Reheating in a modified teleparallel model of inflation

Abstract

We study the cosmological inflation and reheating in a teleparallel model of gravity. Reheating is assumed to be due to the decay of a scalar field to radiation during its rapid oscillation. By using cosmological perturbations during inflation, and subsequent evolutions of the Universe, we calculate the reheating temperature as a function of the spectral index and the power spectrum. * parviz.goodarzi@abru.ac.ir † mohsenisad@ut.ac.irRecently, the theory of gravity in the teleparallel framework [16][17][18][19] has attracted more attention [20][21][22][23][24][25][26][27][28]. This is due to the capacity of this model to describe the late time acceleration of the Universe [29][30][31][32][33][34][35][36][37][38], as well as the inflation in the early Universe [39,40]. In the teleparallel model, the curvatureless Weitzenbock connections are used instead of the torsionless Levi-Civita connections employed in the Einstein theory of gravity. Similar to the well-known extension of Einstein-Hilbert action to modified gravity ( f (R) model), the modified teleparallel gravity (f (T ) model) is an extension of the teleparallel model [29,30]. Scalar and tensor perturbations in teleparallel gravity were studied in [41,42]. Power spectrum and spectral index for scalar and tensor modes in f (T ) gravity have been calculated in [42].In this paper, inspired by the above-mentioned models, we will consider inflation in the modified teleparallel model. In a pure teleparallel model, it is not clear how the Universe is warming up after the inflation, and how particles are created. So we consider also a scalar field which decays to ultrarelativistic particles after the inflation, in a period of its rapid oscillation [12-14, 45, 46]. By studying the evolution of the universe, we compute the reheating temperature as a function of the observable parameters such as the spectral index and the power spectrum derived from Planck 2018 data [47].The scheme of the paper is as follows: In the second section, first we introduce the model and after some preliminaries, we briefly review inflation and cosmological perturbations in the power law modified teleparallel cosmology. In the third section, which is the main part of the paper, by studying the evolution of the Universe, and by using the results of the second section, the reheating temperature is calculated. We use units = c = k B = 1 through the paper.

Inflation with F(T) teleparallel gravity

“…In the theoretical aspect, the Lorentz invariance and conformal invariance of the F(T ) teleparallel theory are also investigated [74][75][76], and many interesting results emerged in the process. Finally, inflation in the context of F(T ) gravity has also been explored extensively [77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93] and in some works inflationary parameters were matched with experimentally observed data. However, most of these tests were made prior to the currently released data from Planck collaborations [94,95].…”

“…Clearly, n s lie much below the experimental data. Authors of [90] considered a minimally coupled scalar field to explore power law inflation, the scalar field being responsible to reheat after inflation. The authors obtain an expression for the reheating temperature in terms of the CMB temperature, the spectral index, the power spectrum and the parameters of the model.…”

Cosmological dynamics of dark energy in scalar-torsion $$f(T,\phi )$$ gravity

“…Even more, an important extension of f (T ) gravity is obtained by a non-minimal coupling between matter and torsion [91][92][93][94], when we consider an analogy with the non-minimal curvature-matter coupling in f (R) gravity [75,[95][96][97][98][99][100][101][102], whose principal motivation are the counterterms that appear at the moment of quantising a scalar field with self-interaction at curved spacetime [45,[103][104][105]. Also, we can go one step further by considering a generalised teleparallel scalar-torsion f (T, φ) gravity [106,107], which for example encompasses f (T ) gravity with scalar field [108][109][110][111][112], non-minimally coupled scalartorsion gravity [113][114][115][116][117][118][119][120][121][122], and its extensions by including a non-linear scalar-torsion coupling [107]. This latter kind of models are motivated by the already mentioned non-minimal torsion-matter coupling extension of f (T ) gravity [91][92][93][94], and its counterpart based on curvature, such as for example the case of a non-linear matter-curvature coupling in curvature-based modified gravity [75,...…”

Reconstructing inflation in scalar-torsion $$f(T,\phi )$$ gravity

“…These generalized scalar-torsion f (T, φ) gravity theories can also be seen as the torsion-based analogue of the so-called generalized f (R, φ) gravity theories [25]. This general action includes f (T ) gravity with scalar field [33][34][35][36], non-minimally coupled scalar-torsion gravity [37][38][39][40][41][42], and its extensions by including a non-linear scalar-torsion coupling [43]. A non-linear coupling between matter and gravity has been first studied in the context of curvature-based models in Refs.…”