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 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 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 tensor-to-scalar 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 slow-roll 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 B-modes of the CMB polarization. This makes the UV complete R 2 gravity a natural target for future CMB probes.

In this paper we consider 3-form dark energy (DE) models with interactions in the dark sector. We aim to distinguish the phenomenological interactions that are defined through the dark matter (DM) and the DE energy densities. We do our analysis mainly in two stages. In the first stage, we identify the non-interacting 3-form DE model which generically leads to an abrupt late-time cosmological event which is known as the little sibling of the Big Rip (LSBR). We classify the interactions which can possibly avoid this late-time abrupt event. We also study the parameter space of the model that is consistent with the interaction between DM and DE energy densities at present as indicated by recent studies based on BAO and SDSS data. In the later stage, we observationally distinguish those interactions using the statefinder hierarchy parameters {SWe also compute the growth factor parameter (z) for the various interactions we consider herein and use the composite null diagnostic (CND) {S (1) 3 , (z)} as a tool to characterise those interactions by measuring their departures from the concordance model. In addition, we make a preliminary analysis of our model in light of the recently released data by SDSS III on the measurement of the linear growth rate of structure.

In this paper we will study R 2-like inflation in a non-local modification of gravity which contains quadratic in Ricci scalar and Weyl tensor terms with analytic infinite derivative form-factors in the action. It is known that the inflationary solution of the local R + R 2 gravity remains a particular exact solution in this model. It was shown earlier that the power spectrum of scalar perturbations generated during inflation in the non-local setup remains the same as in the local R + R 2 inflation, whereas the power spectrum of tensor perturbations gets modified due to the non-local Weyl tensor squared term. In the present paper we go beyond 2-point correlators and compute the non-Gaussian parameter f NL related to 3-point correlations generated during inflation, which we found to be different from those in the original local inflationary model and scenarios alike based on a local gravity. We evaluate non-local corrections to the scalar bi-spectrum which give non-zero contributions to squeezed, equilateral and orthogonal configurations. We show that f NL ∼ O(1) with an arbitrary sign is achievable in this model based on the choice of form-factors and the scale of non-locality. We present the predictions for the tensor-toscalar ratio, r, and the tensor tilt, n t. In contrast to standard inflation in a local gravity, here the possibility n t > 0 is not excluded. Thus, future CMB data can probe non-local behaviour of gravity at high space-time curvatures.

A setting constituted by ℕ 3-form fields, without any direct interaction between them, minimally coupled to gravity, is introduced in this paper as a framework to study the early evolution of the universe. We focus particularly on the two 3-forms case. An inflationary scenario is found, emerging from the coupling to gravity. More concretely, the fields coupled in this manner exhibit a complex interaction, mediated by the time derivative of the Hubble parameter. Our investigation is supported by means of a suitable choice of potentials, employing numerical methods and analytical approximations. In more detail, the oscillations on the small field limit become correlated, and one field is intertwined with the other. In this type of solution, a varying sound speed is present, together with the generation of isocurvature perturbations. The mentioned features allow to consider an interesting model, to test against observation. It is subsequently shown how our results are consistent with current CMB data (viz.Planck and BICEP2).

The dilaton is a possible inflaton candidate following recent CMB data allowing a non-minimal coupling to the Ricci curvature scalar in the early Universe. In this paper, we introduce an approach that has seldom been used in the literature, namely dilaton inflation with non-local features. More concretely, employing non-local features expressed in J. High Energy Phys. 04 (2007) 029, we study quadratic variations around a de Sitter geometry of an effective action with a non-local dilaton. The non-locality refers to an infinite derivative kinetic term involving the operator F ( ). Algebraic roots of the characteristic equation F(z) = 0 play a crucial role in determining the properties of the theory. We subsequently study the cases when F ( ) has one real root and one complex root, from which we retrieve two concrete effective models of inflation. In the first case we retrieve a class of single field inflations with universal prediction of ns ∼ 0.967 with any value of the tensor to scalar ratio r < 0.1 intrinsically controlled by the root of the characteristic equation. The second case involves a new class of two field conformally invariant models with a peculiar quadratic cross-product of scalar fields. In this latter case, we obtain Starobinsky like inflation through a spontaneously broken conformal invariance. Furthermore, an uplifted minimum of the potential, which accounts for the vacuum energy after inflation is produced naturally through this mechanism intrinsically within our approach.