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Generalized Uncertainty Principle and Recent Cosmic Inflation Observations

The recent background imaging of cosmic extragalactic polarization (BICEP2) observations are believed as an evidence for the cosmic inflation. BICEP2 provided a first direct evidence for the inflation, determined its energy scale and debriefed witnesses for the quantum gravitational processes. The ratio of scalar-to-tensor fluctuations $r$ which is the canonical measurement of the gravitational waves, was estimated as $r=0.2_{-0.05}^{+0.07}$. Apparently, this value agrees well with the upper bound value corresponding to PLANCK $r\leq 0.012$ and to WMAP9 experiment $r=0.2$. It is believed that the existence of a minimal length is one of the greatest predictions leading to modifications in the Heisenberg uncertainty principle or a GUP at the Planck scale. In the present work, we investigate the possibility of interpreting recent BICEP2 observations through quantum gravity or GUP. We estimate the slow-roll parameters, the tensorial and the scalar density fluctuations which are characterized by the scalar field $ϕ$. Taking into account the background (matter and radiation) energy density, $ϕ$ is assumed to interact with the gravity and with itself. We first review the Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe and then suggest modification in the Friedmann equation due to GUP. By using a single potential for a chaotic inflation model, various inflationary parameters are estimated and compared with the PLANCK and BICEP2 observations. While GUP is conjectured to break down the expansion of the early Universe (Hubble parameter and scale factor), two inflation potentials based on certain minimal supersymmetric extension of the standard model result in $r$ and spectral index matching well with the observations. Corresponding to BICEP2 observations, our estimation for $r$ depends on the inflation potential and the scalar field. A power-law inflation potential does not.