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Register a new userA quantum state for the late Universe
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We consider the quantum description of a toy model universe in which the Schwarzschild-de Sitter geometry emerges from the coherent state of a massless scalar field. Although highly idealised, this simple model allows us to find clear hints supporting the conclusion that the reaction of the de Sitter background to the presence of matter sources induces i) a modified Newtonian dynamics at galactic scales and ii) different values measured for the present Hubble parameter. Both effects stem from the conditions required to have a normalisable quantum state.
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Using Relativistic Quantum Geometry we study back-reaction effects of space-time inside the causal horizon of a static de Sitter metric, in order to make a quantum thermodynamical description of space-time. We found a finite number of discrete energy levels for a scalar field from a polynomial condition of the confluent hypergeometric functions expanded around $r=0$. As in the previous work, we obtain that the uncertainty principle is valid for each energy level on sub-horizon scales of space-time. We found that temperature and entropy are dependent on the number of sub-states on each energys level and the Bekenstein-Hawking temperature of each energy level is recovered when the number of sub-states of a given level tends to infinity. We propose that the primordial state of the universe could be described by a de Sitter metric with Planck energy $E_p=m_p,c^2$, and a B-H temperature: $T_{BH}=left(frac{hbar,c}{2pi,l_p,K_B}right)$.
So far none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here we outline preliminary results for a model of quantum universe, in which gravity is fundamentally and by construction quantic. The model is based on 3 well motivated assumptions with compelling observational and theoretical evidence: quantum mechanics is valid at all scales; quantum systems are described by their symmetries; Universe has infinite independent degrees of freedom. The last assumption means that the Hilbert space of the Universe has $SU(Nrightarrow infty) cong text{area preserving Diff.} (S_2)$ symmetry, which is parameterized by two angular variables. We show that in absence of a background spacetime, this Universe is trivial and static. Nonetheless, quantum fluctuations break the symmetry and divide the Universe to subsystems. When a subsystem is singled out as reference - {it observer} - and another as {it clock}, two more continuous parameters arise, which can be interpreted as distance and time. We identify the classical spacetime with parameter space of the Hilbert space of the Universe. Therefore, its quantization is meaningless. In this view, the Einstein equation presents the projection of quantum dynamics in the Hilbert space into its parameter space. Finite dimensional symmetries of elementary particles emerge as a consequence of symmetry breaking when the Universe is divided to subsystems/particles without having any implication for the infinite dimensional symmetry and its associated interaction percived as gravity. This explains why gravity is a universal force.
Quantum gravity of a brane-like Universe is formulated, and its Einstein limit is approached. Regge-Teitelboim embedding of Arnowitt-Deser-Misner formalism is carried out. Invoking a novel Lagrange multiplier, accompanying the lapse function and the shift vector, we derive the quadratic Hamiltonian and the corresponding bifurcated Wheeler-Dewitt-like equation. The inclusion of arbitrary matter resembles minimal coupling.
In this work we ask how an Unruh-DeWitt (UD) detector with harmonic oscillator internal degrees of freedom $Q$ measuring an evolving quantum matter field $Phi(bm{x}, t)$ in an expanding universe with scale factor $a(t)$ responds. We investigate the detectors response which contains non-Markovian information about the quantum field squeezed by the dynamical spacetime. The challenge is in the memory effects accumulated over the evolutionary history. We first consider a detector $W$, the `textsl{Witness}, which co-existed and evolved with the quantum field from the beginning. We derive a nonMarkovian quantum Langevin equation for the detectors $Q$ by integrating over the squeezed quantum field. The solution of this integro-differential equation would answer our question, in principle, but very challenging, in practice. Striking a compromise, we then ask, to what extent can a detector $D$ introduced at late times, called the `textsl{Detective}, decipher past memories. This situation corresponds to many cosmological experiments today probing specific stages in the past, such as COBE targeting activities at the surface of last scattering. Somewhat surprisingly we show that it is possible to retrieve to some degree certain global physical quantities, such as the resultant squeezing, particles created, quantum coherence and correlations. The reason is because the quantum field has all the fine-grained information from the beginning in how it was driven by the cosmic dynamics $a(t)$. How long the details of past history can persist in the quantum field depends on the memory time. The fact that a squeezed field cannot come to complete equilibrium under constant driving, as in an evolving spacetime, actually helps to retain the memory. We discuss interesting features and potentials of this `textit{archaeological} perspective toward cosmological issues.
In this study we consider an exponential decaying form for dark energy as EoS parameter in order to discuss the dynamics of the universe. Firstly, assuming that universe is filled with an ideal fluid which consists of exponential decaying dark energy we obtain time dependent behavior of several physical quantities such as energy density, pressure and others for dark energy, dark energy-matter coupling and non-coupling cases. Secondly, using scalar field instead of an ideal fluid we obtain these physical quantities in terms of scalar potential and kinetic term for the same cases in scalar-tensor formalism. Finally we show that ideal fluid and scalar-tensor description of dark energy give mathematically equivalent results for this EoS parameter.
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