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Register a new userEffective dark energy from decoherence
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Chris Fields
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Within the quantum Darwinist framework introduced by W. H. Zurek ({em Nat. Phys.}, 5:181-188, 2009), observers obtain pointer-state information about quantum systems by interacting with a local sample of the surrounding environment, e.g. a local sample of the ambient photon field. Because the environment encodes such pointer state information uniformly and hence redundantly throughout its entire volume, the information is equally available to all observers regardless of their location. This framework is applied to the observation of stellar center-of-mass positions, which are assumed to be encoded by the ambient photon field in a way that is uniformly accessible to all possible observers. Assuming Landauers Principle, constructing such environmental encodings requires $(ln2) kT$ per encoded bit. For the observed 10$^{24}$ stars and a uniform binary encoding of center-of-mass positions into voxels with a linear dimension of 5 km, the free energy required at the current CMB temperature T = 2.7 K is $sim$ 2.5 $cdot$ 10$^{-27}$ kg $cdot$ m$^{-3}$, strikingly close to the observed value of $Omega_{Lambda} rho_{c}$. Decreasing the voxel size to $(l_{P})^{3}$ results in a free energy requirement 10$^{117}$ times larger.
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Quantum Measure Theory (QMT) is a generalization of quantum theory where physical predictions are computed from a matrix known as emph{decoherence functional} (DF). Previous works have noted that, in its original formulation, QMT exhibits a problem with composability, since the composition of two decoherence functionals is, in general, not a valid decoherence functional. This does not occur when the DFs in question happen to be positive semidefinite (a condition known as strong positivity). In this paper, we study the concept of composability of DFs and its consequences for QMT. Firstly, we show that the problem of composability is much deeper than originally envisaged, since, for any $n$, there exists a DF that can co-exist with $n-1$ copies of itself, but not with $n$. Secondly, we prove that the set of strongly positive DFs cannot be enlarged while remaining closed under composition. Furthermore, any closed set of DFs containing all quantum DFs can only contain strongly positive DFs.
We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the systems total entropy increase. We also discuss the relevance of the results in our quantum mechanical model for interacting field theories.
I obtain the quantum correction $Delta V_mathrm{eff}= (hbar^2/8m) [(1- 4xi frac{d+1}{d})(mathcal{S})^2 + 2(1-4xi)mathcal{S}]$ that appears in the effective potential whenever a compact $d$-dimensional subspace (of volume $propto exp[mathcal{S}(x)]$) is discarded from the configuration space of a nonrelativistic particle of mass $m$ and curvature coupling parameter $xi$. This correction gives rise to a force $-langleDelta V_mathrm{eff}rangle$ that pushes the expectation value $langle xrangle$ off its classical trajectory. Because $Delta V_mathrm{eff}$ does not depend on the details of the discarded subspace, these results constitute a generic model of the quantum effect of discarded variables with maximum entropy/information capacity $mathcal{S}(x)$.
We further develop the gravitational model, Thomas-Whitehead Gravity (TW Gravity), that arises when projective connections become dynamical fields. TW Gravity has its origins in geometric actions from string theory where the TW projective connection appears as a rank two tensor, $mathcal{D}_{ab}$, on the spacetime manifold. Using a Gauss-Bonnet (GB) action built from the $(mathrm{d}+1)$-dimensional TW connection, and applying the tensor decomposition $mathcal{D}_{ab} = D_{ab} + 4Lambda /(mathrm{d}(mathrm{d}-1)) g_{ab}$, we arrive at a gravitational model made up of a $mathrm{d}$-dimensional Einstein-Hilbert + GB action sourced by $D_{ab}$ and with cosmological constant $Lambda$. The $mathrm{d}=4$ action is studied and we find that $Lambda propto 1/J_0$, with $J_0$ the coupling constant for $D_{ab}$. For $Lambda$ equal to the current measured value, $J_0$ is on the order of the measured angular momentum of the observable Universe. We view this as $Lambda$ controlling the scale of patches of the Universe that acquire angular momentum, with the net angular momentum of multiple patches vanishing, as required by the cosmological principle. We further find a universal axial scalar coupling to all fermions where the trace, $mathcal{D} = mathcal{D}_{ab}g^{ab}$ acts as the scalar. This suggests that $mathcal{D}$ is also a dark matter portal for non-standard model fermions.
Recent observations provide strong evidence that the universe is accelerating. This confronts theory with a severe challenge. Explanations of the acceleration within the framework of general relativity are plagued by difficulties. General relativistic models require a dark energy field with effectively negative pressure. An alternative to dark energy is that gravity itself may behave differently from general relativity on the largest scales, in such a way as to produce acceleration. The alternative approach of modified gravity also faces severe difficulties, but does provide a new angle on the problem. This review considers an example of modified gravity, provided by brane-world models that self-accelerate at late times.
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