Abstract
It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, R + R2, or shortly R2, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local R2 model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index (ns), a tensor-to-scalar ratio (r) and a tensor tilt (nt). It appears that ns remains the same as in the local R2 inflation in the leading slow-roll approximation, while r and nt get modified due to modification of the tensor power spectrum. This class of models allows for any value of r < 0.07 with a modified consistency relation which can be fixed by future observations of primordial B-modes of the CMB polarization. This makes the UV complete R2 gravity a natural target for future CMB probes.
Highlights
One of the most obvious and at the same time very promising generalization to consider is MP2 2
Recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity
We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local R2 model
Summary
One of the most obvious and at the same time very promising generalization to consider is MP2 2. MP−2 = 8πG, G is the Newtonian constant, c = 1 and M becomes the mass of what is the propagating scalar in this model, dubbed scalaron. We refer it hereafter as the local R2 model or just R2 model (or Lagrangian, etc.). Besides being the simplest one and having only one free parameter M whose value is fixed to M ≈ 1.3 × 10−5MP by the observed Fourier power spectrum PR of primordial scalar (matter density) perturbations in the Universe, this generalization has two major advantages. This ghost is a manifestation of the Ostrogradski instability [11] due to higher derivatives and it appears as long as the required for the full renormalization W 2 term, with W being the
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