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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.
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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.
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.
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.
Thanks to the Planck Collaboration, we know the value of the scalar spectral index of primordial fluctuations with unprecedented precision. In addition, the joint analysis of the data from Planck, BICEP2, and KEK has further constrained the value of the tensor-to-scalar ratio $r$ so that chaotic inflationary scenarios seem to be disfavoured. Inspired by these results, we look for a model that yields a value of $r$ that is larger than the one predicted by the Starobinsky model but is still within the new constraints. We show that purely quadratic, renormalizable, and scale-invariant gravity, implemented by loop-corrections, satisfies these requirements.
Recently, the variation of the Planck mass in the General Relativistic Einstein-Hilbert action was proposed as a self-tuning mechanism of the cosmological constant, preventing Standard Model vacuum energy from freely gravitating and enabling an estimation of the magnitude of its observed value. We explore here new aspects of this proposal. We first develop an equivalent Einstein-frame formalism to the current Jordan-frame formulation of the mechanism and use this to highlight similarities and differences of self-tuning to the sequestering mechanism. We then show how with an extension of the local self-tuning action by a coupled Gauss-Bonnet term and a companion four-form field strength, graviton loops can be prevented from incapacitating the degravitation of the Standard Model vacuum energy. For certain cases, we furthermore find that this extension can be recast as a Horndeski scalar-tensor theory and be embedded in the conventional local self-tuning formalism. We then explore the possibility of a unification of inflation with self-tuning. The resulting equations can alternatively be used to motivate a multiverse interpretation. In this context, we revisit the coincidence problem and provide an estimation for the probability of the emergence of intelligent life in our Universe as a function of cosmic age, inferred from star and terrestrial planet formation processes. We conclude that we live at a very typical epoch, where we should expect the energy densities of the cosmological constant and matter to be of comparable size. For a dimensionless quantity to compare the emergence of life throughout the cosmic history of different universes in an anthropic analysis of the multiverse, we choose the order of magnitude difference of the evolving horizon size of a universe to the size of its proton as the basic building block of atoms, molecules, and eventually life. (abridged)
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