Quantum theories of gravity predict interesting phenomenological features such as a minimum measurable length and maximum momentum. We use the Generalized Uncertainty Principle (GUP), which is an extension of the standard Heisenberg Uncertainty Princ
iple motivated by Quantum Gravity, to model the above features. In particular, we use a GUP with modelling maximum momentum to establish a correspondence between the GUP-modified dynamics of a massless spin-2 field and quadratic (referred to as Stelle) gravity. In other words, Stelle gravity can be regarded as the classical manifestation of a maximum momentum and the related GUP. We explore the applications of Stelle gravity to cosmology and specifically show that Stelle gravity applied to a homogeneous and isotropic background leads to inflation with an exit. Using the above, we obtain strong bounds on the GUP parameter from CMB observations. Unlike previous works, which fixed only upper bounds for GUP parameters, we obtain both emph{lower and upper bounds} on the GUP parameter.
We show that if Dark Matter is made up of light bosons, they form a Bose-Einstein condensate in the early Universe. This in turn naturally induces a Dark Energy of approximately equal density and exerting negative pressure.This explains the so-called coincidence problem.
Applying the seminal work of Bose in 1924 on what was later known as Bose-Einstein statistics, Einstein predicted in 1925 that at sufficiently low temperatures, a macroscopic fraction of constituents of a gas of bosons will drop down to the lowest av
ailable energy state, forming a `giant molecule or a Bose-Einstein condensate (BEC), described by a `macroscopic wavefunction. In this article we show that when the BEC of ultralight bosons extends over cosmological length scales, it can potentially explain the origins of both dark matter and dark energy. We speculate on the nature of these bosons.
We compute quantum corrections to the Raychaudhuri equation, by replacing classical geodesics with quantal (Bohmian) trajectories, and show that they prevent focusing of geodesics, and the formation of conjugate points. We discuss implications for th
e Hawking-Penrose singularity theorems, and for curvature singularities.
We review aspects of the thermodynamics of black holes and in particular take into account the fact that the quantum entanglement between the degrees of freedom of a scalar field, traced inside the event horizon, can be the origin of black hole entro
py. The main reason behind such a plausibility is that the well-known Bekenstein-Hawking entropy-area proportionality -- the so-called `area law of black hole physics -- holds for entanglement entropy as well, provided the scalar field is in its ground state, or in other minimum uncertainty states, such as a generic coherent state or squeezed state. However, when the field is either in an excited state or in a state which is a superposition of ground and excited states, a power-law correction to the area law is shown to exist. Such a correction term falls off with increasing area, so that eventually the area law is recovered for large enough horizon area. On ascertaining the location of the microscopic degrees of freedom that lead to the entanglement entropy of black holes, it is found that although the degrees of freedom close to the horizon contribute most to the total entropy, the contributions from those that are far from the horizon are more significant for excited/superposed states than for the ground state. Thus, the deviations from the area law for excited/superposed states may, in a way, be attributed to the far-away degrees of freedom. Finally, taking the scalar field (which is traced over) to be massive, we explore the changes on the area law due to the mass. Although most of our computations are done in flat space-time with a hypothetical spherical region, considered to be the analogue of the horizon, we show that our results hold as well in curved space-times representing static asymptotically flat spherical black holes with single horizon.
The generalized uncertainty principle, motivated by string theory and non-commutative quantum mechanics, suggests significant modifications to the Hawking temperature and evaporation process of black holes. For extra-dimensional gravity with Planck s
cale O(TeV), this leads to important changes in the formation and detection of black holes at the the Large Hadron Collider. The number of particles produced in Hawking evaporation decreases substantially. The evaporation ends when the black hole mass is Planck scale, leaving a remnant and a consequent missing energy of order TeV. Furthermore, the minimum energy for black hole formation in collisions is increased, and could even be increased to such an extent that no black holes are formed at LHC energies.
