arXiv subjects

João Magueijo

Publications and source records attributed to João Magueijo.

33 records · Page 2Linked to original sources

arXiv2023

Quantum analysis of the recent cosmological bounce in the comoving Hubble length

We formulate the transition from decelerated to accelerated expansion as a bounce in connection space and study its quantum cosmology, knowing that reflections are notorious for bringing quantum effects to the fore. We use a formalism for obtaining a time variable via the demotion of the constants of Nature to integration constants, and focus on a toy Universe containing only radiation and a cosmological constant $Λ$ for its simplicity. We find that, beside the usual factor ordering ambiguities, there is an ambiguity in the order of the quantum equation, leading to two distinct theories: one second, the other first order. In both cases two time variables may be defined, conjugate to $Λ$ and to the radiation constant of motion. We make little headway with the second-order theory, but are able to produce solutions to the first-order theory. They exhibit the well-known "ringing" whereby incident and reflected waves interfere, leading to oscillations in the probability distribution even for well-peaked wave packets. We also examine in detail the probability measure within the semiclassical approximation. Close to the bounce, the probability distribution becomes double-peaked, with one peak following a trajectory close to the classical limit but with a Hubble parameter slightly shifted downwards, and the other with a value of $b$ stuck at its minimum. An examination of the effects still closer to the bounce, and within a more realistic model involving matter and $Λ$, is left to future work.

gr-qc↗

arXiv2022

Lower bound on the cosmological constant from the classicality of the Early Universe

We use the quantum unimodular theory of gravity to relate the value of the cosmological constant, $Λ$, and the energy scale for the emergence of cosmological classicality. The fact that $Λ$ and unimodular time are complementary quantum variables implies a perennially quantum Universe should $Λ$ be zero (or, indeed, fixed at any value). Likewise, the smallness of $Λ$ puts an upper bound on its uncertainty, and so a lower bound on the unimodular clock's uncertainty or the cosmic time for the emergence of classicality. Far from being the Planck scale, classicality arises at around $7 \times 10^{11}$ GeV for the observed $Λ$, and taking the region of classicality to be our Hubble volume. We confirm this argument with a direct evaluation of the wavefunction of the Universe in the connection representation for unimodular theory. Our argument is robust, with the only leeway being in the comoving volume of our cosmological classical patch, which should be bigger than that of the observed last scattering surface. Should it be taken to be the whole of a closed Universe, then the constraint depends weakly on $Ω_k$: for $-Ω_k < 10^{-3}$ classicality is reached at $ > 4 \times 10^{12}$ GeV. If it is infinite, then this energy scale is infinite, and the Universe is always classical within the minisuperspace approximation. It is a remarkable coincidence that the only way to render the Universe classical just below the Planck scale is to define the size of the classical patch as the scale of non-linearity for a red spectrum with the observed spectral index $n_s = 0.967(4)$ (about $10^{11}$ times the size of the current Hubble volume). In the context of holographic cosmology, we may interpret this size as the scale of confinement in the dual 3D quantum field theory, which may be probed (directly or indirectly) with future cosmological surveys.

hep-th↗

arXiv2021

Non-Gaussian Signatures of a Thermal Big Bang

What if Big Bang was hot from its very inception? This is possible in a bimetric theory where the source of fluctuations is thermal, requiring the model to live on a critical boundary in the space of parameters and can be realized when an anti-DBI brane moves within an $EAdS_2 \times E_3$ geometry. This setup renders the model unique, with sharp predictions for the scalar spectral index and its running. We investigate the non-Gaussian signatures of this thermal bimetric model, or "bi-thermal" for short. We adapt the standard calculation of non-Gaussianities for $P(X,ϕ)$ models to the thermal nature of the model, emphasising how the bi-thermal peculiarities affect the calculation and alter results. This leads to precise predictions for the shape and amplitude of the three-point function of the bi-thermal model (at tree-level): $f^{\rm local} _{\rm NL} = -3/2$ and $f^{\rm equil} _{\rm NL} = -2 + 4 \sqrt{3}π/9 \simeq 0.4$. We also discover a new shape of flattened non-gaussianity $\propto (k_1+k_2-k_3)^{-3/2} +$ permutations, which is expected due to the excited thermal initial conditions. These results, along with our earlier predictions for the scalar power spectrum, provide sharp targets for the future generation of cosmological surveys.

hep-th↗

arXiv2021

Gravity waves in parity-violating Copernican Universes

In recent work minimal theories allowing the variation of the cosmological constant by means of a balancing torsion, have been proposed. It was found that such theories contain parity violating homogeneous and isotropic solutions, due to a torsion structure called the Cartan spiral staircase. Their dynamics are controlled by Euler and Pontryagin quasi-topological terms in the action. Here we show that such theories predict a dramatically different picture for gravitational wave fluctuations in the parity violating branch. If the dynamics are ruled solely by the Euler-type term, then linear tensor mode perturbations are entirely undetermined, hinting at a new type of gauge invariance. The Pontryagin term not only permits for phenomenologically sounder background solutions (as found in previous literature), but for realistic propagation of gravitational wave modes. We discuss the observational constraints and predictions of these theories.

gr-qc↗

arXiv2021

Semiclassical limit problems with concurrent use of several clocks in quantum cosmology

We revisit a recent proposal for a definition of time in quantum cosmology, to investigate the effects of having more than one possible type of clock "at the same time". We use as test tube an extension of Einstein gravity with a massless scalar field in which the gravitational coupling $G_N$ is only a constant on-shell, mimicking the procedure for $Λ$ in unimodular gravity. Hence we have two "simultaneous" clocks in the theory: a scalar field clock, and the conjugate of $G_N$. We find that attempts to use two coherent clocks concurrently are disastrous for recovering the classical limit. The Heisenberg relations, instead of being saturated, are always realized abundantly above their bound, with strong quantum effects expected at least in parts of the trajectory. Semi-classical states always result from situations where we effectively impose a single clock, either by making the other clock a failed clock (i.e. by choosing a state where its conjugate constant is infinitely sharp), or by choosing a basis of constants where all clocks but one are redundant, i.e. motion or change in phase space does not occur with the passing of their "times". We show how this conclusion generalizes to fluids with any equation of state. It also applies to systems where "sub-clocks" of the same type could be used, for example in mixtures of different fluids with the same equation of state.

gr-qc↗

arXiv2021

Linking the Baum-Hawking-Coleman Mechanism with Unimodular Gravity and Vilenkin's Probability Flux

We revisit a mechanism proposed by Hawking to resolve the cosmological constant problem (and the controversy it generated) to identify possibly more palatable alternatives and explore new connections and interpretations. In particular, through the introduction of a new action coupling the four-form field strength $F = dA$ to the cosmological constant via a dynamical field $λ(x)$, a novel Baum-Hawking-Coleman type mechanism is presented. This mechanism can be seen as a generalisation of Unimodular Gravity. A theory with a similar coupling to "$F^2$" is also presented, with promising results. We show how in such theories the 3-form is closely related to the Chern-Simons density, and its associated definition of time. On the interpretational front, we propose a method avoiding the standard Euclidean action prescription, which makes use of Vilenkin's probability flux.

hep-th↗

arXiv2020

Quantum torsion and a Hartle-Hawking "beam''

In the Einstein-Cartan framework the torsion-free conditions arise within the Hamiltonian treatment as second-class constraints. The standard strategy is to solve these constraints, eliminating the torsion from the classical theory, before quantization. Here we advocate leaving the torsion inside the other constraints before quantization, leading at first to wave functions that can be called ``kinematical'' with regards to the torsion, but not the other constraints. The torsion-free condition can then be imposed as a condition upon the physical wave packets one constructs, satisfying the usual uncertainty relations, and so with room for quantum fluctuations in the torsion. This alternative strategy has the surprising effect of clarifying the sense in which the wave functions solving an explicitly real theory are ``delta-function normalizable''. Such solutions with zero (or any fixed) torsion, should be interpreted as plane waves in torsion space. Properly constructed wave packets are therefore normalizable in the standard sense. Given that they are canonical duals, this statement applies equally well to the Chern-Simons state (connection representation) and the Hartle-Hawking wave function (metric representation). We show how, when torsion is taken into account, the Hartle-Hawking wave function is replaced by a Gauss-Airy function, with finite norm, which we call the Hartle-Hawking beam. The Chern-Simons state, instead, becomes a packet with a Gaussian probability distribution in connection space. We conclude the paper with two sections explaining how to generalize these results beyond minisuperspace.

gr-qc↗

arXiv2019

Parity violating Friedmann Universes

We revisit models, within the Einstein-Cartan theory, where the cosmological constant $Λ$ is promoted to a variable, at the cost of allowing for torsion even in the absence of spinors. We remark that some standard notions about FRW Universes collapse in these theories, most notably spatial homogeneity and isotropy may now co-exist with violations of parity invariance. The parity violating solutions have non-vanishing Weyl curvature even within FRW models. The presence of parity violating torsion opens up the space of possible such theories with relevant FRW modifications: in particular the Pontryagin term can play an important role even in the absence of spinorial matter. We present a number of parity violating solutions with and without matter. The former are the non-self dual vacuum solutions long suspected to exist. The latter lead to tracking and non-tracking solutions with a number of observational problems, unless we invoke the Pontryagin term. An examination of the Hamiltonian structure of the theory reveals that the parity even and the parity violating solutions belong to two distinct branches of the theory, with different gauge symmetries (constraints) and different numbers of degrees of freedom. The parity even branch is nothing but standard relativity with a cosmological constant which has become pure gauge under conformal invariance if matter is absent, or a slave of matter (and so not an independent degree of freedom) if non-conformally invariant matter is present. In contrast, the parity violating branch contains a genuinely new degree of freedom.

gr-qc↗

arXiv2019

A Zero-Parameter Extension of General Relativity with Varying Cosmological Constant

We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological constant to have a consistent space-time variation, through coding its dynamics in the torsion tensor. We demonstrate this mechanism by adding a `quasi-topological' term to the Einstein action, which naturally realizes a dynamical torsion with an automatic satisfaction of the Bianchi identities. Moreover, variation of the action with respect to this dynamical $Λ$ fixes it in terms of other variables, thus providing a scenario with less freedom than general relativity with a cosmological constant. Once matter is introduced, at least in the homogeneous and isotropic reduction, $Λ$ is uniquely determined by the field content of the model. We make an explicit construction using the Palatini formulation of GR and describe the striking properties of this new theory. We also highlight some possible extensions to the theory. A companion paper [1] explores the Friedmann--Robertson--Walker reduction for cosmology, and future work will study Solar System tests of the theory.

gr-qc↗

arXiv2019

The cosmology of minimal varying Lambda theories

Inserting a varying Lambda in Einstein's field equations can be made consistent with the Bianchi identities by allowing for torsion, without the need to add scalar field degrees of freedom. In the minimal such theory, Lambda is totally free and undetermined by the field equations in the absence of matter. Inclusion of matter ties Lambda algebraically to it, at least when homogeneity and isotropy are assumed, i.e. when there is no Weyl curvature. We show that Lambda is proportional to the matter density, with a proportionality constant depending on the equation of state. Unfortunately, the proportionality constant becomes infinite for pure radiation, ruling out the minimal theory prima facie despite of its novel internal consistency. It is possible to generalize the theory still without the addition of kinetic terms, leading to a new algebraically-enforced proportionality between Lambda and the matter density. Lambda and radiation may now coexist in a form consistent with Big Bang Nucleosynthesis, though this places strict constraints on the single free parameter of the theory, $θ$. In the matter epoch Lambda behaves just like a dark matter component. Its density is proportional to the baryonic and/or dark matter, and its presence and gravitational effects would need to be included in accounting for the necessary dark matter in our Universe. This is a companion paper to Ref. [1] where the underlying gravitational theory is developed in detail.

gr-qc↗

arXiv2018

Solving the flatness problem with an anisotropic instanton in Hořava-Lifshitz gravity

In Hořava-Lifshitz gravity a scaling isotropic in space but anisotropic in spacetime, often called anisotropic scaling with the dynamical critical exponent z=3, lies at the base of its renormalizability. This scaling also leads to a novel mechanism of generating scale-invariant cosmological perturbations, solving the horizon problem without inflation. In this paper we propose a possible solution to the flatness problem, in which we assume that the initial condition of the Universe is set by a small instanton respecting the same scaling. We argue that the mechanism may be more general than the concrete model presented here, and rely simply on the deformed dispersion relations of the theory, and on equipartition of the various forms of energy at the starting point.

hep-th↗

arXiv2014

Observational constraints on dual intermediate inflation

We explore the observational implications of models of intermediate inflation driven by modified dispersion relations, specifically those representing the phenomenon of dimensional reduction in the ultraviolet limit. These models are distinct from the standard ones because they do not require violations of the strong energy condition, and this is reflected in their structure formation properties. We find that they can naturally accommodate deviations from exact scale-invariance. They also make clear predictions for the running of the spectral index and tensor modes, rendering the models straightforwardly falsifiable. We discuss the observational prospects for these models and the implications these may have for quantum gravity scenarios.

astro-ph.CO↗

arXiv2004

Non-commutative geometry as a realization of varying speed of light cosmology

We examine the cosmological implications of space-time non-commutativity, discovering yet another realization of the varying speed of light model. Our starting point is the well-known fact that non-commutativity leads to deformed dispersion relations, relating energy and momentum, implying a frequency dependent speed of light. A Hot Big Bang Universe therefore experiences a higher speed of light as it gets hotter. We study the statistical physics of this "deformed radiation", recovering standard results at low temperatures, but a number of novelties at high temperatures: a deformed Planck's spectrum, a temperature dependent equation of state $w=p/ρ$ (ranging from 1/3 to infinity), a new Stephan-Boltzmann law, and a new entropy relation. These new photon properties closely mimic those of phonons in crystals, hardly a surprising analogy. They combine to solve the horizon and flatness problems, explaining also the large entropy of the Universe. We also show how one would find a direct imprint of non-commutativity in the spectrum of a cosmic graviton background, should it ever be detected.

hep-th↗

arXiv2004

Non-Linear Relativity in Position Space

We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently of the chosen representation in momentum space. This requires a non-linear definition for the invariant contraction between momentum and position spaces. The second approach, instead, respects the linearity of the invariant contraction. This fully fixes the dual of momentum space and dictates a set of energy-dependent space-time Lorentz transformations. We discuss a variety of physical implications that would distinguish these two strategies. We also show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.

gr-qc↗

arXiv2003

On the bispectrum of COBE and WMAP

The COBE-DMR 4-year maps displayed a strong non-Gaussian signal in the ``inter-scale'' components of the bispectrum: their observed values did not display the scatter expected from Gaussian maps. We re-examine this and other suggested non-Gaussian features in the light of WMAP. We find that they all disappear. Given that it was proved that COBE-DMR high noise levels and documented systematics could at most {\it dilute} the observed non-Gaussian features, we conclude that this dataset must have contained non-negligible undocumented systematic errors. It turns out that the culprit is a combination of QuadCube pixelization and data collected during the ``eclipse season''.

astro-ph↗