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Register a new userScale-invariance, dynamically induced Planck scale and inflation in the Palatini formulation
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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.
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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.
Ultraviolet completion of the standard model plus gravity at and beyond the Planck scale is a daunting problem to which no generally accepted solution exists. Principal obstacles include (a) lack of data at the Planck scale (b) nonrenormalizability of gravity and (c) unitarity problem. Here we make a simple observation that, if one treats all Planck scale operators of equal canonical dimension democratically, one can tame some of the undesirable features of these models. With a reasonable amount of fine tuning one can satisfy slow roll conditions required in viable inflationary models. That remains true even when the number of such operators becomes very large.
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.
We study a scale-invariant model of quadratic gravity with a non-minimally coupled scalar field. We focus on cosmological solutions and find that scale invariance is spontaneously broken and a mass scale naturally emerges. Before the symmetry breaking, the Universe undergoes an inflationary expansion with nearly the same observational predictions of Starobinskys model. At the end of inflation, the Hubble parameter and the scalar field converge to a stable fixed point through damped oscillations and the usual Einstein-Hilbert action is recovered. The oscillations around the fixed point can reheat the Universe in various ways and we study in detail some of these possibilities.
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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