result is the GWs that propagates in space-time at the speed of light. This process is analogous to the moment of an electric charge when accelerating in an electromagnetic field. The study of compact binary systems, as one of the main sources of access to information about GWs, is one of the topic interesting the theoretical physics [1, 2, 3, 4]. Einstein’s predication about the existence of GWs [5] really happened by the discovery of the GW events GW150914, GW170814 and GW170817 by LIGO and VIRGO scientific [6, 7, 8] and opens a new window to probe gravitational physics. In this paper, we focus on one-dimensional GW caused by quadratic gravity model R 2 as a possible probe of the early universe. one of the well-known of the quadratic action is Starobinsky model for Cosmic Inflation. Other kinds of f (R) models can be found in [9, 10, 11, 12]. In this work, we consider the GW which come from quadratic action. Due to non-linearity, the evolution equations has problematic form and one solve them for one-dimensional. Our results indicates the quadratic model produces a stronger power spectrum although it has decreasing charter. This work is organized as follows: In section 2, we obtain the equation of GWs due to perturbed FRW background metric in quadratic action for an isotropic and perfect fluid. In section 3 we investigate one - dimensional GWs and the obtain spectrum of them in f(R) gravity. Conclusions are given in section 4. 2 The equation of GWs in f(R) gravity In order to obtain the equation of GWs in f(R) gravity we consider a perturbed Friedman–Robertson–Walker (FRW) space-time metric with the line element shown as bellow [3, 13] ds 2 = g μν dx μ dx ν = (¯ g μν + h μν ) dx μ dx ν = a 2  -dτ 2 +(δ ij + h ij (t, x)) dx i dx j  (1) * Department of Physics, University of Kurdistan, P.O.Box 66177-15175, Sanandaj, Iran. Email: t.mohammadi@uok.ac.ir † Department of Physics, University of Kurdistan, P.O.Box 66177-15175, Sanandaj, Iran. Email: b.malakolkalami@uok.ac.ir 1