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Register a new userBroken scale invariance, $alpha$-attractors and vector impurity
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Added by
Emre Kahya Assoc. Prof. Dr.
Publication date
2016
fields
Physics
and research's language is
English
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We show that if the $alpha$-attractor model is realized by the spontaneous breaking of the scale symmetry, then the stability and the dynamics of the vector field that gauges the scale symmetry can severely constrain the $alpha$-parameter as $5/6 < alpha < 1$ restricting the inflationary predictions in a very tiny region in the $n_s - r$ plane that are in great agreement with the latest Planck data. Although the different values of $alpha$ do not make a tangible difference for $n_s$ and $r$, they provide radically different scenarios for the post-inflationary dynamics which determines the standard BBN processes and the large scale isotropy of the universe.
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We analyze and compare the multi-field dynamics during inflation and preheating in symmetric and asymmetric models of $alpha$-attractors, characterized by a hyperbolic field-space manifold. We show that the generalized (asymmetric) E- and (symmetric) T-models exhibit identical two-field dynamics during inflation for a wide range of initial conditions. The resulting motion can be decomposed in two approximately single-field segments connected by a sharp turn in field-space. The details of preheating can nevertheless be different. For the T-model one main mass-scale dominates the evolution of fluctuations of the spectator field, whereas for the E-model, a competing mass-scale emerges due to the steepness of the potential away from the inflationary plateau, leading to different contributions to parametric resonance for small and large wave-numbers. Our linear multi-field analysis of fluctuations indicates that for highly curved manifolds, both the E- and T-models preheat almost instantaneously. For massless fields this is always due to efficient tachyonic amplification of the spectator field, making single-field results inaccurate. Interestingly, there is a parameter window corresponding to $r={cal O}(10^{-5})$ and massive fields, where the preheating behavior is qualitatively and quantitatively different for symmetric and asymmetric potentials. In that case, the E-model can completely preheat due to self-resonance for values of the curvature where preheating in the T-model is inefficient. This provides a first distinguishing feature between models that otherwise behave identically, both at the single-field and multi-field level. Finally, we discuss how one can describe multi-field preheating on a hyperbolic manifold by identifying the relevant mass-scales that control the growth of inflaton and spectator fluctuations, which can be applied to any $alpha$-attractor model and beyond.
We present a comparative analysis of observational low-redshift background constraints on three candidate models for explaining the low-redshift acceleration of the universe. The generalized coupling model by Feng and Carloni and the scale invariant model by Maeder (both of which can be interpreted as bimetric theories) are compared to the traditional parametrization of Chevallier, Polarski and Linder. In principle the generalized coupling model, which in vacuum is equivalent to General Relativity, contains two types of vacuum energy: the usual cosmological constant plus a second contribution due to the matter fields. We show that the former is necessary for the model to agree with low-redshift observations, while there is no statistically significant evidence for the presence of the second. On the other hand the scale invariant model effectively has a time-dependent cosmological constant. In this case we show that a matter density $Omega_msim0.3$ is a relatively poor fit to the data, and the best-fit model would require a fluid with a much smaller density and a significantly positive equation of state parameter.
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in terms of scale invariant fields. They correspond to exact scaling solutions of functional renormalization flow equations. Such theories are highly predictive since all relevant parameters for deviations from the exact scaling solution vanish. Realistic particle physics and quantum gravity are compatible with this setting. The non-linear restrictions for scaling solutions can explain properties as an asymptotically vanishing cosmological constant or dynamical dark energy that would seem to need fine tuning of parameters from a perturbative viewpoint. As an example we discuss a pregeometry based on a diffeomorphism invariant Yang-Mills theory. It is a candidate for an ultraviolet completion of quantum gravity with a well behaved graviton propagator at short distances.
We consider cosmological inflationary models in which vector fields play some role in the generation of the primordial curvature perturbation $zeta$. Such models are interesting because the involved vector fields naturally seed statistical anisotropy in the primordial fluctuations which could eventually leave a measurable imprint on the cosmic microwave background fluctuations. In this article, we estimate the scale and shape dependent effects on the non-Gaussianity (NG) parameters due to the scale dependent statistical anisotropy in the distribution of the fluctuations. For concreteness, we use a power spectrum (PS) of the fluctuations of the quadrupolar form: $P_zeta(vec{k})equiv P_zeta(k)[1+g_zeta(k)(hat{n} cdot hat{k})^2 ]$, where $g_{zeta}(k)$ is the only quantity which parametrizes the level of statistical anisotropy and $hat{n}$ is a unitary vector which points towards the preferred direction. Then, we evaluate the contribution of the running of $g_{zeta}(k)$ on the NG parameters by means of the $delta N$ formalism. We focus specifically on the details for the $f_{rm NL}$ NG parameter, associated with the bispectrum $B_zeta$, but the structure of higher order NG parameters is straightforward to generalize. Although the level of statistical anisotropy in the PS is severely constrained by recent observations, the importance of statistical anisotropy signals in higher order correlators remains to be determined, this being the main task that we address here. The precise measurement of the shape and scale dependence (or running) of statistical parameters such as the NG parameters and the statistical anisotropy level could provide relevant elements for model building and for the determination of the presence (or nonpresence) of inflationary vector fields and their role in the inflationary mechanism.
We consider a model of inflation consisting a triplet of $U(1)$ vector fields with the parity violating interaction which is non-minimally coupled to inflaton. The vector field sector enjoys global $O(3)$ symmetry which admits isotropic configuration and provides not only vector modes but also scalar and tensor modes. We decompose the scalar perturbations into the adiabatic, entropy and isocurvature perturbations and compute all power spectra and cross correlations of the scalar and the tensor sectors. The tensor modes associated with the vector fields contribute to the power spectrum of gravitational waves while the parity violating term generates chirality in gravitational power spectra and bispectra. We study nonlinear scalar and tensor perturbations and compute all bispectra and three-point cross-correlations. In particular, it is shown that the non-Gaussianity of curvature perturbations and gravitational waves are enhanced by the vector field perturbations. We show that non-Gaussianities put strong constraints on the model parameters such as the parity violating coupling and the fractional energy of the vector fields.
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