Slow-roll inflation in generalized scalar-torsion gravity

Abstract

We study the dynamics of inflation in a generalized scalar-torsion gravity scenario by assuming a canonical scalar field non-minimally coupled to torsion with a Galileon-type self-interaction. After obtaining the field equations for a flat FRW background, we derive the second order action for both scalar and tensor perturbations to compute the power spectra of primordial fluctuations. As particular models, we studied at first, a power-law form of coupling function F (x) = 1 + ξx 2 /2, with x ≡ φ/M pl , and a monomial scalar field potential V (x) = λx n /n which is ruled out by current observational data for n ≥ 2. Under slow-roll approximation we obtain analytical expressions for the background as well as perturbative dynamics, and we show that the predictions of the model are consistent with current Planck 2018 constraints on the spectral index n s and the tensor-to-scalar ratio r through the n s − r plane. Accordingly, this model is in agreement with current observational bounds only within the 95% C.L. region in the case of chaotic quadratic inflation (n = 2), whereas that for the other monomial potentials such as n = 4/3, n = 1 and n = 2/3, it is found that they are even more favoured, overlapping their results with the 68% C.L. region from last Planck data. Secondly, we studied a model in which the presence of both non-minimal coupling to gravity and the Galileon non-linear self-interaction γ(∂φ) 2 φ leads to a suppression of the tensor-to-scalar ratio compared to those predicted in the standard scenario, then predicting 0.024 r 0.069. This result allows us to reconcile chaotic quadratic inflation with current Planck data up to the 68% C.L. region. In despite of this, next generation CMB experiments such as BICEP3 or LiteBIRD are expected to put stronger constraints, making possible to either support this model or rule it out.

Higgs inflation and teleparallel gravity

“…So if there is no matter apart from ϕ, there are no scalar metric perturbations. This result has previously been discussed in [109,120,124]. If other matter is included, the combination (3.26) remains zero regardless of the form of the matter action S (m) .…”

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

“…These non-linear scalar-torsion coupling terms can also be seen as a torsion-based analogue of non-linear matter-gravity couplings in extended f (R) gravity theories [75,95,96], but neglecting the coupling to the kinetic term of the scalar field. Including the kinetic term in the non-minimal coupling function could deviate the squared tensor propagation speed from 1 [122], which is something undesirable [35,36].…”

“…This expression is inspired by modify gravity models with non-linear matter-gravity coupling [75,95,96], but neglecting the kinetic term of the scalar field. Including the kinetic term could deviate the squared tensor propagation speed from 1 [122], which is something undesirable [35,36]. This non-linear scalar-torsion coupling is also motivated from the physics of the very early universe, where it is associated with the generation of primordial fluctuations during inflation, in the context of f (T, φ) gravity [107].…”

“…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,...…”

Cosmological inflation driven by a scalar torsion function

“…Although being difficult to obtain experimental evidence about the real effects of space-time torsion, once that such effects require a high energy density at cosmological events, there are predictive studies of how torsion signatures could manifest via inflation [23,24] and gravitational waves [25,26]. In the works [27,28] there are interesting studies and suggestions for experimental tests of non-zero torsion for gravity, concerning the Moon and Mercury motion.…”