Power-law and intermediate inflationary models in f(T)-gravity

Published for SISSA by Springer Received: October 14, 2015 Revised: January 7, 2016 Accepted: January 8, 2016 Published: January 21, 2016 K. Rezazadeh,a A. Abdolmalekib and K. Karamia a Department of Physics, University of Kurdistan, Pasdaran St., Sanandaj, Iran b Research Institute for Astronomy & Astrophysics of Maragha (RIAAM), P.O. Box 55134-441, Maragha, Iran E-mail: , , Abstract: We study inflation in the framework of f (T )-gravity in the presence of a canonical scalar field. After reviewing the basic equations governing the background cosmology in f (T )-gravity, we turn to study the cosmological perturbations and obtain the evolutionary equations for the scalar and tensor perturbations. Solving those equations, we find the power spectra for the scalar and tensor perturbations. Then, we consider a power-law f (T ) function and investigate the inflationary models with the power-law and intermediate scale factors. We see that in contrast with the standard inflationary scenario based on the Einstein gravity, the power-law and intermediate inflationary models in f (T )-gravity can be compatible with the observational results of Planck 2015 at 68% CL. We find that in our f (T ) setting, the potentials responsible for the both power-law and intermediate inflationary models have the power-law form V (φ) ∝ φm but the power m is different for them. Therefore, we can refine some of power-law inflationary potentials in the framework of f (T )-gravity while they are disfavored by the observational data in the standard inflationary scenario. Interestingly enough, is that the self-interacting quartic potential V (φ) ∝ φ4 which has special reheating properties, can be consistent with the Planck 2015 data in our f (T ) scenario while it is ruled out in the standard inflationary scenario. Keywords: Cosmology of Theories beyond the SM, Classical Theories of Gravity ArXiv ePrint: 1509.08769 Open Access, c The Authors. Article funded by SCOAP3 . doi:10.1007/JHEP01(2016)131 JHEP01(2016)131 Power-law and intermediate inflationary models in f (T )-gravity Contents 1 2 f (T )-gravity 3 3 Cosmological perturbations in f (T )-gravity 5 4 Power-law inflation in f (T )-gravity 10 5 Intermediate inflation in f (T )-gravity 16 6 Conclusions 22 1 Introduction Inflationary scenario was proposed to overcome some of the basic problems of the Hot Big Bang cosmology such as the flatness problem, the horizon problem and also the magnetic monopole problem [1–7]. In addition, growth of the perturbations seeded during inflationary era can successfully explain the large-scale structure (LSS) formation as well as the anisotropy observed in the cosmic microwave background (CMB) radiation [8–11]. Therefore, applying the experimental results from LSS and CMB radiation, we are able to obtain useful information about the inflationary stage of the universe. Important observational results are represented by the Planck 2015 collaboration [12] that they are obtained from probing of the CMB radiation anisotropies in both temperature and polarization. Using these observational results, we can distinguish viable inflationary models and also constrain them. In inflation theory, a rapid accelerating expansion is considered before the radiation dominated era. In the standard inflationary scenario, a canonical scalar field is regarded in the framework of Einstein’s general relativity (GR) to explain the accelerating expansion of the inflationary era. Viability of different inflationary models in the framework of standard inflationary scenario in light of observational results has been extensively investigated in the literature [13–19]. However, there are other inflationary models represented on the base of extended theories of gravity. One important class of this category includes the models based on f (R)-gravity in which the Ricci curvature scalar R in the action is replaced by an arbitrary function of f (R) [20]. The well-known instance for this class is the Starobinsky R2 inflation [1] which is the first inflationary model and it is based on addition of the term R2 to the Einstein-Hilbert term R in the action. Although this model is the first inflationary model, it is in well agreement with the experimental data as it has been demonstrated by the Planck 2015 collaboration [12]. In order to find other inflationary models in the framework of f (R)-gravity see [21–25]. –1– JHEP01(2016)131 1 Introduction –2– JHEP01(2016)131 Another important class of the inflationary models based on the extended theories of gravity includes the models founded on the teleparallel gravity (TG) and its extension, f (T )-gravity. TG was originally proposed by Einstein [26] in an attempt of unifying gravity and electromagnetism. Later, Einstein left TG because it failed in the attempt of this unification and also the curvature tensor of the Weitzenbock connection vanishes. It has been shown that TG can provide an alternative for GR [27]. Then, the idea of the teleparallel equivalent to general relativity (TEGR) was developed. Subsequently, the TEGR was generalized to f (T )-gravity by replacing a general f (T ) function instead of the torsion scalar T in the action [28, 29]. The basic variables in f (T )-gravity are the tetrad fields eiµ where the Weitzenbock connection instead of the Levi-Civita connection is used to define the covariant derivative. Consequently, the spacetime has no curvature but contains torsion. The main advantage of f (T ) theory is the fact that its field equations are second order which are significantly simpler than the fourth order equations of f (R)-gravity [30–34]. Although, the models based on f (T )-gravity can be regarded as an alternative to f (R) theories [35], in contrast with f (R) scenario, f (T )-gravity is not dynamically equivalent to teleparallel action plus a scalar field via conformal transformation [36]. Recently, f (T )-gravity has aroused a great interest in cosmological applications. At first, f (T )-gravity was proposed as models for inflation [28, 29]. Then, models based on f (T )-gravity was considered to describe the present accelerating expansion of the universe without resorting to dark energy (DE) [30–43]. Also, thermodynamics of f (T )-gravity models has been investigated in [44–46]. Reconstructing of f (T ) theories equivalent to models based on scalar fields is subject of [47]. LSS formation in the framework of f (T )gravity has been regarded in [48, 49]. Cosmological perturbations in f (T )-gravity has been studied in [50–56]. Also, recently, some inflationary models in the framework of f (T )gravity have been investigated in [57–60]. In the present work, we focus on the study of inflation in the framework of f (T )-gravity in the presence of a canonical scalar field. We choose a power-law form for f (T ) function in the action and then investigate inflationary models with the power-law and intermediate scale factors in our setting. The power-law inf (...truncated)