948 research outputs found
Emergence of Cosmic Space and Minimal Length in Quantum Gravity
An emergence of cosmic space has been suggested by Padmanabhan in
[arXiv:1206.4916]. This new interesting approach argues that the expansion of
the universe is due to the difference between the number of degrees of freedom
on a holographic surface and the one in the emerged bulk. In this paper, we
derive, using emergence of cosmic space framework, the general dynamical
equation of FRW universe filled with a perfect fluid by considering a generic
form of the entropy as a function of area. Our derivation is considered as a
generalization of emergence of cosmic space with a general form of entropy. We
apply our equation with higher dimensional spacetime and derive modified
Friedmann equation in Gauss-Bonnet gravity. We then apply our derived equation
with the corrected entropy-area law that follows from Generalized Uncertainty
Principle (GUP) and derive a modified Friedmann equations due to the GUP. We
then derive the modified Raychaudhuri equation due to GUP in emergence of
cosmic space framework and investigate it using fixed point method. Studying
this modified Raychaudhuri equation leads to non-singular solutions which may
resolve singularities in FRW universe.Comment: 10 pages, revtex4, 1 figure, to match published version in PL
Planck-Scale Corrections to Friedmann Equation
Recently, Verlinde proposed that gravity is an emergent phenomenon which
originates from an entropic force. In this work, we extend Verlinde's proposal
to accommodate generalized uncertainty principles (GUP), which are suggested by
some approaches to \emph{quantum gravity} such as string theory, black hole
physics and doubly special relativity (DSR). Using Verlinde's proposal and two
known models of GUPs, we obtain modifications to Newton's law of gravitation as
well as the Friedmann equation. Our modification to the Friedmann equation
includes higher powers of the Hubble parameter which is used to obtain a
corresponding Raychaudhuri equation. Solving this equation, we obtain a leading
Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the
equation of state.Comment: 15 pages, no figure, to appear in Central Eur.J.Phys. arXiv admin
note: text overlap with arXiv:1301.350
Modified Newton's Law of Gravitation Due to Minimal Length in Quantum Gravity
A recent theory about the origin of the gravity suggests that the gravity is
originally an entropic force. In this work, we discuss the effects of
generalized uncertainty principle (GUP) which is proposed by some approaches to
quantum gravity such as string theory, black hole physics and doubly special
relativity theories (DSR), on the area law of the entropy. This leads to a
-type correction to the area law of entropy which imply that the
number of bits is modified. Therefore, we obtain a modified Newton's law of
gravitation. Surprisingly, this modification agrees with different sign with
the prediction of Randall-Sundrum II model which contains one uncompactified
extra dimension. Furthermore, such modification may have observable
consequences at length scales much larger than the Planck scale.Comment: 12 pages, no figures, references adde
Minimal Length, Friedmann Equations and Maximum Density
Inspired by Jacobson's thermodynamic approach[gr-qc/9504004], Cai et al
[hep-th/0501055,hep-th/0609128] have shown the emergence of Friedmann equations
from the first law of thermodynamics. We extend Akbar--Cai derivation
[hep-th/0609128] of Friedmann equations to accommodate a general entropy-area
law. Studying the resulted Friedmann equations using a specific entropy-area
law, which is motivated by the generalized uncertainty principle (GUP), reveals
the existence of a maximum energy density closed to Planck density. Allowing
for a general continuous pressure leads to bounded curvature
invariants and a general nonsingular evolution. In this case, the maximum
energy density is reached in a finite time and there is no cosmological
evolution beyond this point which leaves the big bang singularity inaccessible
from a spacetime prospective. The existence of maximum energy density and a
general nonsingular evolution is independent of the equation of state and the
spacial curvature . As an example we study the evolution of the equation of
state through its phase-space diagram to show the existence of
a maximum energy which is reachable in a finite time.Comment: 15 pages, 1 figure, minor revisions, To appear in JHE
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