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Register a new userA new approach to the vacuum of inflationary models
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A new approach is given for the implementation of boundary conditions used in solving the Mukhanov-Sasaki equation in the context of inflation. The familiar quantization procedure is reviewed, along with a discussion of where one might expect deviations from the standard approach to arise. The proposed method introduces a (model dependent) fitting function for the z/z and a/a terms in the Mukhanov-Sasaki equation for scalar and tensor modes, as well as imposes the boundary conditions at a finite conformal time. As an example, we employ a fitting function, and compute the spectral index, along with its running, for a specific inflationary model which possesses background equations that are analytically solvable. The observational upper bound on the tensor to scalar ratio is used to constrain the parameters of the boundary conditions in the tensor sector as well. An overview on the generalization of this method is also discussed.
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We study observational signatures of two classes of anisotropic inflationary models in which an inflaton field couples to (i) a vector kinetic term F_{mu nu}F^{mu nu} and (ii) a two-form kinetic term H_{mu nu lambda}H^{mu nu lambda}. We compute the corrections from the anisotropic sources to the power spectrum of gravitational waves as well as the two-point cross correlation between scalar and tensor perturbations. The signs of the anisotropic parameter g_* are different depending on the vector and the two-form models, but the statistical anisotropies generally lead to a suppressed tensor-to-scalar ratio r and a smaller scalar spectral index n_s in both models. In the light of the recent Planck bounds of n_s and r, we place observational constraints on several different inflaton potentials such as those in chaotic and natural inflation in the presence of anisotropic interactions. In the two-form model we also find that there is no cross correlation between scalar and tensor perturbations, while in the vector model the cross correlation does not vanish. The non-linear estimator f_{NL} of scalar non-Gaussianities in the two-form model is generally smaller than that in the vector model for the same orders of |g_*|, so that the former is easier to be compatible with observational bounds of non-Gaussianities than the latter.
The so-called trans-Planckian problem of inflation may be evaded by positing that modes come into existence only when they became cis-Planckian by virtue of expansion. However, this would imply that for any mode a new random realization would have to be drawn every $N$ wavelengths, with $N$ typically of order 1000 (but it could be larger or smaller). Such a re-drawing of realizations leads to a heteroskodastic distribution if the region under observation contains several such independent domains. This has no effect on the sampled power spectrum for a scale-invariant raw spectrum, but at very small scales it leads to a spectral index bias towards scale-invariance and smooths oscillations in the spectrum. The domain structure would also unsqueeze some of the propagating waves, i.e., dismantle their standing wave character. By describing standing waves as travelling waves of the same amplitude moving in opposite directions we determine the observational effects of unsqueezing. We find that it would erase the Doppler peaks in the CMB, but only on very small angular scales, where the primordial signal may not be readily accessible. The standing waves in a primordial gravitational wave background would also be turned into travelling waves. This unsqueezing of the gravitational wave background may constitute a detectable phenomenon.
We derive for the first time the growth index of matter perturbations of the FLRW flat cosmological models in which the vacuum energy depends on redshift. A particularly well motivated model of this type is the so-called quantum field vacuum, in which apart from a leading constant term $Lambda_0$ there is also a $H^{2}$-dependence in the functional form of vacuum, namely $Lambda(H)=Lambda_{0}+3 u (H^{2}-H^{2}_{0})$. Since $| u|ll1$ this form endows the vacuum energy of a mild dynamics which affects the evolution of the main cosmological observables at the background and perturbation levels. Specifically, at the perturbation level we find that the growth index of the running vacuum cosmological model is $gamma_{Lambda_{H}} approx frac{6+3 u}{11-12 u}$ and thus it nicely extends analytically the result of the $Lambda$CDM model, $gamma_{Lambda}approx 6/11$.
The $R^2$ term in the Starobinsky inflationary model can be regarded as a leading quantum correction to the gravitational effective action. We assume that parity-preserving and parity-violating (axial) non-minimal couplings between curvature and electromagnetic field are also present in the effective action. In the Einstein frame, they turn into non-trivial couplings of the scalaron and curvature to the electromagnetic field. We make an assessment of inflationary magnetogenesis in this model. In the case of parity-preserving couplings, amplification of magnetic field is negligibly small. In the case of axial couplings, magnetogenesis is hampered by strong back-reaction on the inflationary process, resulting in possible amplification of magnetic field at most by the factor $10^5$ relative to its vacuum fluctuations.
Massive fields during inflation provide an interesting opportunity to test new physics at very high energy scales. Meanwhile in fundamental realizations, the inflationary field space typically has a curved geometry, which may leave detectable imprints in primordial observables. In this paper we study an extension of quasi-single field inflation where the inflaton and the massive field belong to a curved field manifold. Because of the nontrivial field space curvature, the massive field here can get significant mass corrections of order the Hubble scale, thus the quasi-single field predictions on primordial non-Gaussianity are affected. We derive the same result in an equivalent approach by using the background effective field theory of inflation, where a dimension-6 operator is identified to play an important role and its cutoff scale is associated with the curvature scale of the field space. In addition, due to the slow-roll evolution of the inflaton, this type of mass correction has intrinsic time-dependence. Consequently, the running mass modifies the scaling behaviour in the squeezed limit of the scalar bispectrum, while the resulting running index measures the curvature of the internal field space. Therefore the minimal setup of a massive field within curved field space during inflation may naturally lead to new observational signatures of the field space geometry.
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