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How can holonomy corrections be introduced in gravity?
We study the introduction of holonomy corrections in gravity. We will
show that there are infinitely many ways, as many as canonical transformations,
to introduce this kind of corrections, depending on the canonical variables
(two coordinates and its conjugate momenta) used to obtain the Hamiltonian. In
each case, these corrections lead, at effective level, to different modified
holonomy corrected Friedmann equations in gravity, which are in practice
analytically unworkable, i.e. only numerical analysis can be used to understand
its dynamics. Finally, we give arguments in favour of one preferred set of
variables, the one that conformally maps to Einstein gravity, because
for these variables the dynamics of the system has a clear physical meaning:
the same as in standard Loop Quantum Cosmology, where the effective dynamics of
a system can be analytically studied
Bouncing cosmologies in geometries with positively curved spatial sections
Background boucing cosmologies in the framework of General Relativity, driven
by a single scalar field filling the Universe, and with a quasi-matter
domination period, i.e., depicting the so-called Matter Bounce Scenario, are
reconstructed for geometries with positive spatial curvature. These cosmologies
lead to a nearly flat power spectrum of the curvature fluctuations in co-moving
coordinates for modes that leave the Hubble radius during the quasi-matter
domination period, and whose spectral index and its running, which are related
with the effective Equation of State parameter given by the quotient of the
pressure over the energy density, are compatible with observational data.Comment: Version accepted for publication in PL
Spacetime and Physical Equivalence
In this essay I begin to lay out a conceptual scheme for: (i) analysing
dualities as cases of theoretical equivalence; (ii) assessing when cases of
theoretical equivalence are also cases of physical equivalence. The scheme is
applied to gauge/gravity dualities. I expound what I argue to be their
contribution to questions about: (iii) the nature of spacetime in quantum
gravity; (iv) broader philosophical and physical discussions of spacetime.
(i)-(ii) proceed by analysing duality through four contrasts. A duality will be
a suitable isomorphism between models: and the four relevant contrasts are as
follows:
(a) Bare theory: a triple of states, quantities, and dynamics endowed with
appropriate structures and symmetries; vs. interpreted theory: which is endowed
with, in addition, a suitable pair of interpretative maps.
(b) Extendable vs. unextendable theories: which can, respectively cannot, be
extended as regards their domains of application.
(c) External vs. internal intepretations: which are constructed,
respectively, by coupling the theory to another interpreted theory vs. from
within the theory itself.
(d) Theoretical vs. physical equivalence: which contrasts formal equivalence
with the equivalence of fully interpreted theories.
I apply this scheme to answering questions (iii)-(iv) for gauge/gravity
dualities. I argue that the things that are physically relevant are those that
stand in a bijective correspondence under duality: the common core of the two
models. I therefore conclude that most of the mathematical and physical
structures that we are familiar with, in these models, are largely, though
crucially never entirely, not part of that common core. Thus, the
interpretation of dualities for theories of quantum gravity compels us to
rethink the roles that spacetime, and many other tools in theoretical physics,
play in theories of spacetime.Comment: 25 pages. Winner of the essay contest "Space and Time After Quantum
Gravity" of the University of Illinois at Chicago and the University of
Genev
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