Abstract
In this paper, we investigate the potential-driven inflation models with a disformal coupling to Einstein Gravity, to find out the effects of such a coupling on these models. We consider a simple coupling form which introduces only one parameter, and three inflation models, namely the chaotic inflation, the Higgs inflation, and the monodromy inflation. We find that the disformal coupling can have some modifications to the observational variables of these models such as the power spectrum, the spectral index as well as the tensor/scalar ratio, although not too large due to the constraints on the disformal coupling parameter. With these modifications, one has the opportunity of improving models that lie on the edge of the favorable regions of Planck observational data, such as monodromy inflation. Moreover, the non-trivial sound speed of tensor perturbations (gravitational waves) may come out, due to the coupling of gravity and kinetic terms of the field.
Highlights
One of the most mysterious fields in our Universe might be the inflaton field [1,2,3] that played an important role in the early stages of cosmic evolution
We find that the disformal coupling can have some modifications to the observational variables of these models such as the power spectrum, the spectral index as well as the tensor/scalar ratio, not too large due to the constraints on the disformal coupling parameter
The simplest case of such a consideration is the Brans-Dicke theory [4], which later on has been extended to the so-called scalar-tensor theory [5], where what couples to gravity is an arbitrary function of the inflaton φ. Such a case has been applied on many inflation models, the most famous of which might be that on Higgs inflation [6], where the inflaton field is recognized as the Higgs field that appeared in the Standard Model of particle physics
Summary
One of the most mysterious fields in our Universe might be the inflaton field [1,2,3] that played an important role in the early stages of cosmic evolution. More examples include coupling with GaussBonnet term [11], coupling to torsion [12,13], etc Among these various couplings, we consider a kind of “disformal coupling,” which is based on the so-called “disformal” relationship between two metrics in terms of: gμν 1⁄4 Aðφ; XÞgμν þ Bðφ; XÞ∂μφ∂νφ; ð1Þ where φ is some scalar field with its kinetic term X ≡ −∂μφ∂μφ=2, and A and B are arbitrary functions. The rest of the paper is scheduled as follows: in Sec. II we performed the model in its general way and transform it to its Einstein frame, where we consider a simple form of coupling which contains only one more parameter, in Sec. III we take into account the explicit examples and calculated the observational variables such as power spectrum, spectral index, and tensor/scalar ratio.
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