Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPlanck mass and inflation as consequences of dynamically broken scale invariance
138
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Classical scale invariance represents a promising framework for model building beyond the Standard Model. However, once coupled to gravity, any scale-invariant microscopic model requires an explanation for the origin of the Planck mass. In this paper, we provide a minimal example for such a mechanism and show how the Planck mass can be dynamically generated in a strongly coupled gauge sector. We consider the case of hidden SU(N_c) gauge interactions that link the Planck mass to the condensation of a scalar bilinear operator that is nonminimally coupled to curvature. The effective theory at energies below the Planck mass contains two scalar fields: the pseudo-Nambu--Goldstone boson of spontaneously broken scale invariance (the dilaton) and a gravitational scalar degree of freedom that originates from the R^2 term in the effective action (the scalaron). We compute the effective potential for the coupled dilaton-scalaron system at one-loop order and demonstrate that it can be used to successfully realize a stage of slow-roll inflation in the early Universe. Remarkably enough, our predictions for the primordial scalar and tensor power spectra interpolate between those of standard R^2 inflation and linear chaotic inflation. For comparatively small gravitational couplings, we thus obtain a spectral index n_s ~= 0.97 and a tensor-to-scalar ratio as large as r ~= 0.08.
rate research
Read More
Scalar fields, $phi_i$ can be coupled non-minimally to curvature and satisfy the general criteria: (i) the theory has no mass input parameters, including the Planck mass; (ii) the $phi_i$ have arbitrary values and gradients, but undergo a general expansion and relaxation to constant values that satisfy a nontrivial constraint, $K(phi_i) =$ constant; (iii) this constraint breaks scale symmetry spontaneously, and the Planck mass is dynamically generated; (iv) there can be adequate inflation associated with slow roll in a scale invariant potential subject to the constraint; (v) the final vacuum can have a small to vanishing cosmological constant (vi) large hierarchies in vacuum expectation values can naturally form; (vii) there is a harmless dilaton which naturally eludes the usual constraints on massless scalars. These models are governed by a global Weyl scale symmetry and its conserved current, $K_mu$ . At the quantum level the Weyl scale symmetry can be maintained by an invariant specification of renormalized quantities.
We present two scale invariant models of inflation in which the addition of quadratic in curvature terms in the usual Einstein-Hilbert action, in the context of Palatini formulation of gravity, manages to reduce the value of the tensor-to-scalar ratio. In both models the Planck scale is dynamically generated via the vacuum expectation value of the scalar fields.
We study non-minimal Coleman-Weinberg inflation in the Palatini formulation of gravity in the presence of an $R^2$ term. The Planck scale is dynamically generated by the vacuum expectation value of the inflaton via its non-minimal coupling to the curvature scalar $R$. We show that the addition of the $R^2$ term in Palatini gravity makes non-minimal Coleman-Weinberg inflation again compatible with observational data.
Hilltop inflation models are often described by potentials $V = V_{0}(1-{phi^{n}over m^{n}}+...)$. The omitted terms indicated by ellipsis do not affect inflation for $m lesssim 1$, but the most popular models with $n =2$ and $4$ for $m lesssim 1$ are ruled out observationally. Meanwhile in the large $m$ limit the results of the calculations of the tensor to scalar ratio $r$ in the models with $V = V_{0}(1-{phi^{n}over m^{n}})$, for all $n$, converge to $r= 4/N lesssim 0.07$, as in chaotic inflation with $V sim phi$, suggesting a reasonably good fit to the Planck data. We show, however, that this is an artifact related to the inconsistency of the model $V = V_{0}(1-{phi^{n}over m^{n}})$ at $phi > m$. Consistent generalizations of this model in the large $m$ limit typically lead to a much greater value $r= 8/N$, which negatively affects the observational status of hilltop inflation. Similar results are valid for D-brane inflation with $V = V_{0}(1-{m^{n}over phi^{n}})$, but consistent generalizations of D-brane inflation models may successfully complement $alpha$-attractors in describing most of the area in the ($n_{s}$, $r$) space favored by Planck 2018.
We discuss the phenomenological implications of hybrid natural inflation models in which the inflaton is a pseudo-Goldstone boson but inflation is terminated by a second scalar field. A feature of the scheme is that the scale of breaking of the Goldstone symmetry can be lower than the Planck scale and so gravitational corrections are under control. We show that, for supersymmetric models, the scale of inflation can be chosen anywhere between the Lyth upper bound and a value close to the electroweak breaking scale. Unlike previous models of low scale inflation the observed density perturbations and spectral index are readily obtained by the choice of the free parameters.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
