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Is ΛCDM Holographic?

 $\Lambda$CDM and Holographic Dark Energy   Holographic dark energy (HDE) starts from a simple thought: the energy inside a region of size $L$ shouldn't exceed that of a black hole of the same size. Saturate that bound, up to a dimensionless number $c$ (not the speed of light), and $$\rho_{\rm DE}=3M_p^2\frac{c^2}{L^2}, \qquad\text{i.e.}\qquad c=HL\sqrt{\Omega_{\rm DE}}.$$ Units $\hbar=k=1$, $M_p^2=1/8\pi G$, prime $=d/d\ln a$, flat universe, $\Omega_X=\rho_X/3M_p^2H^2$. Li's Model In Li's 2004 model, $L$ is the future event horizon , the farthest a light ray sent today will ever get: $$L_e=a\int_t^\infty\frac{dt'}{a(t')}, \qquad \dot L_e=HL_e-1.$$ Li took $c$ constant, giving $w_{\rm DE}=-\frac13\left(1+\frac{2\sqrt{\Omega_{\rm DE}}}{c}\right)$. And this is where the problems begin. With $c=1$ and $\Omega_{\rm DE,0}=0.6889$, $w_0=-0.887$, about $5\sigma$ from Planck 2018 $w_0=-1.03\pm0.03$. Does not match observations! And any constant $c<1$ gives $w<...
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Our cosmic event horizon on a string

A Cosmic Stringy Adventure ! As we previously discussed, our spacetime characterised by a positive cosmological constant $\Lambda$. The natural bounds are then a minimal  ultraviolet (UV) length $l_{UV} = 2L_P$ and an infrared (IR) cosmological horizon $l_{\Lambda}$.  This dual-boundary spacetime enforces a fundamental Compton–gravitational duality . Every geometric scale $r$ carries two natural mass definitions: $$m_C(r) = \frac{\hbar}{rc}, \qquad m_G(r) = \frac{c^2}{4G}\ r$$ The product of these masses, $m_C \ m_G = M_P^2/4$, is scale-independent. They intersect exclusively at the UV boundary $r = l_{UV}$, defining a maximal local force in GR: $F_{max} = c^4 / 4G$. At the opposite extreme, the Compton mass evaluated at the IR horizon yields the fundamental  spectral gap  (not a particle) of the universe: $m_s = \hbar / (l_{\Lambda} c)$.  In this post, to explore how energy propagates through this dual-scale geometry, we model the mass gap $m_s$ as a null-ener...
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The Cosmological Constant Problem Revisited

  You will find some people claiming this is a non-problem , however, the CCP is actually one of the two great naturalness problems in modern physics.   $$\Lambda \simeq 1.3 \times 10^{-52}\ \mathrm{m}^{-2}$$ yet naïve quantum field theory (QFT) estimates of vacuum energy overshoot the observed value by an astonishing factor of order $10^{121}$. This discrepancy is often expressed as the ratio between the Planck energy density and the observed dark energy density: $$\frac{\rho_{\text{Planck}}}{\rho_\Lambda} \sim 10^{121}$$ where $$\rho_\Lambda = \frac{\Lambda c^2}{8\pi G}, \qquad \rho_{\text{Planck}} = \frac{c^5}{\hbar G^2}$$   At face value, this looks like a total failure of theoretical physics. However, this interpretation rests on an assumption that turns out to be wrong :   that vacuum  degrees of freedom  scale with volume .  Where the naive QFT estimate comes from   Now, Rugh and Zinkernagel's   paper from 2000 works out the Q...
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The fabric of space-time: stiffer than steel or weaker than jello?

  The notorious rubber sheet analogy of spacetime teaches one concept and once concept only: Mass-energy causes curvature of space-time.   When a gravitating mass recedes from a region of space-time the curvature diminishes. The field equations of General Relativity don’t have an explicit term for this elastic property, but the framework as a whole does have that property. As very large mass-energies are required to generate gravitational waves (ripples in space-time), the elastic property of space-time is generally regarded as very stiff One other interesting consideration here is that elasticity is an emergent phenomenon. There is a great deal of interest in the idea that gravity is similarly emergent .   In 2018, McDonald quantified the classical stiffness of space-time via Youngs Modulus .  Classical answer: Youngs Modulus of space-time $\sim$ 20 orders of magnitude greater than steel.   DALL.E2 depiction of classical space-time. (Credit SR Anderso...
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Zitter at the Edge of Spacetime

 In a previous post we introduced the idea that our current Universe has boundary conditions.     We also showed a diagram similar to Figure 1 below. Except here, we are once again thinking about the future dS state . Figure 1 . For an observer at O inside the cosmic event horizon (CEH) with radius $l_{\Lambda}$, the universe can be divided into two sub-vacuums, $(A)$ inside the CEH, and $(B)$, outside. The horizon surface $\Sigma$ has entanglement entropy $S_{dS}$ and rest energy $E_H$   Figure 2. The maximum entropy of the Universe (credit: Lineweaver ).   Now, a comoving volume of the Universe, when considered together with its associated cosmic event horizon, forms a thermodynamically closed system obeying the generalised second law, $$dS_{\text{bulk}} + dS_{\text{horizon}} \ge 0.$$ The maximum entropy of a closed system, in this case  ( Figure 2 ) with $L=2 \pi l_{\Lambda}$, the circumference of a circle with radius  $l_{\Lambda}$, ...
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Blurring the horizon - the quantum width of the cosmic event horizon

A  paper by Zurek applied a random walk argument to a black hole horizon. Credit, Zurek, 2021 Zurek  ( Snowmass 2021 White Paper: Observational Signatures of Quantum Gravity )  called this a blurring of the horizon — a fuzzy, or uncertain horizon — and went through derivations supporting the idea that this length scale is the quantum uncertainty in the position of the black hole horizon: a dynamic quantum width of an event horizon. This is a concept which fundamentally applies to the Universe's own Cosmic Event Horizon (CEH). The Bekenstein-Hawking entropy gives the number of quantum degrees of freedom that can fluctuate. Below, we step out our own cosmic de Sitter derivation of the random walk argument. To do this, let $l_{\Lambda}$ represent the generalised de Sitter horizon scale. Due to the holographic UV/IR correspondence, this scale manifests dually: at the fundamental microscopic limit as $l_{UV} = 2L_p$ (the gravitational/casual limit, aka the Schwarzschild radi...
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The Cosmic Strange Metal

      Strange metals, quantum spin liquids, and SYK-like systems share a striking transport pattern: no quasiparticles, strong collective dynamics, Planckian relaxation, near-minimal viscosity, and maximal chaos. Their characteristic data are $$\frac{\eta}{s}=\frac{\hbar}{4\pi k_B}, \qquad \lambda_L=\frac{2\pi k_BT}{\hbar}, \qquad \tau_P=\frac{\hbar}{k_BT}.$$ The claim is not that the three-dimensional de Sitter bulk is literally a strange metal. The sharper claim is: $$\boxed{\text{The de Sitter stretched horizon belongs to the same transport universality class as a Planckian strange metal.}}$$ The correspondence applies to the horizon membrane, not to bulk spacetime. Membrane Paradigm and the KSS Value In the membrane paradigm, an event horizon behaves for exterior observers as a stretched viscous membrane with transport coefficients fixed by Einstein gravity. This does not require an assumed AdS/CFT dual. For de Sitter, $$\ell_\Lambda=\frac{c}{H}, \qquad T_{dS...
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Our cosmic event horizon on a string

A Cosmic Stringy Adventure ! As we previously discussed, our spacetime characterised by a positive cosmological constant $\Lambda$. The natural bounds are then a minimal  ultraviolet (UV) length $l_{UV} = 2L_P$ and an infrared (IR) cosmological horizon $l_{\Lambda}$.  This dual-boundary spacetime enforces a fundamental Compton–gravitational duality . Every geometric scale $r$ carries two natural mass definitions: $$m_C(r) = \frac{\hbar}{rc}, \qquad m_G(r) = \frac{c^2}{4G}\ r$$ The product of these masses, $m_C \ m_G = M_P^2/4$, is scale-independent. They intersect exclusively at the UV boundary $r = l_{UV}$, defining a maximal local force in GR: $F_{max} = c^4 / 4G$. At the opposite extreme, the Compton mass evaluated at the IR horizon yields the fundamental  spectral gap  (not a particle) of the universe: $m_s = \hbar / (l_{\Lambda} c)$.  In this post, to explore how energy propagates through this dual-scale geometry, we model the mass gap $m_s$ as a null-ener...
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