Generalized Uncertainty Principle and Recent Cosmic Inflation Observations

Abstract

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 +0.07 −0.05 . Apparently, this value agrees well with the upper bound value corresponding to PLANCK r ≤ 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 generalization of the uncertainty principle (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.

The fragmentation instability of a black hole with f(R) global monopole under GUP

“…The discussion on the fragmentation of a black hole with f (R) global monopole is performed in the context of GUP. The Heisenberg's uncertainty principle can be generalized within the microphysics regime as [25,[29][30][31][35][36][37][38][39][40][41][42][43][44]…”

“…In the research on black holes, it is impossible to neglect the gravitational effect, so the terms associated with the Newtonian constant would be added in the Heisenberg's uncertainty principle [23][24][25][26][27][28][29]. The generalized uncertainty principle (GUP) with the additional terms can be used to cure the divergence from states density near the black hole horizon and relate the entropy of black hole to a minimal length as quantum gravity scale [30,31]. The influence from the GUP modifying the black hole horizon and definitely changing the black hole entropy further was considered in the radiation from black holes [30,31].…”

“…The generalized uncertainty principle (GUP) with the additional terms can be used to cure the divergence from states density near the black hole horizon and relate the entropy of black hole to a minimal length as quantum gravity scale [30,31]. The influence from the GUP modifying the black hole horizon and definitely changing the black hole entropy further was considered in the radiation from black holes [30,31].…”

The tunneling radiation of a black hole with a f(R) global monopole under generalized uncertainty principle

“…Within the tiny region, the momentum difference is large, so the deviations are obvious according to the inequality (1). The GUP is used to study the quantum gravity phenomenology of black holes and to cure the divergence from states density near the black hole horizon while relating the entropy of black hole to a minimal length as quantum gravity scale [35][36][37][38]. The GUP also modifies the black hole horizon and further changes the black hole entropy [35][36][37][38].…”

“…The GUP is used to study the quantum gravity phenomenology of black holes and to cure the divergence from states density near the black hole horizon while relating the entropy of black hole to a minimal length as quantum gravity scale [35][36][37][38]. The GUP also modifies the black hole horizon and further changes the black hole entropy [35][36][37][38]. In an anti-de Sitter spacetime, the Heisenberg uncertainty principle should be deformed with a suitably chosen parameterization [39].…”