Inflationary stage in the early Universe: what is known about it and what may be discovered in future

Presented is a review of physical properties of an inflationary stage in the early Universe (space-time curvature, its rate of change, an inflaton mass, etc.) which follow from the latest observational cosmological data [1,2] for the two simplest classes of inflationary models based either on a scalar field with some potential and minimal coupling to gravity, or on $f(R)$ gravity. It is shown how the form of these phenomenological models can be reconstructed using observational data on the Fourier power spectrum of inhomogeneous perturbations of matter density in the Universe.
From what can be done more in the nearest future, the most fundamental would still be the discovery of primordial quantum gravitational waves generated during inflation. It is argued that the measured value of the slope $n_s-1$ of the primordial power spectrum of scalar (adiabatic) perturbations, under some natural additional assumptions, implies small, but not too small tensor-to-scalar ratio of powers of perturbations $r \sim 3(1-n_s)^2 \sim 0.0003$ or more, similar to that in the original $R+R^2$ inflationary model [3]. Another possible future discovery is related to local features in the CMB temperature anisotropy power spectrum in the multipole range $l= (20{-}40)$ beyond which new physics during inflation may be hidden, in particular, the existence of particles more massive than the inflaton [4].

References

1. Planck Collaboration: P. A. R. Ade et al., arXiv: 1502.02114
2. Keck Array, BICEP2 Collaborations: P. A. R. Ade et al., Phys. Rev. Lett., 116 (2016), 031302, arXiv: 1510.09217    
3. A. A. Starobinsky, Phys. Lett. B, 91 (1980), 99    
4. D. K. Hazra, A. Shafieloo, G. F. Smoot, A. A. Starobinsky, JCAP, 2014 (2014), 048, arXiv: 1405.2012