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Register a new userAnisotropic inflation with coupled $boldsymbol{p}$-forms
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We study the cosmology in the presence of arbitrary couplings between $p$-forms in 4-dimensional space-time for a general action respecting gauge symmetry and parity invariance. The interaction between 0-form (scalar field $phi$) and 3-form fields gives rise to an effective potential $V_{rm eff}(phi)$ for the former after integrating out the contribution of the latter. We explore the dynamics of inflation on an anisotropic cosmological background for a coupled system of 0-, 1-, and 2-forms. In the absence of interactions between 1- and 2-forms, we derive conditions under which the anisotropic shear endowed with nearly constant energy densities of 1- and 2-forms survives during slow-roll inflation for an arbitrary scalar potential $V_{rm eff}(phi)$. If 1- and 2-forms are coupled to each other, we show the existence of a new class of anisotropic inflationary solutions in which the energy density of 2-form is sustained by that of 1-form through their interactions. Our general analytic formulas for the anisotropic shear are also confirmed by the numerical analysis for a concrete inflaton potential.
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We examine whether an extended scenario of a two-scalar-field model, in which a mixed kinetic term of canonical and phantom scalar fields is involved, admits the Bianchi type I metric, which is homogeneous but anisotropic spacetime, as its power-law solutions. Then we analyze the stability of the anisotropic power-law solutions to see whether these solutions respect the cosmic no-hair conjecture or not during the inflationary phase. In addition, we will also investigate a special scenario, where the pure kinetic terms of canonical and phantom fields disappear altogether in field equations, to test again the validity of cosmic no-hair conjecture. As a result, the cosmic no-hair conjecture always holds in both these scenarios due to the instability of the corresponding anisotropic inflationary solutions.
Effect of non-canonical scalar fields on the CMB imprints of the anisotropic inflation will be discussed in details in this paper. In particular, we are able to obtain the general formalism of the angular power spectra in the scalar perturbations, tensor perturbations, cross-correlations, and linear polarization in the context of the anisotropic inflation model involving non-canonical scalar fields. Furthermore, some significant numerical spectra will be plotted using the most recent data of Planck as well as the BICEP2 and Keck array. As a result, we find a very interesting point that the $TT$ spectra induced by the tensor perturbations as well as by the linear polarization will increase when the speed of sound decreases.
We perform adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation with varying speed of sound. The subtraction is performed within the framework of earlier study by Urakawa and Starobinsky dealing with the canonical inflation. Inspired by Fakir and Unruhs model on nonminimally coupled chaotic inflation, we find upon imposing near scale-invariant condition, that the subtraction term exponentially decays with the number of $ e $-folds. As in the result for the canonical inflation, the regularized power spectrum tends to the bare power spectrum as the Universe expands during (and even after) inflation. This work justifies the use of the bare power spectrum in standard calculation in the most general context of slow-roll single-field inflation involving non-minimal coupling and varying speed of sound.
The predictions of standard Higgs inflation in the framework of the metric formalism yield a tensor-to-scalar ratio $r sim 10^{-3}$ which lies well within the expected accuracy of near-future experiments $ sim 10^{-4}$. When the Palatini formalism is employed, the predicted values of $r$ get highly-suppressed $rsim 10^{-12}$ and consequently a possible non-detection of primordial tensor fluctuations will rule out only the metric variant of the model. On the other hand, the extremely small values predicted for $r$ by the Palatini approach constitute contact with observations a hopeless task for the foreseeable future. In this work, we propose a way to remedy this issue by extending the action with the inclusion of a generalized non-minimal derivative coupling term between the inflaton and the Einstein tensor of the form $m^{-2}(phi) G_{mu u} abla^{mu}phi abla^{ u}phi$. We find that with such a modification, the Palatini predictions can become comparable with the ones obtained in the metric formalism, thus providing ample room for the model to be in contact with observations in the near future.
We study inflation in Weyl gravity. The original Weyl quadratic gravity, based on Weyl conformal geometry, is a theory invariant under Weyl symmetry of (gauged) local scale transformations. In this theory Planck scale ($M$) emerges as the scale where this symmetry is broken spontaneously by a geometric Stueckelberg mechanism, to Einstein-Proca action for the Weyl photon (of mass near $M$). With this action as a low energy broken phase of Weyl gravity, century-old criticisms of the latter (due to non-metricity) are avoided. In this context, inflation with field values above $M$ is natural, since this is just a phase transition scale from Weyl gravity (geometry) to Einstein gravity (Riemannian geometry), where the massive Weyl photon decouples. We show that inflation in Weyl gravity coupled to a scalar field has results close to those in Starobinsky model (recovered for vanishing non-minimal coupling), with a mildly smaller tensor-to-scalar ratio ($r$). Weyl gravity predicts a specific, narrow range $0.00257 leq rleq 0.00303$, for a spectral index $n_s$ within experimental bounds at $68%$CL and e-folds number $N=60$. This range of values will soon be reached by CMB experiments and provides a test of Weyl gravity. Unlike in the Starobinsky model, the prediction for $(r, n_s)$ is not affected by unknown higher dimensional curvature operators (suppressed by some large mass scale) since these are forbidden by the Weyl gauge symmetry.
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