R ^{2} inflation to probe nonperturbative quantum gravity
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 + R ^{2}, or shortly R ^{2}, 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 ultraviolet (UV) complete via an embedding into an analytic infinite derivative (AID) nonlocal gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric spacetimes. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the EinsteinHilbert 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 spacetimes, a space of solutions to the equations of motion is identical to the space of backgrounds in a local R ^{2} 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 ( n _{ s }), a tensortoscalar ratio ( r) and a tensor tilt ( n _{ t }). It appears that n _{ s } remains the same as in the local R ^{2} inflation in the leading slowroll approximation, while r and n _{ t } 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 Bmodes of the CMB polarization. This makes the UV complete R ^{2} gravity a natural target for future CMB probes.
 Publication:

Journal of High Energy Physics
 Pub Date:
 March 2018
 DOI:
 10.1007/JHEP03(2018)071
 arXiv:
 arXiv:1711.08864
 Bibcode:
 2018JHEP...03..071K
 Keywords:

 Cosmology of Theories beyond the SM;
 Models of Quantum Gravity;
 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 37 pages