Abstract
We consider the possibility of enhancing the inflationary tensor mode by introducing a spectator scalar field with a small sound speed which induces gravitational waves as a second-order effect. We analytically obtain the power spectra of gravitational waves and curvature perturbation induced by the spectator scalar field. We find that the small sound speed amplifies the curvature perturbation much more than the tensor mode and the current observational constraint forces the induced gravitational waves to be negligible compared with those from the vacuum fluctuation during inflation.
Highlights
The rest of the paper is organized as follows
The inflaton φ is assumed to be responsible for both the occurrence of inflation and the generation of the scalar perturbations imprinted in the cosmic microwave background radiation (CMB) [14, 15]
We focus on the term with δN (∂iδσ)2 (the second term in eq (3.1)) because it has a similar form to the graviton coupling term and it is easy to compare them.As we see later, the curvature perturbation induced only by this term excludes the dominant production of gravitational waves via the spectator field
Summary
We perturb the action and derive the equations of motion for the perturbed fields. One can show that the gravity sector of the perturbed action up to the second order is given by. We ignore the third and higher order terms in the gravity sector. A general multi-field perturbed action can be found in ref. Where the prime denotes the derivative with respect to the conformal time η and we introduce the sound speed of the canonical field Σ, c2s ≡. Since these equations are coupled to each other due to the mixing terms (see the third line in eq (2.16)), it is hard to solve them if the mixing is significantly strong. Note that the power spectrum of the σ field is amplified by the factor of (csPX )−1
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